research topic in mathematics

251+ Math Research Topics [2024 Updated]

Mathematics, often dubbed as the language of the universe, holds immense significance in shaping our understanding of the world around us. It’s not just about crunching numbers or solving equations; it’s about unraveling mysteries, making predictions, and creating innovative solutions to complex problems. In this blog, we embark on a journey into the realm of math research topics, exploring various branches of mathematics and their real-world applications.

How Do You Write A Math Research Topic?

Writing a math research topic involves several steps to ensure clarity, relevance, and feasibility. Here’s a guide to help you craft a compelling math research topic:

• Identify Your Interests: Start by exploring areas of mathematics that interest you. Whether it’s pure mathematics, applied mathematics, or interdisciplinary topics, choose a field that aligns with your passion and expertise.
• Narrow Down Your Focus: Mathematics is a broad field, so it’s essential to narrow down your focus to a specific area or problem. Consider the scope of your research and choose a topic that is manageable within your resources and time frame.
• Review Existing Literature: Conduct a thorough literature review to understand the current state of research in your chosen area. Identify gaps, controversies, or unanswered questions that could form the basis of your research topic.
• Formulate a Research Question: Based on your exploration and literature review, formulate a clear and concise research question. Your research question should be specific, measurable, achievable, relevant, and time-bound (SMART).
• Consider Feasibility: Assess the feasibility of your research topic in terms of available resources, data availability, and research methodologies. Ensure that your topic is realistic and achievable within the constraints of your project.
• Consult with Experts: Seek feedback from mentors, advisors, or experts in the field to validate your research topic and refine your ideas. Their insights can help you identify potential challenges and opportunities for improvement.
• Refine and Iterate: Refine your research topic based on feedback and further reflection. Iterate on your ideas to ensure clarity, coherence, and relevance to the broader context of mathematics research.
• Craft a Title: Once you have finalized your research topic, craft a compelling title that succinctly summarizes the essence of your research. Your title should be descriptive, engaging, and reflective of the key themes of your study.
• Write a Research Proposal: Develop a comprehensive research proposal outlining the background, objectives, methodology, and expected outcomes of your research. Your research proposal should provide a clear roadmap for your study and justify the significance of your research topic.

By following these steps, you can effectively write a math research topic that is well-defined, relevant, and poised to make a meaningful contribution to the field of mathematics.

251+ Math Research Topics: Beginners To Advanced

• Prime Number Distribution in Arithmetic Progressions
• Diophantine Equations and their Solutions
• Applications of Modular Arithmetic in Cryptography
• The Riemann Hypothesis and its Implications
• Graph Theory: Exploring Connectivity and Coloring Problems
• Knot Theory: Unraveling the Mathematics of Knots and Links
• Fractal Geometry: Understanding Self-Similarity and Dimensionality
• Differential Equations: Modeling Physical Phenomena and Dynamical Systems
• Chaos Theory: Investigating Deterministic Chaos and Strange Attractors
• Combinatorial Optimization: Algorithms for Solving Optimization Problems
• Computational Complexity: Analyzing the Complexity of Algorithms
• Game Theory: Mathematical Models of Strategic Interactions
• Number Theory: Exploring Properties of Integers and Primes
• Algebraic Topology: Studying Topological Invariants and Homotopy Theory
• Analytic Number Theory: Investigating Properties of Prime Numbers
• Algebraic Geometry: Geometry Arising from Algebraic Equations
• Galois Theory: Understanding Field Extensions and Solvability of Equations
• Representation Theory: Studying Symmetry in Linear Spaces
• Harmonic Analysis: Analyzing Functions on Groups and Manifolds
• Mathematical Logic: Foundations of Mathematics and Formal Systems
• Set Theory: Exploring Infinite Sets and Cardinal Numbers
• Real Analysis: Rigorous Study of Real Numbers and Functions
• Complex Analysis: Analytic Functions and Complex Integration
• Measure Theory: Foundations of Lebesgue Integration and Probability
• Topological Groups: Investigating Topological Structures on Groups
• Lie Groups and Lie Algebras: Geometry of Continuous Symmetry
• Differential Geometry: Curvature and Topology of Smooth Manifolds
• Algebraic Combinatorics: Enumerative and Algebraic Aspects of Combinatorics
• Ramsey Theory: Investigating Structure in Large Discrete Structures
• Analytic Geometry: Studying Geometry Using Analytic Methods
• Hyperbolic Geometry: Non-Euclidean Geometry of Curved Spaces
• Nonlinear Dynamics: Chaos, Bifurcations, and Strange Attractors
• Homological Algebra: Studying Homology and Cohomology of Algebraic Structures
• Topological Vector Spaces: Vector Spaces with Topological Structure
• Representation Theory of Finite Groups: Decomposition of Group Representations
• Category Theory: Abstract Structures and Universal Properties
• Operator Theory: Spectral Theory and Functional Analysis of Operators
• Algebraic Number Theory: Study of Algebraic Structures in Number Fields
• Cryptanalysis: Breaking Cryptographic Systems Using Mathematical Methods
• Discrete Mathematics: Combinatorics, Graph Theory, and Number Theory
• Mathematical Biology: Modeling Biological Systems Using Mathematical Tools
• Population Dynamics: Mathematical Models of Population Growth and Interaction
• Epidemiology: Mathematical Modeling of Disease Spread and Control
• Mathematical Ecology: Dynamics of Ecological Systems and Food Webs
• Evolutionary Game Theory: Evolutionary Dynamics and Strategic Behavior
• Mathematical Neuroscience: Modeling Brain Dynamics and Neural Networks
• Mathematical Physics: Mathematical Models in Physical Sciences
• Quantum Mechanics: Foundations and Applications of Quantum Theory
• Statistical Mechanics: Statistical Methods in Physics and Thermodynamics
• Fluid Dynamics: Modeling Flow of Fluids Using Partial Differential Equations
• Mathematical Finance: Stochastic Models in Finance and Risk Management
• Option Pricing Models: Black-Scholes Model and Beyond
• Portfolio Optimization: Maximizing Returns and Minimizing Risk
• Stochastic Calculus: Calculus of Stochastic Processes and Itô Calculus
• Financial Time Series Analysis: Modeling and Forecasting Financial Data
• Operations Research: Optimization of Decision-Making Processes
• Linear Programming: Optimization Problems with Linear Constraints
• Integer Programming: Optimization Problems with Integer Solutions
• Network Flow Optimization: Modeling and Solving Flow Network Problems
• Combinatorial Game Theory: Analysis of Games with Perfect Information
• Algorithmic Game Theory: Computational Aspects of Game-Theoretic Problems
• Fair Division: Methods for Fairly Allocating Resources Among Parties
• Auction Theory: Modeling Auction Mechanisms and Bidding Strategies
• Voting Theory: Mathematical Models of Voting Systems and Social Choice
• Social Network Analysis: Mathematical Analysis of Social Networks
• Algorithm Analysis: Complexity Analysis of Algorithms and Data Structures
• Machine Learning: Statistical Learning Algorithms and Data Mining
• Deep Learning: Neural Network Models with Multiple Layers
• Reinforcement Learning: Learning by Interaction and Feedback
• Natural Language Processing: Statistical and Computational Analysis of Language
• Computer Vision: Mathematical Models for Image Analysis and Recognition
• Computational Geometry: Algorithms for Geometric Problems
• Symbolic Computation: Manipulation of Mathematical Expressions
• Numerical Analysis: Algorithms for Solving Numerical Problems
• Finite Element Method: Numerical Solution of Partial Differential Equations
• Monte Carlo Methods: Statistical Simulation Techniques
• High-Performance Computing: Parallel and Distributed Computing Techniques
• Quantum Computing: Quantum Algorithms and Quantum Information Theory
• Quantum Information Theory: Study of Quantum Communication and Computation
• Quantum Error Correction: Methods for Protecting Quantum Information from Errors
• Topological Quantum Computing: Using Topological Properties for Quantum Computation
• Quantum Algorithms: Efficient Algorithms for Quantum Computers
• Quantum Cryptography: Secure Communication Using Quantum Key Distribution
• Topological Data Analysis: Analyzing Shape and Structure of Data Sets
• Persistent Homology: Topological Invariants for Data Analysis
• Mapper Algorithm: Method for Visualization and Analysis of High-Dimensional Data
• Algebraic Statistics: Statistical Methods Based on Algebraic Geometry
• Tropical Geometry: Geometric Methods for Studying Polynomial Equations
• Model Theory: Study of Mathematical Structures and Their Interpretations
• Descriptive Set Theory: Study of Borel and Analytic Sets
• Ergodic Theory: Study of Measure-Preserving Transformations
• Combinatorial Number Theory: Intersection of Combinatorics and Number Theory
• Additive Combinatorics: Study of Additive Properties of Sets
• Arithmetic Geometry: Interplay Between Number Theory and Algebraic Geometry
• Proof Theory: Study of Formal Proofs and Logical Inference
• Reverse Mathematics: Study of Logical Strength of Mathematical Theorems
• Nonstandard Analysis: Alternative Approach to Analysis Using Infinitesimals
• Computable Analysis: Study of Computable Functions and Real Numbers
• Graph Theory: Study of Graphs and Networks
• Random Graphs: Probabilistic Models of Graphs and Connectivity
• Spectral Graph Theory: Analysis of Graphs Using Eigenvalues and Eigenvectors
• Algebraic Graph Theory: Study of Algebraic Structures in Graphs
• Metric Geometry: Study of Geometric Structures Using Metrics
• Geometric Measure Theory: Study of Measures on Geometric Spaces
• Discrete Differential Geometry: Study of Differential Geometry on Discrete Spaces
• Algebraic Coding Theory: Study of Error-Correcting Codes
• Information Theory: Study of Information and Communication
• Coding Theory: Study of Error-Correcting Codes
• Cryptography: Study of Secure Communication and Encryption
• Finite Fields: Study of Fields with Finite Number of Elements
• Elliptic Curves: Study of Curves Defined by Cubic Equations
• Hyperelliptic Curves: Study of Curves Defined by Higher-Degree Equations
• Modular Forms: Analytic Functions with Certain Transformation Properties
• L-functions: Analytic Functions Associated with Number Theory
• Zeta Functions: Analytic Functions with Special Properties
• Analytic Number Theory: Study of Number Theoretic Functions Using Analysis
• Dirichlet Series: Analytic Functions Represented by Infinite Series
• Euler Products: Product Representations of Analytic Functions
• Arithmetic Dynamics: Study of Iterative Processes on Algebraic Structures
• Dynamics of Rational Maps: Study of Dynamical Systems Defined by Rational Functions
• Julia Sets: Fractal Sets Associated with Dynamical Systems
• Mandelbrot Set: Fractal Set Associated with Iterations of Complex Quadratic Polynomials
• Arithmetic Geometry: Study of Algebraic Geometry Over Number Fields
• Diophantine Geometry: Study of Solutions of Diophantine Equations Using Geometry
• Arithmetic of Elliptic Curves: Study of Elliptic Curves Over Number Fields
• Rational Points on Curves: Study of Rational Solutions of Algebraic Equations
• Galois Representations: Study of Representations of Galois Groups
• Automorphic Forms: Analytic Functions with Certain Transformation Properties
• L-functions: Analytic Functions Associated with Automorphic Forms
• Selberg Trace Formula: Tool for Studying Spectral Theory and Automorphic Forms
• Langlands Program: Program to Unify Number Theory and Representation Theory
• Hodge Theory: Study of Harmonic Forms on Complex Manifolds
• Riemann Surfaces: One-dimensional Complex Manifolds
• Shimura Varieties: Algebraic Varieties Associated with Automorphic Forms
• Modular Curves: Algebraic Curves Associated with Modular Forms
• Hyperbolic Manifolds: Manifolds with Constant Negative Curvature
• Teichmüller Theory: Study of Moduli Spaces of Riemann Surfaces
• Mirror Symmetry: Duality Between Calabi-Yau Manifolds
• Kähler Geometry: Study of Hermitian Manifolds with Special Symmetries
• Algebraic Groups: Linear Algebraic Groups and Their Representations
• Lie Algebras: Study of Algebraic Structures Arising from Lie Groups
• Representation Theory of Lie Algebras: Study of Representations of Lie Algebras
• Quantum Groups: Deformation of Lie Groups and Lie Algebras
• Algebraic Topology: Study of Topological Spaces Using Algebraic Methods
• Homotopy Theory: Study of Continuous Deformations of Spaces
• Homology Theory: Study of Algebraic Invariants of Topological Spaces
• Cohomology Theory: Study of Dual Concepts to Homology Theory
• Singular Homology: Homology Theory Defined Using Simplicial Complexes
• Sheaf Theory: Study of Sheaves and Their Cohomology
• Differential Forms: Study of Multilinear Differential Forms
• De Rham Cohomology: Cohomology Theory Defined Using Differential Forms
• Morse Theory: Study of Critical Points of Smooth Functions
• Symplectic Geometry: Study of Symplectic Manifolds and Their Geometry
• Floer Homology: Study of Symplectic Manifolds Using Pseudoholomorphic Curves
• Gromov-Witten Invariants: Invariants of Symplectic Manifolds Associated with Pseudoholomorphic Curves
• Mirror Symmetry: Duality Between Symplectic and Complex Geometry
• Calabi-Yau Manifolds: Ricci-Flat Complex Manifolds
• Moduli Spaces: Spaces Parameterizing Geometric Objects
• Donaldson-Thomas Invariants: Invariants Counting Sheaves on Calabi-Yau Manifolds
• Algebraic K-Theory: Study of Algebraic Invariants of Rings and Modules
• Homological Algebra: Study of Homology and Cohomology of Algebraic Structures
• Derived Categories: Categories Arising from Homological Algebra
• Stable Homotopy Theory: Homotopy Theory with Stable Homotopy Groups
• Model Categories: Categories with Certain Homotopical Properties
• Higher Category Theory: Study of Higher Categories and Homotopy Theory
• Higher Topos Theory: Study of Higher Categorical Structures
• Higher Algebra: Study of Higher Categorical Structures in Algebra
• Higher Algebraic Geometry: Study of Higher Categorical Structures in Algebraic Geometry
• Higher Representation Theory: Study of Higher Categorical Structures in Representation Theory
• Higher Category Theory: Study of Higher Categorical Structures
• Homotopical Algebra: Study of Algebraic Structures in Homotopy Theory
• Homotopical Groups: Study of Groups with Homotopical Structure
• Homotopical Categories: Study of Categories with Homotopical Structure
• Homotopy Groups: Algebraic Invariants of Topological Spaces
• Homotopy Type Theory: Study of Foundations of Mathematics Using Homotopy Theory

In conclusion, the world of mathematics is vast and multifaceted, offering endless opportunities for exploration and discovery. Whether delving into the abstract realms of pure mathematics or applying mathematical principles to solve real-world problems, mathematicians play a vital role in advancing human knowledge and shaping the future of our world.

By embracing diverse math research topics and interdisciplinary collaborations, we can unlock new possibilities and harness the power of mathematics to address the challenges of today and tomorrow. So, let’s embark on this journey together as we unravel the mysteries of numbers and explore the boundless horizons of mathematical inquiry.

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181 Mathematics Research Topics From PhD Experts

If you are reading this blog post, it means you are looking for some exceptional math research topics. You want them to be original, unique even. If you manage to find topics like this, you can be sure your professor will give you a top grade (if you write a decent paper, that is). The good news is that you have arrived at just the right place – at the right time. We have just finished updating our list of topics, so you will find plenty of original ideas right on this page. All our topics are 100 percent free to use as you see fit. You can reword them and you don’t need to give us any credit.

And remember: if you need assistance from a professional, don’t hesitate to reach out to us. We are not just the best place for math research topics for high school students; we are also the number one choice for students looking for top-notch research paper writing services.

Our Newest Research Topics in Math

We know you probably want the best and most recent research topics in math. You want your paper to stand out from all the rest. After all, this is the best way to get some bonus points from your professor. On top of this, finding some great topics for your next paper makes it easier for you to write the essay. As long as you know at least something about the topic, you’ll find that writing a great paper or buy phd thesis isn’t as difficult as you previously thought.

So, without further ado, here are the 181 brand new topics for your next math research paper:

Cool Math Topics to Research

Are you looking for some cool math topics to research? We have a list of original topics for your right here. Pick the one you like and start writing now:

• Roll two dice and calculate a probability
• Discuss ancient Greek mathematics
• Is math really important in school?
• Discuss the binomial theorem
• The math behind encryption
• Game theory and its real-life applications
• Analyze the Bernoulli scheme
• What are holomorphic functions and how do they work?
• Describe big numbers
• Solving the Tower of Hanoi problem

Undergraduate Math Research Topics

If you are an undergraduate looking for some research topics for your next math paper, you will surely appreciate our list of interesting undergraduate math research topics:

• Methods to count discrete objects
• The origins of Greek symbols in mathematics
• Methods to solve simultaneous equations
• Real-world applications of the theorem of Pythagoras
• Discuss the limits of diffusion
• Use math to analyze the abortion data in the UK over the last 100 years
• Discuss the Knot theory
• Analyze predictive models (take meteorology as an example)
• In-depth analysis of the Monte Carlo methods for inverse problems
• Squares vs. rectangles (compare and contrast)

Number Theory Topics to Research

Interested in writing about number theory? It is not an easy subject to discuss, we know. However, we are sure you will appreciate these number theory topics:

• Discuss the greatest common divisor
• Explain the extended Euclidean algorithm
• What are RSA numbers?
• Discuss Bézout’s lemma
• In-depth analysis of the square-free polynomial
• Discuss the Stern-Brocot tree
• Analyze Fermat’s little theorem
• What is a discrete logarithm?
• Gauss’s lemma in number theory
• Analyze the Pentagonal number theorem

Math Research Topics for High School

High school students shouldn’t be too worried about their math papers because we have some unique, and quite interesting, math research topics for high school right here:

• Discuss Brun’s constant
• An in-depth look at the Brahmagupta–Fibonacci identity
• What is derivative algebra?
• Describe the Symmetric Boolean function
• Discuss orders of approximation in limits
• Solving Regiomontanus’ angle maximization problem
• What is a Quadratic integral?
• Define and describe complementary angles
• Analyze the incircle and excircles of a triangle
• Analyze the Bolyai–Gerwien theorem in geometry
• Math in our everyday life

Complex Math Topics

If you want to give some complex math topics a try, we have the best examples below. Remember, these topics should only be attempted by students who are proficient in mathematics:

• Mathematics and its appliance in Artificial Intelligence
• Try to solve an unsolved problem in math
• Discuss Kolmogorov’s zero-one law
• What is a discrete random variable?
• Analyze the Hewitt–Savage zero-one law
• What is a transferable belief model?
• Discuss 3 major mathematical theorems
• Describe and analyze the Dempster-Shafer theory
• An in-depth analysis of a continuous stochastic process
• Identify and analyze Gauss-Markov processes

Easy Math Research Paper Topics

Perhaps you don’t want to spend too much time working on your next research paper. Who can blame you? Check out these easy math research paper topics:

• Define the hyperbola
• Do we need to use a calculator during math class?
• The binomial theorem and its real-world applications
• What is a parabola in geometry?
• How do you calculate the slope of a curve?
• Define the Jacobian matrix
• Solving matrix problems effectively
• Why do we need differential equations?
• Should math be mandatory in all schools?
• What is a Hessian matrix?

Logic Topics to Research

We have some interesting logical topics for research papers. These are perfect for students interested in writing about math logic. Pick one right now:

• Discuss the reductio ad absurdum approach
• Discuss Boolean algebra
• What is consistency proof?
• Analyze Trakhtenbrot’s theorem (the finite model theory)
• Discuss the Gödel completeness theorem
• An in-depth analysis of Morley’s categoricity theorem
• How does the Back-and-forth method work?
• Discuss the Ehrenfeucht–Fraïssé game technique
• Discuss Aleph numbers (Aleph-null and Aleph-one)
• Solving the Suslin problem

Algebra Topics for a Research Paper

Would you like to write about an algebra topic? No problem, our seasoned writers have compiled a list of the best algebra topics for a research paper:

• Discuss the differential equation
• Analyze the Jacobson density theorem
• The 4 properties of a binary operation in algebra
• Analyze the unary operator in depth
• Analyze the Abel–Ruffini theorem
• Epimorphisms vs. monomorphisms: compare and contrast
• Discuss the Morita duality in algebraic structures
• Idempotent vs. nilpotent in Ring theory
• Discuss the Artin-Wedderburn theorem
• What is a commutative ring in algebra?
• Analyze and describe the Noetherian ring

Math Education Research Topics

There is nothing wrong with writing about math education, especially if your professor did not give you writing prompts. Here are some very nice math education research topics:

• What are the goals a mathematics professor should have?
• What is math anxiety in the classroom?
• Teaching math in UK schools: the difficulties
• Computer programming or math in high school?
• Is math education in Europe at a high enough level?
• Common Core Standards and their effects on math education
• Culture and math education in Africa
• What is dyscalculia and how does it manifest itself?
• When was algebra first thought in schools?
• Math education in the United States versus the United Kingdom

Computability Theory Topics to Research

Writing about computability theory can be a very interesting adventure. Give it a try! Here are some of our most interesting computability theory topics to research:

• What is a multiplication table?
• Analyze the Scholz conjecture
• Explain exponentiating by squaring
• Analyze the Myhill-Nerode theorem
• What is a tree automaton?
• Compare and contrast the Pushdown automaton and the Büchi automaton
• Discuss the Markov algorithm
• What is a Turing machine?
• Analyze the post correspondence problem
• Discuss the linear speedup theorem
• Discuss the Boolean satisfiability problem

Interesting Math Research Topics

We know you want topics that are interesting and relatively easy to write about. This is why we have a separate list of our most interesting math research topics:

• What is two-element Boolean algebra?
• The life of Gauss
• The life of Isaac Newton
• What is an orthodiagonal quadrilateral?
• Tessellation in Euclidean plane geometry
• Describe a hyperboloid in 3D geometry
• What is a sphericon?
• Discuss the peculiarities of Borel’s paradox
• Analyze the De Finetti theorem in statistics
• What are Martingales?
• The basics of stochastic calculus

Applied Math Research Topics

Interested in writing about applied mathematics? Our team managed to create a list of awesome applied math research topics from scratch for you:

• Discuss Newton’s laws of motion
• Analyze the perpendicular axes rule
• How is a Galilean transformation done?
• The conservation of energy and its applications
• Discuss Liouville’s theorem in Hamiltonian mechanics
• Analyze the quantum field theory
• Discuss the main components of the Lorentz symmetry
• An in-depth look at the uncertainty principle

Geometry Topics for a Research Paper

Geometry can be a very captivating subject, especially when you know plenty about it. Check out our list of geometry topics for a research paper and pick the best one today:

• Most useful trigonometry functions in math
• The life of Archimedes and his achievements
• Trigonometry in computer graphics
• Using Vincenty’s formulae in geodesy
• Define and describe the Heronian tetrahedron
• The math behind the parabolic microphone
• Discuss the Japanese theorem for concyclic polygons
• Analyze Euler’s theorem in geometry

Math Research Topics for Middle School

Yes, even middle school children can write about mathematics. We have some original math research topics for middle school right here:

• Finding critical points in a graph
• The basics of calculus
• What makes a graph ultrahomogeneous?
• How do you calculate the area of different shapes?
• What contributions did Euclid have to the field of mathematics?
• What is Diophantine geometry?
• What makes a graph regular?
• Analyze a full binary tree

Math Research Topics for College Students

As you’ve probably already figured out, college students should pick topics that are a bit more complex. We have some of the best math research topics for college students right here:

• What are extremal problems and how do you solve them?
• Discuss an unsolvable math problem
• How can supercomputers solve complex mathematical problems?
• An in-depth analysis of fractals
• Discuss the Boruvka’s algorithm (related to the minimum spanning tree)
• Discuss the Lorentz–FitzGerald contraction hypothesis in relativity
• An in-depth look at Einstein’s field equation
• The math behind computer vision and object recognition

Calculus Topics for a Research Paper

Let’s face it: calculus is not a very difficult field. So, why don’t you pick one of our excellent calculus topics for a research paper and start writing your essay right away:

• When do we need to apply the L’Hôpital rule?
• Discuss the Leibniz integral rule
• Calculus in ancient Egypt
• Discuss and analyze linear approximations
• The applications of calculus in real life
• The many uses of Stokes’ theorem
• Discuss the Borel regular measure
• An in-depth analysis of Lebesgue’s monotone convergence theorem

Simple Math Research Paper Topics for High School

This is the place where you can find some pretty simple topics if you are a high school student. Check out our simple math research paper topics for high school:

• The life and work of the famous Pierre de Fermat
• What are limits and why are they useful in calculus?
• Explain the concept of congruency
• The life and work of the famous Jakob Bernoulli
• Analyze the rhombicosidodecahedron and its applications
• Calculus and the Egyptian pyramids
• The life and work of the famous Jean d’Alembert
• Discuss the hyperplane arrangement in combinatorial computational geometry
• The smallest enclosing sphere method in combinatorics

Business Math Topics

If you want to surprise your professor, why don’t you write about business math? We have some exceptional topics that nobody has thought about right here:

• Is paying a loan with another loan a good approach?
• Discuss the major causes of a stock market crash
• Best debt amortization methods in the US
• How do bank loans work in the UK?
• Calculating interest rates the easy way
• Discuss the pros and cons of annuities
• Basic business math skills everyone should possess
• Business math in United States schools
• Analyze the discount factor

Probability and Statistics Topics for Research

Probability and statistics are not easy fields. However, you can impress your professor with one of our unique probability and statistics topics for research:

• What is the autoregressive conditional duration?
• Applying the ANOVA method to ranks
• Discuss the practical applications of the Bates distribution
• Explain the principle of maximum entropy
• Discuss Skorokhod’s representation theorem in random variables
• What is the Factorial moment in the Theory of Probability?
• Compare and contrast Cochran’s C test and his Q test
• Analyze the De Moivre-Laplace theorem
• What is a negative probability?

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Department members engage in cutting-edge research on a wide variety of topics in mathematics and its applications. Topics continually evolve to reflect emerging interests and developments, but can roughly grouped into the following areas.

Algebra, Combinatorics, and Geometry

Algebra, combinatorics, and geometry are areas of very active research at the University of Pittsburgh.

Analysis and Partial Differential Equations

The research of the analysis group covers functional analysis, harmonic analysis, several complex variables, partial differential equations, and analysis on metric and Carnot-Caratheodory spaces.

Applied Analysis

The department is a leader in the analysis of systems of nonlinear differential equations and dynamical systems  that arise in modeling a variety of physical phenomena. They include problems in biology, chemistry, phase transitions, fluid flow, flame propagation, diffusion processes, and pattern formation in nonlinear stochastic partial differential equations.

Mathematical Biology

The biological world stands as the next great frontier for mathematical modeling and analysis. This group studies complex systems and dynamics arising in various biological phenomena.

Mathematical Finance

A rapidly growing area of mathematical finance is Quantitative Behavioral Finance. The high-tech boom and bust of the late 1990s followed by the housing and financial upheavals of 2008 have made a convincing case for the necessity of adopting broader assumptions in finance.

Numerical Analysis and Scientific Computing

The diversity of this group is reflected in its research interests: numerical analysis of partial differential equations , adaptive methods for scientific computing, computational methods of fluid dynamics and turbulence, numerical solution of nonlinear problems arising from porous media flow and transport, optimal control, and simulation of stochastic reaction diffusion systems.

Topology and Differential Geometry

Research in analytic topology continues in the broad area of generalized metric spaces. This group studies relativity theory and differential geometry, with emphasis on twistor methods, as well as geometric and topological aspects of quantum field theory, string theory, and M-theory.

Research Areas

Analysis & pde, applied math, combinatorics, financial math, number theory, probability, representation theory, symplectic geometry & topology.

Mathematics Research Paper Topics

See our list of mathematics research paper topics . Mathematics is the science that deals with the measurement, properties, and relationships of quantities, as expressed in either numbers or symbols. For example, a farmer might decide to fence in a field and plant oats there. He would have to use mathematics to measure the size of the field, to calculate the amount of fencing needed for the field, to determine how much seed he would have to buy, and to compute the cost of that seed. Mathematics is an essential part of every aspect of life—from determining the correct tip to leave for a waiter to calculating the speed of a space probe as it leaves Earth’s atmosphere.

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• Boolean algebra
• Chaos theory
• Complex numbers
• Correlation
• Fraction, common
• Game theory
• Graphs and graphing
• Imaginary number
• Multiplication
• Natural numbers
• Number theory
• Numeration systems
• Probability theory
• Proof (mathematics)
• Pythagorean theorem
• Trigonometry

Mathematics undoubtedly began as an entirely practical activity— measuring fields, determining the volume of liquids, counting out coins, and the like. During the golden era of Greek science, between about the sixth and third centuries B.C., however, mathematicians introduced a new concept to their study of numbers. They began to realize that numbers could be considered as abstract concepts. The number 2, for example, did not necessarily have to mean 2 cows, 2 coins, 2 women, or 2 ships. It could also represent the idea of “two-ness.” Modern mathematics, then, deals both with problems involving specific, concrete, and practical number concepts (25,000 trucks, for example) and with properties of numbers themselves, separate from any practical meaning they may have (the square root of 2 is 1.4142135, for example).

Fields of Mathematics

Mathematics can be subdivided into a number of special categories, each of which can be further subdivided. Probably the oldest branch of mathematics is arithmetic, the study of numbers themselves. Some of the most fascinating questions in modern mathematics involve number theory. For example, how many prime numbers are there? (A prime number is a number that can be divided only by 1 and itself.) That question has fascinated mathematicians for hundreds of years. It doesn’t have any particular practical significance, but it’s an intriguing brainteaser in number theory.

Geometry, a second branch of mathematics, deals with shapes and spatial relationships. It also was established very early in human history because of its obvious connection with practical problems. Anyone who wants to know the distance around a circle, square, or triangle, or the space contained within a cube or a sphere has to use the techniques of geometry.

Algebra was established as mathematicians recognized the fact that real numbers (such as 4 and 5.35) can be represented by letters. It became a way of generalizing specific numerical problems to more general situations.

Analytic geometry was founded in the early 1600s as mathematicians learned to combine algebra and geometry. Analytic geometry uses algebraic equations to represent geometric figures and is, therefore, a way of using one field of mathematics to analyze problems in a second field of mathematics.

Over time, the methods used in analytic geometry were generalized to other fields of mathematics. That general approach is now referred to as analysis, a large and growing subdivision of mathematics. One of the most powerful forms of analysis—calculus—was created almost simultaneously in the early 1700s by English physicist and mathematician Isaac Newton (1642–1727) and German mathematician Gottfried Wilhelm Leibniz (1646–1716). Calculus is a method for analyzing changing systems, such as the changes that take place as a planet, star, or space probe moves across the sky.

Statistics is a field of mathematics that grew in significance throughout the twentieth century. During that time, scientists gradually came to realize that most of the physical phenomena they study can be expressed not in terms of certainty (“A always causes B”), but in terms of probability (“A is likely to cause B with a probability of XX%”). In order to analyze these phenomena, then, they needed to use statistics, the field of mathematics that analyzes the probability with which certain events will occur.

Each field of mathematics can be further subdivided into more specific specialties. For example, topology is the study of figures that are twisted into all kinds of bizarre shapes. It examines the properties of those figures that are retained after they have been deformed.

Back to Science Research Paper Topics .

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Articles on Mathematics

Displaying 1 - 20 of 548 articles.

‘Dancing’ raisins − a simple kitchen experiment reveals how objects can extract energy from their environment and come to life

Saverio Eric Spagnolie , University of Wisconsin-Madison

Why are algorithms called algorithms? A brief history of the Persian polymath you’ve likely never heard of

Debbie Passey , The University of Melbourne

Homeschooled kids face unique college challenges − here are 3 ways they can be overcome

Kenneth V. Anthony , Mississippi State University and Mark E. Wildmon , Mississippi State University

Maths degrees are becoming less accessible – and this is a problem for business, government and innovation

Neil Saunders , City, University of London

Supercomputers can take months to simulate the climate – but my new algorithm can do it ten times faster

Samar Khatiwala , University of Oxford

Mind-bending maths could stop quantum hackers, but few understand it

Nalini Joshi , University of Sydney

The luck of the puck in the Stanley Cup – why chance plays such a big role in hockey

Mark Robert Rank , Arts & Sciences at Washington University in St. Louis

From thousands to millions to billions to trillions to quadrillions and beyond: Do numbers ever end?

Manil Suri , University of Maryland, Baltimore County

It’s common to ‘stream’ maths classes. But grouping students by ability can lead to ‘massive disadvantage’

Elena Prieto-Rodriguez , University of Newcastle

South Africa is short of academic statisticians: why and what can be done

Inger Fabris-Rotelli , University of Pretoria ; Ansie Smit , University of Pretoria ; Danielle Jade Roberts , University of KwaZulu-Natal ; Daniel Maposa , University of Limpopo ; Fabio Mathias Correa , University of the Free State ; Michael Johan von Maltitz , University of the Free State , and Sonali Das , University of Pretoria

Dali hit Key Bridge with the force of 66 heavy trucks at highway speed

Amanda Bao , Rochester Institute of Technology

How do we solve the maths teacher shortage? We can start by training more existing teachers to teach maths

Ian Gordon , The University of Melbourne ; Mary P. Coupland , University of Technology Sydney , and Merrilyn Goos , University of the Sunshine Coast

How AI and a popular card game can help engineers predict catastrophic failure – by finding the absence of a pattern

John Edward McCarthy , Arts & Sciences at Washington University in St. Louis

The ‘average’ revolutionized scientific research, but overreliance on it has led to discrimination and injury

Zachary del Rosario , Olin College of Engineering

Understanding how the brain works can transform how school students learn maths

Colin Foster , Loughborough University

Anyone can play Tetris, but architects, engineers and animators alike use the math concepts underlying the game

Leah McCoy , Wake Forest University

GOP primary elections use flawed math to pick nominees

Ismar Volić , Wellesley College

What are ‘multiplication facts’? Why are they essential to your child’s success in maths?

Bronwyn Reid O'Connor , University of Sydney and Ben Zunica , University of Sydney

How bats ‘leapfrog’ their way home at night – new research

Thomas Woolley , Cardiff University and Fiona Mathews , University of Sussex

Orbital resonance − the striking gravitational dance done by planets with aligning orbits

Chris Impey , University of Arizona

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260 Interesting Math Topics for Essays & Research Papers

Mathematics is the science of numbers and shapes. Writing about it can give you a fresh perspective and help to clarify difficult concepts. You can even use mathematical writing as a tool in problem-solving.

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In this article, you will find plenty of interesting math topics. Besides, you will learn about branches of mathematics that you can choose from. And if the thought of letters and numbers makes your head swim, try our custom writing service . Our professionals will craft a paper for you in no time!

And now, let’s proceed to math essay topics and tips.

🔝 Top 10 Interesting Math Topics

✅ branches of mathematics, ✨ fun math topics.

• 🏫 Math Topics for High School
• 🎓 College Math Topics
• 🤔 Advanced Math
• 📚 Math Research
• ✏️ Math Education
• 💵 Business Math

🔍 References

• Number theory in everyday life.
• Logicist definitions of mathematics.
• Multivariable vs. vector calculus.
• 4 conditions of functional analysis.
• Random variable in probability theory.
• How is math used in cryptography?
• The purpose of homological algebra.
• Concave vs. convex in geometry.
• The philosophical problem of foundations.
• Is numerical analysis useful for machine learning?

What exactly is mathematics ? First and foremost, it is very old. Ancient Greeks and Persians were already utilizing mathematical tools. Nowadays, we consider it an interdisciplinary language.

Biologists, linguists, and sociologists alike use math in their work. And not only that, we all deal with it in our daily lives. For instance, it manifests in the measurement of time. We often need it to calculate how much our groceries cost and how much paint we need to buy to cover a wall.

Simply put, mathematics is a universal instrument for problem-solving. We can divide pure math into three branches: geometry, arithmetic, and algebra. Let’s take a closer look:

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• Geometry By studying geometry, we try to comprehend our physical surroundings. Geometric shapes can be simple, like a triangle. Or, they can form complicated figures, like a rhombicosidodecahedron.
• Arithmetic Arithmetic deals with numbers and simple operations: subtraction, addition, division, and multiplication.
• Algebra Algebra is used when the exact numbers are unclear. Instead, they are replaced with letters. Businesses often need algebra to predict their sales.

It’s true that most high school students don’t like math. However, that doesn’t mean it can’t be a fun and compelling subject. In the following section, you will find plenty of enthralling mathematical topics for your paper.

If you’re struggling to start working on your essay, we have some fun and cool math topics to offer. They will definitely engage you and make the writing process enjoyable. Besides, fun math topics can show everyone that even math can be entertaining or even a bit silly.

• The link between mathematics and art – analyzing the Golden Ratio in Renaissance-era paintings.
• An evaluation of Georg Cantor’s set theory.
• The best approaches to learning math facts and developing number sense.
• Different approaches to probability as explored through analyzing card tricks.
• Chess and checkers – the use of mathematics in recreational activities.
• The five types of math used in computer science.
• Real-life applications of the Pythagorean Theorem .
• A study of the different theories of mathematical logic.
• The use of game theory in social science.
• Mathematical definitions of infinity and how to measure it.
• What is the logic behind unsolvable math problems?
• An explanation of mean, mode, and median using classroom math grades.
• The properties and geometry of a Möbius strip.
• Using truth tables to present the logical validity of a propositional expression.
• The relationship between Pascal’s Triangle and The Binomial Theorem.
• The use of different number types: the history.
• The application of differential geometry in modern architecture.
• A mathematical approach to the solution of a Rubik’s Cube.
• Comparison of predictive and prescriptive statistical analyses.
• Explaining the iterations of the Koch snowflake.
• The importance of limits in calculus.
• Hexagons as the most balanced shape in the universe.
• The emergence of patterns in chaos theory.
• What were Euclid’s contributions to the field of mathematics?
• The difference between universal algebra and abstract algebra.

🏫 Math Essay Topics for High School

When writing a math paper, you want to demonstrate that you understand a concept. It can be helpful if you need to prepare for an exam. Choose a topic from this section and decide what you want to discuss.

• Explain what we need Pythagoras’ theorem for. 
• What is a hyperbola? 
• Describe the difference between algebra and arithmetic. 
• When is it unnecessary to use a calculator ? 
• Find a connection between math and the arts. 
• How do you solve a linear equation? 
• Discuss how to determine the probability of rolling two dice. 
• Is there a link between philosophy and math? 
• What types of math do you use in your everyday life? 
• What is the numerical data? 
• Explain how to use the binomial theorem. 
• What is the distributive property of multiplication? 
• Discuss the major concepts in ancient Egyptian mathematics . 
• Why do so many students dislike math? 
• Should math be required in school? 
• How do you do an equivalent transformation? 
• Why do we need imaginary numbers? 
• How can you calculate the slope of a curve? 
• What is the difference between sine, cosine, and tangent? 
• How do you define the cross product of two vectors? 
• What do we use differential equations for? 
• Investigate how to calculate the mean value. 
• Define linear growth. 
• Give examples of different number types. 
• How can you solve a matrix? 

🎓 College Math Topics for a Paper

Sometimes you need more than just formulas to explain a complex idea. That’s why knowing how to express yourself is crucial. It is especially true for college-level mathematics. Consider the following ideas for your next research project:

• What do we need n-dimensional spaces for?
• Explain how card counting works.
• Discuss the difference between a discrete and a continuous probability distribution .
• How does encryption work?
• Describe extremal problems in discrete geometry.
• What can make a math problem unsolvable?
• Examine the topology of a Möbius strip.

• What is K-theory?  
• Discuss the core problems of computational geometry. 
• Explain the use of set theory . 
• What do we need Boolean functions for? 
• Describe the main topological concepts in modern mathematics. 
• Investigate the properties of a rotation matrix. 
• Analyze the practical applications of game theory.  
• How can you solve a Rubik’s cube mathematically? 
• Explain the math behind the Koch snowflake. 
• Describe the paradox of Gabriel’s Horn. 
• How do fractals form? 
• Find a way to solve Sudoku using math. 
• Why is the Riemann hypothesis still unsolved? 
• Discuss the Millennium Prize Problems. 
• How can you divide complex numbers? 
• Analyze the degrees in polynomial functions. 
• What are the most important concepts in number theory? 
• Compare the different types of statistical methods. 

🤔 Advanced Topics in Math to Write a Paper on

Once you have passed the trials of basic math, you can move on to the advanced section. This area includes topology, combinatorics, logic, and computational mathematics. Check out the list below for enticing topics to write about:

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• What is an abelian group?
• Explain the orbit-stabilizer theorem.
• Discuss what makes the Burnside problem influential.
• What fundamental properties do holomorphic functions have?
• How does Cauchy’s integral theorem lead to Cauchy’s integral formula?
• How do the two Picard theorems relate to each other?
• When is a trigonometric series called a Fourier series?
• Give an example of an algorithm used for machine learning.
• Compare the different types of knapsack problems.
• What is the minimum overlap problem?
• Describe the Bernoulli scheme.
• Give a formal definition of the Chinese restaurant process.
• Discuss the logistic map in relation to chaos.
• What do we need the Feigenbaum constants for?
• Define a difference equation.
• Explain the uses of the Fibonacci sequence.
• What is an oblivious transfer?
• Compare the Riemann and the Ruelle zeta functions.
• How can you use elementary embeddings in model theory?
• Analyze the problem with the wholeness axiom and Kunen’s inconsistency theorem.
• How is Lie algebra used in physics ?
• Define various cases of algebraic cycles.
• Why do we need étale cohomology groups to calculate algebraic curves?
• What does non-Euclidean geometry consist of?
• How can two lines be ultraparallel?

📚 Math Research Topics for a Paper

Choosing the right topic is crucial for a successful research paper in math. It should be hard enough to be compelling, but not exceeding your level of competence. If possible, stick to your area of knowledge. This way your task will become more manageable. Here are some ideas:

• Write about the history of calculus.
• Why are unsolved math problems significant?
• Find reasons for the gender gap in math students.
• What are the toughest mathematical questions asked today?
• Examine the notion of operator spaces.
• How can we design a train schedule for a whole country?
• What makes a number big?

• How can infinities have various sizes?
• What is the best mathematical strategy to win a game of Go?
• Analyze natural occurrences of random walks in biology.
• Explain what kind of mathematics was used in ancient Persia.
• Discuss how the Iwasawa theory relates to modular forms.
• What role do prime numbers play in encryption?
• How did the study of mathematics evolve?
• Investigate the different Tower of Hanoi solutions.
• Research Napier’s bones. How can you use them?
• What is the best mathematical way to find someone who is lost in a maze?
• Examine the Traveling Salesman Problem. Can you find a new strategy?
• Describe how barcodes function.
• Study some real-life examples of chaos theory. How do you define them mathematically?
• Compare the impact of various ground-breaking mathematical equations .
• Research the Seven Bridges of Königsberg. Relate the problem to the city of your choice.
• Discuss Fisher’s fundamental theorem of natural selection.
• How does quantum computing work?
• Pick an unsolved math problem and say what makes it so difficult.

✏️ Math Education Research Topics

For many teachers, the hardest part is to keep the students interested. When it comes to math, it can be especially challenging. It’s crucial to make complicated concepts easy to understand. That’s why we need research on math education.

• Compare traditional methods of teaching math with unconventional ones.
• How can you improve mathematical education in the U.S.?
• Describe ways of encouraging girls to pursue careers in STEM fields.
• Should computer programming be taught in high school?
• Define the goals of mathematics education .
• Research how to make math more accessible to students with learning disabilities .
• At what age should children begin to practice simple equations?
• Investigate the effectiveness of gamification in algebra classes.
• What do students gain from taking part in mathematics competitions?
• What are the benefits of moving away from standardized testing ?
• Describe the causes of “ math anxiety .” How can you overcome it?
• Explain the social and political relevance of mathematics education.
• Define the most significant issues in public school math teaching.
• What is the best way to get children interested in geometry?
• How can students hone their mathematical thinking outside the classroom?
• Discuss the benefits of using technology in math class.
• In what way does culture influence your mathematical education?
• Explore the history of teaching algebra.
• Compare math education in various countries.

• How does dyscalculia affect a student’s daily life?
• Into which school subjects can math be integrated?
• Has a mathematics degree increased in value over the last few years?
• What are the disadvantages of the Common Core Standards?
• What are the advantages of following an integrated curriculum in math?
• Discuss the benefits of Mathcamp.

🧮 Algebra Topics for a Paper

The elegance of algebra stems from its simplicity. It gives us the ability to express complex problems in short equations. The world was changed forever when Einstein wrote down the simple formula E=mc². Now, if your algebra seminar requires you to write a paper, look no further! Here are some brilliant prompts:

• Give an example of an induction proof.
• What are F-algebras used for?
• What are number problems?
• Show the importance of abstract algebraic thinking .
• Investigate the peculiarities of Fermat’s last theorem.
• What are the essentials of Boolean algebra?
• Explore the relationship between algebra and geometry.
• Compare the differences between commutative and noncommutative algebra.
• Why is Brun’s constant relevant?
• How do you factor quadratics?
• Explain Descartes’ Rule of Signs.
• What is the quadratic formula?
• Compare the four types of sequences and define them.
• Explain how partial fractions work.
• What are logarithms used for?
• Describe the Gaussian elimination.
• What does Cramer’s rule state?
• Explore the difference between eigenvectors and eigenvalues.
• Analyze the Gram-Schmidt process in two dimensions.
• Explain what is meant by “range” and “domain” in algebra.
• What can you do with determinants?
• Learn about the origin of the distance formula.
• Find the best way to solve math word problems.
• Compare the relationships between different systems of equations.
• Explore how the Rubik’s cube relates to group theory.

📏 Geometry Topics for a Research Paper

Shapes and space are the two staples of geometry. Since its appearance in ancient times, it has evolved into a major field of study. Geometry’s most recent addition, topology, explores what happens to an object if you stretch, shrink, and fold it. Things can get pretty crazy from here! The following list contains 25 interesting geometry topics:

• What are the Archimedean solids? 
• Find real-life uses for a rhombicosidodecahedron. 
• What is studied in projective geometry? 
• Compare the most common types of transformations. 
• Explain how acute square triangulation works. 
• Discuss the Borromean ring configuration. 
• Investigate the solutions to Buffon’s needle problem. 
• What is unique about right triangles? 

• Describe the notion of Dirac manifolds.
• Compare the various relationships between lines.
• What is the Klein bottle?
• How does geometry translate into other disciplines, such as chemistry and physics?
• Explore Riemannian manifolds in Euclidean space.
• How can you prove the angle bisector theorem?
• Do a research on M.C. Escher’s use of geometry.
• Find applications for the golden ratio .
• Describe the importance of circles.
• Investigate what the ancient Greeks knew about geometry.
• What does congruency mean?
• Study the uses of Euler’s formula.
• How do CT scans relate to geometry?
• Why do we need n-dimensional vectors?
• How can you solve Heesch’s problem?
• What are hypercubes?
• Analyze the use of geometry in Picasso’s paintings.

➗ Calculus Topics to Write a Paper on

You can describe calculus as a more complicated algebra. It’s a study of change over time that provides useful insights into everyday problems. Applied calculus is required in a variety of fields such as sociology, engineering, or business. Consult this list of compelling topics on a calculus paper:

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• What are the differences between trigonometry, algebra, and calculus?
• Explain the concept of limits.
• Describe the standard formulas needed for derivatives.
• How can you find critical points in a graph?
• Evaluate the application of L’Hôpital’s rule.
• How do you define the area between curves?
• What is the foundation of calculus?

• How does multivariate calculus work?
• Discuss the use of Stokes’ theorem.
• What does Leibniz’s integral rule state?
• What is the Itô stochastic integral?
• Explore the influence of nonstandard analysis on probability theory.
• Research the origins of calculus.
• Who was Maria Gaetana Agnesi?
• Define a continuous function.
• What is the fundamental theorem of calculus?
• How do you calculate the Taylor series of a function?
• Discuss the ways to resolve Runge’s phenomenon.
• Explain the extreme value theorem.
• What do we need predicate calculus for?
• What are linear approximations?
• When does an integral become improper?
• Describe the Ratio and Root Tests.
• How does the method of rings work?
• Where do we apply calculus in real-life situations?

💵 Business Math Topics to Write About

You don’t have to own a company to appreciate business math. Its topics range from credits and loans to insurance, taxes, and investment. Even if you’re not a mathematician, you can use it to handle your finances. Sounds interesting? Then have a look at the following list:

• What are the essential skills needed for business math?
• How do you calculate interest rates?
• Compare business and consumer math.
• What is a discount factor?
• How do you know that an investment is reasonable?
• When does it make sense to pay a loan with another loan?
• Find useful financing techniques that everyone can use.
• How does critical path analysis work?
• Explain how loans work.
• Which areas of work utilize operations research?
• How do businesses use statistics?
• What is the economic lot scheduling problem?
• Compare the uses of different chart types.
• What causes a stock market crash?
• How can you calculate the net present value?
• Explore the history of revenue management.
• When do you use multi-period models?
• Explain the consequences of depreciation.
• Are annuities a good investment?
• Would the U.S. financially benefit from discontinuing the penny?
• What caused the United States housing crash in 2008?
• How do you calculate sales tax?
• Describe the notions of markups and markdowns.
• Investigate the math behind debt amortization.
• What is the difference between a loan and a mortgage?

With all these ideas, you are perfectly equipped for your next math paper. Good luck!

• What Is Calculus?: Southern State Community College
• What Is Mathematics?: Tennessee Tech University
• What Is Geometry?: University of Waterloo
• What Is Algebra?: BBC
• Ten Simple Rules for Mathematical Writing: Ohio State University
• Practical Algebra Lessons: Purplemath
• Topics in Geometry: Massachusetts Institute of Technology
• The Geometry Junkyard: All Topics: Donald Bren School of Information and Computer Sciences
• Calculus I: Lamar University
• Business Math for Financial Management: The Balance Small Business
• What Is Mathematics: Life Science
• What Is Mathematics Education?: University of California, Berkeley
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202 Math Research Topics: List To Vary Your Ideas

Mathematics is an exceptional field of study dealing primarily with numbers. It also deals with structures, formulas, shapes, spaces, and quantities of where they are contained.

Maths encompasses different types of computations that are applied in the real world.

Math requires a lot of analysis. This is why there are different types of maths. They all encompass different subjects and deal with different things. What are the types of maths?

Arithmetic This is perhaps the commonest type or branch of maths. It is one of the oldest and it encompasses basic numbers operations. These are addition, subtraction, multiplication, and divisions; in some schools, the short word for it is BODMAS. This is known as the Bracket of Division, Multiplication, Addition, and Subtraction. Algebra This is where unknown quantities are represented by alphabets and used along with numbers. The letters these unknown quantities are represented by are usually A, B, X, and Y, and they could also be symbols. Geometry This is considered one of the practical branches of maths as it examines sizes, shapes, figures, and the features of these entities. The most common parts of geometry are lines, points, solids, surfaces, and angles.

There are many other types but the above are the most popular. Others are trigonometry, topology, mathematical analysis, calculus, probability, statistics, and a few others.

As many students find it hard to develop maths research topics on their own, this is a chance for you. It’s okay to be worked up when you can’t find undergraduate math research topics that fit your project, essay or paper choices. This article will provide custom maths education research topics for your use. Before that, how do you structure your math essay or paper?

How to Structure Your Math Essay or Paper

Structuring your essay or paper may require that you’ve been reading critical math journals. Reading them could have made it easy to understand how to structure your paper. However, you don’t have to worry if you haven’t. Structuring your paper as expected is an essential part of writing and you’ll know about it in this section. Before you learn that, how do you choose a topic?

Choosing a Topic to Discuss

One of the difficult yet significant parts of any math essay or paper is choosing your topic. This is because you need to solve a problem or engage in a subject that has got less attention. You also need to understand the background to the subject you want to discuss as you can’t write blindly.

You must also be able to articulate your thoughts well as you must show visible knowledge before you commence the research and writing. How do you go about this? You can consider reading existing research. You can even take notes during classes to see the areas you think more work needs to be done.

After choosing your topic, conduct your research to see if you can investigate the sphere. If you can, you need to structure your research thus:

The Background This includes the discussion on what the essay is about. Depending on what you’re writing about, you need to discuss the primary concepts, including the history of some terms, where essential, in this section. This section is more like general information about the subject you want to discuss with your paper. This helps your readers familiarize themselves with your intended discussion. The Introduction This is where the main ideas behind your essays (and the solutions you hope to proffer) are tended to the readers. This is where you also explain the symbols you’ll use and the principles which are required in your essay. Aside from this, you need to state the basic issues, the solutions you could offer, the laws which are essential to discuss to make your work comprehensible. The Main Body This is where you elaborate on your findings. You need to state the research problem, the formulas, the theories you’ll use in tackling the problem, and many other things. You also need to introduce different sections of maths into the main body which is divided by paragraphs and/or chapters as well as mathematical analysis where needed. Implications This is the last part of your essay or paper. This is where you share the insights of your research with your readers. You offer short explanations of the things you have discussed. If you have treated a subject in applied mathematics, this is where you give summaries of how math is connected to human life and the strategic importance of these to people.

By adhering to this structure, you would have crafted the best rated and high-quality maths paper. Furthermore, remember you always have an option to get help with dissertations and save your time. Since it is sometimes challenging to choose cool maths topics to research on your own, these are some for you:

Research Topics in Math

Math is a broad subject. There is a study of the history of math as well as its influence in education, amongst many other sub-sections. If you’d like to create stunning research, you may choose to discuss any of these research topics in math to fulfill one of your academic requirements:

• What are the distinctions between commutative and noncommutative algebra?
• Discuss the methods of factoring quadratics
• Types of sequences and your understanding of them
• Partial fractions: what are they and how do they work?
• Logarithms: what are they and how do they work?
• An overview of Gaussian elimination
• An overview of Brun’s constant relevant
• A description of the effect of dyscalculia on daily student lives
• Describe Descartes’s Dukes of Signs and their application
• Greeks and geometry: discuss
• Describe Euler’s formula
• The progression in the study of math
• Congruence meaning and methods
• Describe the correlation of CT scans to geometry
• Hypercubes and how they work
• The basis of Cramer’s rule
• The examination of Archimedean solids
• Projective geometry and why it’s studied
• Types of Transformations and the available types
• Picasso’s works and the application of geometry
• Difference between the conventional and unconventional approaches to teaching
• Math education and the process of Improvement in the US
• Rhombicosidodecahedron and how it operates in real life
• What are the STEM career fields and why are they important?
• Why women are needed in STEM
• The goals of teaching maths
• How to teach maths to special students
• The correlation between maths and accounting
• The distinction between computer programming and applied maths
• Applied maths and its dynamics
• Processes of solving Heesch’s problem
• Why should kids learn equations?
• History of calculus
• Why there is a need for math camps in schools
• The need for more maths competition in the US
• Methods of draining flight schedule for a country
• Why are some math problems unsolved?
• Discuss the consequences of the gender gap in math students
• Encryption and prime numbers: how do they apply?
• The significance of maths in day to day living.

Undergraduate Math Research Topics

As an undergraduate, you may also have a difficult time wrapping your head around math research topics. You may need to offer both practical and theoretical assessments while writing your paper or essay. The following are undergraduate math research topics:

• Show the proofs of what F-algebras are used
• Abstract algebra, what does it mean?
• Algebra and geometry: discuss
• Acute square triangulation: how it works
• Right triangles: discuss their importance
• Discuss number problems
• Why every math student should study non-Euclidean geometry
• Dirac manifolds and what it means
• Influence of geometry in physics, chemistry, and others
• The application of Riemannian manifolds in the Euclidean space
• How to improve your mathematical thinking ability
• Technology in maths: how is it used?
• Studies of maths in Europe
• Math anxiety and what it truly means
• Standardized testing and the goals of such
• Challenges of learning maths from public schools
• The significance of circles in maths
• The political and social significance of learning maths
• Research into how to increase student interest in maths
• How painting and drawing could help with maths
• Relationship of culture and maths
• History of algebra
• Role of maths in everyday life
• How math is used in Artificial intelligence
• The transferable belief model and its application
• An analysis of the Dempster-Shafer theory
• The role of continuous stochastic process in mathematics
• The major math theorems: discuss how they work
• Understanding the Gauss-Markov: The Evolution of maths
• Discrete random variable: an in-depth understanding of what it means in math and how to identify one.

Math Research Topics for High School Students

As a high school student writing a research paper, one way to get high grades is to write what you know. If you know any math research paper topics for high school, they are the topics you should pick. You can consider:

• Hyperbola: what it is and how it’s used in math
• When to use a calculator in class
• How to find solutions to linear equations
• The need for Pythagoras theorem in maths
• The role of art in maths and vice versa
• Role of philosophy in maths
• An overview of numerical data
• Egyptian mathematics explained
• Binomial theorem and its importance
• Probability, and how to solve a question on dice
• Why is math made compulsory in schools?
• Why do students hate maths?
• Why do students hate math teachers?
• How is math applied in the workplace?
• What are imaginary numbers and why are they needed
• How to calculate the interest rate and what is their importance in the banking sector?
• Discount factor: how is it achieved and why is it important for students?
• Types of techniques to be used while finding solutions to mathematical and finance gaps
• Solving a matrix: what are the important formulas and principles to embrace?
• How to create a chart on a company’s financial analysis for the past 5 years.

Interesting Math Research Topics

Writing a mathematical essay may seem complex to you if you can’t find simple topics to write about. There are many easy topics which are also general in maths. If you want to choose a relaxing topic for your math essay or paper, you can write about the following:

• The basic elements of Boolean algebra
• The life, time, and contribution of Isaac Newton to maths
• Sphericon and what it means
• Martingales and what they mean
• Hyperboloid and importance in geometry
• Describe the life, times, and contribution of Gauss to maths
• The most famous work of Jakob Bernoulli
• The most famous work of Jean d’Alembert
• Meaning and application of calculus in the banking field
• The meaning of congruence in math
• Analysis of De Finetti theorem in probability and statistics
• Describe Egyptian pyramids in concert with calculus
• Describe the enclosing sphere technique as used in combinatorics
• Tree automation meaning
• Pushdown automaton and Buchi automaton: differences and similarities
• What is the Markov algorithm?
• Describe what a Turing machine is
• What is the linear speedup theory in math?
• The Boolean satisfiability problem and what it means for students
• Why is the multiplication table important?
• Computational maths and its classes
• What does the post correspondence problem mean?
• What does the Scholz conjecture mean?
• How to calculate mean, median, and mode
• A study of the most difficult equations in math.

Cool Math Topics to Research

As a student of any level, you may love to create math topics that are not exactly complex. These are topics that lean on the history of maths, math education research topics, and others. Consider these math research topics for college students for your next essay or paper:

• Discuss what the Golden Ratio means in the paintings of the Renaissance period
• How to learn math
• An overview of the multiple ideas to probability
• How chess and checkers is essential in understanding mathematics
• How Pythagorean theorem is applied in real-life maths
• How to measure infinity
• The features of Mobius strip in geometry
• Describe what is meant by the Pascal’s Triangle
• Evaluate the Georg Cantor set theory
• What is the history of the number types?
• How does probability relate to card tricks?
• Compare and contrast abstract and universal algebra
• Describe Euclid’s role in the evolution of maths
• Evaluate the role of Indians in maths
• Explain the limits of calculus
• Discuss what predictive and prescriptive statistical analysis means
• What does chaos theory mean?
• Explain how to solve the Rubik’s Cube
• Why are some math equations so complex?
• How is geometry used in contemporary architectural designs?

Math Research Topics for Middle School

It’s okay to be worried about math topics for your research as a middle school student. There are still different unique topics that are rebranded from existing ones. You can find some of the right math research paper topics for you here:

• The role of statistics in business
• Definition of economic lot scheduling
• Why stock market crash
• The contribution of many traders in the New York Stock Exchange
• Revenue management and its history
• What are the financial indicators of a good investment?
• What are the odds of depreciation?
• How can any country benefit from the poor currency?
• Describe debt amortization and how math helps
• How to calculate net worth
• Distinctions in calculus, trigonometry, and algebra
• How did calculus start?
• How did trigonometry start?
• Why is Ito stochastic important in math?
• What do limits in math mean?
• How to know critical points in graphs
• What does nonstandard analysis in the probability theory mean?
• Describe continuous function
• The main principles of calculus
• The main principles of Pythagoras theorem
• Application of calculus in finance
• Value theorem in math
• Ratio and root test definition
• Linear approximations and how they work
• What is the Jacobson density theorem?
• Similarities and differences between epimorphisms and monopolists
• What does the Artin-Wedderburn theorem mean?
• Commutative ring and its meaning in algebra
• How difficult is it to teach maths?
• How standards examination curriculum affects math education.

Applied Math Research Topics

Applied math is a branch which deals with the application of mathematical methods in real life. These are manifested by applications in finance, physics, engineering, biology, medicine, and others. Through specialized knowledge, applied math is made possible. These are some topics for you in this area:

• How discovering genes can help determine healthy and unhealthy patients
• Role of algorithms in probabilistic modeling
• The need for mathematicians in developing robots
• The role of mathematicians in crime data analysis and prevention
• How did Isaac’s Laws of Motion help in real life?
• How math helped with energy conservation
• The role of math in quantum theory
• Analyze the features of the Lorentz symmetry
• Evaluate statistical signal processing in details
• Discuss how Galilean Transformation was achieved
• Examine nonlinear models
• Elucidate on the importance of data mining in banking
• The importance of step-stress modeling
• The significance of computer tomography
• What are the dimensions used in examining fingerprints?

Math Research Topics for College Students

As college students, you are at a critical level. You need maths topics for your essays and paper. You may also need them to prepare for your exams. These are some math research topics for you:

• Evolution of mathematics
• Explore the varieties of the Tower of Hanoi solutions
• Discuss how to use Napier’s bones
• Give examples of chaos theory and explain
• Discuss the important mathematical equations of all times
• Examine the nitty-gritty of barcodes
• What is the Traveling Salesman Problem?
• Natural selection and Fisher’s fundamental theorem of understanding it
• The Influence of math in biology
• The Influence of math in chemistry
• What is quantum computing?
• How to solve extremal problems in maths
• Analyze the meaning of fractals
• Discuss Einstein’s field equation theory
• Who created computer vision and object recognition?
• Five formulas and how they are applied
• Give three approaches to understanding maths
• Explain the origin and importance of algebra
• What do you know about the Fibonacci sequence?
• Trace the origin of math
• How does math help in geography?
• What does the operator spaces notion mean?

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Mathematics Theses, Projects, and Dissertations

Theses/projects/dissertations from 2024 2024.

On Cheeger Constants of Knots , Robert Lattimer

Information Based Approach for Detecting Change Points in Inverse Gaussian Model with Applications , Alexis Anne Wallace

Theses/Projects/Dissertations from 2023 2023

DNA SELF-ASSEMBLY OF TRAPEZOHEDRAL GRAPHS , Hytham Abdelkarim

An Exposition of the Curvature of Warped Product Manifolds , Angelina Bisson

Jackknife Empirical Likelihood Tests for Equality of Generalized Lorenz Curves , Anton Butenko

MATHEMATICS BEHIND MACHINE LEARNING , Rim Hammoud

Statistical Analysis of Health Habits for Incoming College Students , Wendy Isamara Lizarraga Noriega

Reverse Mathematics of Ramsey's Theorem , Nikolay Maslov

Distance Correlation Based Feature Selection in Random Forest , Jose Munoz-Lopez

Constructing Hyperbolic Polygons in the Poincaré Disk , Akram Zakaria Samweil

KNOT EQUIVALENCE , Jacob Trubey

Theses/Projects/Dissertations from 2022 2022

SYMMETRIC GENERATIONS AND AN ALGORITHM TO PROVE RELATIONS , Diddier Andrade

The Examination of the Arithmetic Surface (3, 5) Over Q , Rachel J. Arguelles

Error Terms for the Trapezoid, Midpoint, and Simpson's Rules , Jessica E. Coen

de Rham Cohomology, Homotopy Invariance and the Mayer-Vietoris Sequence , Stacey Elizabeth Cox

Symmetric Generation , Ana Gonzalez

SYMMETRIC PRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Samar Mikhail Kasouha

Simple Groups and Related Topics , Simrandeep Kaur

Homomorphic Images and Related Topics , Alejandro Martinez

LATTICE REDUCTION ALGORITHMS , Juan Ortega

THE DECOMPOSITION OF THE SPACE OF ALGEBRAIC CURVATURE TENSORS , Katelyn Sage Risinger

Verifying Sudoku Puzzles , Chelsea Schweer

AN EXPOSITION OF ELLIPTIC CURVE CRYPTOGRAPHY , Travis Severns

Theses/Projects/Dissertations from 2021 2021

Non-Abelian Finite Simple Groups as Homomorphic Images , Sandra Bahena

Matroids Determinable by Two Partial Representations , Aurora Calderon Dojaquez

SYMMETRIC REPRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Connie Corona

Symmetric Presentation of Finite Groups, and Related Topics , Marina Michelle Duchesne

MEASURE AND INTEGRATION , JeongHwan Lee

A Study in Applications of Continued Fractions , Karen Lynn Parrish

Partial Representations for Ternary Matroids , Ebony Perez

Theses/Projects/Dissertations from 2020 2020

Sum of Cubes of the First n Integers , Obiamaka L. Agu

Permutation and Monomial Progenitors , Crystal Diaz

Tile Based Self-Assembly of the Rook's Graph , Ernesto Gonzalez

Research In Short Term Actuarial Modeling , Elijah Howells

Hyperbolic Triangle Groups , Sergey Katykhin

Exploring Matroid Minors , Jonathan Lara Tejeda

DNA COMPLEXES OF ONE BOND-EDGE TYPE , Andrew Tyler Lavengood-Ryan

Modeling the Spread of Measles , Alexandria Le Beau

Symmetric Presentations and Related Topics , Mayra McGrath

Minimal Surfaces and The Weierstrass-Enneper Representation , Evan Snyder

ASSESSING STUDENT UNDERSTANDING WHILE SOLVING LINEAR EQUATIONS USING FLOWCHARTS AND ALGEBRAIC METHODS , Edima Umanah

Excluded minors for nearly-paving matroids , Vanessa Natalie Vega

Theses/Projects/Dissertations from 2019 2019

Fuchsian Groups , Bob Anaya

Tribonacci Convolution Triangle , Rosa Davila

VANISHING LOCAL SCALAR INVARIANTS ON GENERALIZED PLANE WAVE MANIFOLDS , Brian Matthew Friday

Analogues Between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle , Lacey Taylor James

Geodesics on Generalized Plane Wave Manifolds , Moises Pena

Algebraic Methods for Proving Geometric Theorems , Lynn Redman

Pascal's Triangle, Pascal's Pyramid, and the Trinomial Triangle , Antonio Saucedo Jr.

THE EFFECTIVENESS OF DYNAMIC MATHEMATICAL SOFTWARE IN THE INSTRUCTION OF THE UNIT CIRCLE , Edward Simons

CALCULUS REMEDIATION AS AN INDICATOR FOR SUCCESS ON THE CALCULUS AP EXAM , Ty Stockham

Theses/Projects/Dissertations from 2018 2018

PROGENITORS, SYMMETRIC PRESENTATIONS AND CONSTRUCTIONS , Diana Aguirre

Monomial Progenitors and Related Topics , Madai Obaid Alnominy

Progenitors Involving Simple Groups , Nicholas R. Andujo

Simple Groups, Progenitors, and Related Topics , Angelica Baccari

Exploring Flag Matroids and Duality , Zachary Garcia

Images of Permutation and Monomial Progenitors , Shirley Marina Juan

MODERN CRYPTOGRAPHY , Samuel Lopez

Progenitors, Symmetric Presentations, and Related Topics , Joana Viridiana Luna

Symmetric Presentations, Representations, and Related Topics , Adam Manriquez

Toroidal Embeddings and Desingularization , LEON NGUYEN

THE STRUGGLE WITH INVERSE FUNCTIONS DOING AND UNDOING PROCESS , Jesus Nolasco

Tutte-Equivalent Matroids , Maria Margarita Rocha

Symmetric Presentations and Double Coset Enumeration , Charles Seager

MANUAL SYMMETRIC GENERATION , Joel Webster

Theses/Projects/Dissertations from 2017 2017

Investigation of Finite Groups Through Progenitors , Charles Baccari

CONSTRUCTION OF HOMOMORPHIC IMAGES , Erica Fernandez

Making Models with Bayes , Pilar Olid

An Introduction to Lie Algebra , Amanda Renee Talley

SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS , Ulyses Velasco

CONSTRUCTION OF FINITE GROUP , Michelle SoYeong Yeo

Theses/Projects/Dissertations from 2016 2016

Upset Paths and 2-Majority Tournaments , Rana Ali Alshaikh

Regular Round Matroids , Svetlana Borissova

GEODESICS IN LORENTZIAN MANIFOLDS , Amir A. Botros

REALIZING TOURNAMENTS AS MODELS FOR K-MAJORITY VOTING , Gina Marie Cheney

Solving Absolute Value Equations and Inequalities on a Number Line , Melinda A. Curtis

BIO-MATHEMATICS: INTRODUCTION TO THE MATHEMATICAL MODEL OF THE HEPATITIS C VIRUS , Lucille J. Durfee

ANALYSIS AND SYNTHESIS OF THE LITERATURE REGARDING ACTIVE AND DIRECT INSTRUCTION AND THEIR PROMOTION OF FLEXIBLE THINKING IN MATHEMATICS , Genelle Elizabeth Gonzalez

LIFE EXPECTANCY , Ali R. Hassanzadah

PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS , Sean M. Hearon

A Dual Fano, and Dual Non-Fano Matroidal Network , Stephen Lee Johnson

Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity , Nitish Mittal

The Kauffman Bracket and Genus of Alternating Links , Bryan M. Nguyen

Probabilistic Methods In Information Theory , Erik W. Pachas

THINKING POKER THROUGH GAME THEORY , Damian Palafox

Indicators of Future Mathematics Proficiency: Literature Review & Synthesis , Claudia Preciado

Ádám's Conjecture and Arc Reversal Problems , Claudio D. Salas

AN INTRODUCTION TO BOOLEAN ALGEBRAS , Amy Schardijn

The Evolution of Cryptology , Gwendolyn Rae Souza

Theses/Projects/Dissertations from 2015 2015

SYMMETRIC PRESENTATIONS AND RELATED TOPICS , Mashael U. Alharbi

Homomorphic Images And Related Topics , Kevin J. Baccari

Geometric Constructions from an Algebraic Perspective , Betzabe Bojorquez

Discovering and Applying Geometric Transformations: Transformations to Show Congruence and Similarity , Tamara V. Bonn

Symmetric Presentations and Generation , Dustin J. Grindstaff

HILBERT SPACES AND FOURIER SERIES , Terri Joan Harris Mrs.

SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS , Leonard B. Lamp

Simple Groups and Related Topics , Manal Abdulkarim Marouf Ms.

Elliptic Curves , Trinity Mecklenburg

A Fundamental Unit of O_K , Susana L. Munoz

CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES , Jessica Luna Ramirez

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• 14 May 2024

Why mathematics is set to be revolutionized by AI

• Thomas Fink 0

Thomas Fink is the director of the London Institute for Mathematical Sciences, UK.

You can also search for this author in PubMed   Google Scholar

You have full access to this article via your institution.

Giving birth to a conjecture — a proposition that is suspected to be true, but needs definitive proof — can feel to a mathematician like a moment of divine inspiration. Mathematical conjectures are not merely educated guesses. Formulating them requires a combination of genius, intuition and experience. Even a mathematician can struggle to explain their own discovery process. Yet, counter-intuitively, I think that this is the realm in which machine intelligence will initially be most transformative.

In 2017, researchers at the London Institute for Mathematical Sciences, of which I am director, began applying machine learning to mathematical data as a hobby. During the COVID-19 pandemic, they discovered that simple artificial intelligence (AI) classifiers can predict an elliptic curve’s rank 1 — a measure of its complexity. Elliptic curves are fundamental to number theory, and understanding their underlying statistics is a crucial step towards solving one of the seven Millennium Problems, which are selected by the Clay Mathematics Institute in Providence, Rhode Island, and carry a prize of US$1 million each. Few expected AI to make a dent in this high-stakes arena.

AI now beats humans at basic tasks — new benchmarks are needed, says major report

AI has made inroads in other areas, too. A few years ago, a computer program called the Ramanujan Machine produced new formulae for fundamental constants 2 , such as π and e . It did so by exhaustively searching through families of continued fractions — a fraction whose denominator is a number plus a fraction whose denominator is also a number plus a fraction and so on. Some of these conjectures have since been proved, whereas others remain open problems.

Another example pertains to knot theory, a branch of topology in which a hypothetical piece of string is tangled up before the ends are glued together. Researchers at Google DeepMind, based in London, trained a neural network on data for many different knots and discovered an unexpected relationship between their algebraic and geometric structures 3 .

How has AI made a difference in areas of mathematics in which human creativity was thought to be essential?

First, there are no coincidences in maths. In real-world experiments, false negatives and false positives abound. But in maths, a single counterexample leaves a conjecture dead in the water. For example, the Pólya conjecture states that most integers below any given integer have an odd number of prime factors. But in 1960, it was found that the conjecture does not hold for the number 906,180,359. In one fell swoop, the conjecture was falsified.

Second, mathematical data — on which AI can be trained — are cheap. Primes, knots and many other types of mathematical object are abundant. The On-Line Encyclopedia of Integer Sequences (OEIS) contains almost 375,000 sequences — from the familiar Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, ...) to the formidable Busy Beaver sequence (0, 1, 4, 6, 13, …), which grows faster than any computable function. Scientists are already using machine-learning tools to search the OEIS database to find unanticipated relationships.

DeepMind AI outdoes human mathematicians on unsolved problem

AI can help us to spot patterns and form conjectures. But not all conjectures are created equal. They also need to advance our understanding of mathematics. In his 1940 essay A Mathematician’s Apology , G. H. Hardy explains that a good theorem “should be one which is a constituent in many mathematical constructs, which is used in the proof of theorems of many different kinds”. In other words, the best theorems increase the likelihood of discovering new theorems. Conjectures that help us to reach new mathematical frontiers are better than those that yield fewer insights. But distinguishing between them requires an intuition for how the field itself will evolve. This grasp of the broader context will remain out of AI’s reach for a long time — so the technology will struggle to spot important conjectures.

But despite the caveats, there are many upsides to wider adoption of AI tools in the maths community. AI can provide a decisive edge and open up new avenues for research.

Mainstream mathematics journals should also publish more conjectures. Some of the most significant problems in maths — such as Fermat’s Last Theorem, the Riemann hypothesis, Hilbert’s 23 problems and Ramanujan’s many identities — and countless less-famous conjectures have shaped the course of the field. Conjectures speed up research by pointing us in the right direction. Journal articles about conjectures, backed up by data or heuristic arguments, will accelerate discovery.

Last year, researchers at Google DeepMind predicted 2.2 million new crystal structures 4 . But it remains to be seen how many of these potential new materials are stable, can be synthesized and have practical applications. For now, this is largely a task for human researchers, who have a grasp of the broad context of materials science.

Similarly, the imagination and intuition of mathematicians will be required to make sense of the output of AI tools. Thus, AI will act only as a catalyst of human ingenuity, rather than a substitute for it.

Nature 629 , 505 (2024)

doi: https://doi.org/10.1038/d41586-024-01413-w

He, Y.-H., Lee, K.-H., Oliver, T. & Pozdnyakov, A. Preprint at arXiv https://doi.org/10.48550/arXiv.2204.10140 (2024).

Raayoni, G. et al. Nature 590 , 67–73 (2021).

Article   PubMed   Google Scholar  

Davies, A. et al. Nature 600 , 70–74 (2021).

Merchant, A. et al. Nature 624 , 80–85 (2023).

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Providing an overview of the accumulated scientific knowledge regarding the learning of geometry with dynamic software by pre-service mathematics teachers is currently a pertinent issue in Mathematics Education. The interest in this topic within the field is reflected in the significance attributed to the role of the teacher as a pivotal actor in their students learning. Considering this, we present a systematic review that seeks to understand how the learning of school geometry content with dynamic software has been promoted and studied during pre-service mathematics teacher education. To do so, we have reviewed a group of journal articles, published between 2017 and 2023, following the principles of PRISMA declaration. The results reveal how researchers understand such learning, the pre-service teachers, the teacher educator, the tasks that promote it, and the production and analysis of data. Given these findings, we identify gaps in the research on this topic, among which stand out the view of pre-service teachers as autonomous subjects, the instrumentalist conception of dynamic software, and methodological approaches to data analysis that do not fully consider the role of the body in the act of knowing. These gaps reveal that the promotion of and study of learning of school geometry content with dynamic software have been explored little from sociocultural perspectives. Because of this, we believe it necessary to develop studies regarding learning from theoretical and methodological perspectives that demonstrate pathways for future explorations on the addressed topic and thus allow for the reduction of these gaps.

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The data generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Prieto-González, J.L., Gutiérrez-Araujo, R.E. Geometry learning with dynamic software in pre-service mathematics teacher education: A systematic review. Educ Inf Technol (2024). https://doi.org/10.1007/s10639-024-12756-2

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• OpenIntro Statistics (OER textbooks) OpenIntro Statistics, Intro Statistics with Randomization and Simulation, and Intro Statistics for the Life and Biomedical Sciences textbooks, videos, slides, labs, and more. PDF format available for free. CC BY SA (Creative Commons - Attribution - ShareAlike) license.

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• MATH 96/140 (TCC OER course) Tip: Log into your TCC Canvas faculty account *before* clicking on this link! OER Canvas course shared by TCC instructor Mike Flodin, 2020. "Web-enhanced Introduction to Precalculus class (in between Intermediate Algebra and Precalculus)." Includes modules, assignments, and discussions. Public domain license.

Canvas course shells:

• Technical Mathematics (OER textbook) OER textbook by Morgan Chase, Clackamas Community College, published by Oregon State University, 2021. "This developmental-level mathematics textbook is intended for career-technical students." Organized into 30 modules, from "Order of Operations" to "Standard Deviation." Includes exercises and exercise answers for each module. Online, PDF, and e-book formats. CC BY NC SA (Creative Commons Attribution NonCommercial ShareAlike) license.
• Transitions Math I (WACTC OER course) Tip: Log into your Clark College Canvas faculty account *before* clicking on this link! OER Canvas course shared by Grays Harbor College instructor, 2020. "Transitions Math I course is comprised of six modules that focus on arithmetic: whole numbers, fractions (2 modules), decimals, ratios and proportions, and percents. Most lessons have a pretest, video lesson(s), follow up quiz(zes) and homework. At the end of each module, there is a practice test and answer key. The module does not include the module tests or the final exam. The course is designed for GED students, high school completion students, and students brushing up for the college placement test." Includes modules, assignments, quizzes, and discussions. CC BY NC SA (Creative Commons - Attribution - NonCommercial - ShareAlike) license.
• Fundamentals of Mathematics (open textbook) "This text will help the student develop the insight and intuition necessary to master arithmetic techniques and manipulative skills." 11 chapters. Peer reviews of the text are available on this site. Online, PDF, and offline zip file formats available. CC BY (Creative Commons - Attribution) license.
• MAT082 – Basic Arithmetic OER (Scottsdale Community College) Materials developed by Scottsdale Community College instructors for developmental math sequence, 2013. Student workbook, mini-lesson worksheets, practice problem worksheets, and mini-lesson videos, organized into 11 weeks. CC BY SA (Creative Commons - Attribution - ShareAlike) license.
• MAT09x Introductory Algebra OER (Scottsdale Community College) Materials developed by Scottsdale Community College instructors for developmental math sequence, 2014. Student workbook, worksheets, and mini-lesson videos, organized into 12 weeks. CC BY SA (Creative Commons - Attribution - ShareAlike) license.
• MAT12x – Intermediate Algebra OER (Scottsdale Community College) Materials developed by Scottsdale Community College instructors for developmental math sequence, 2015. Student workbook, mini-lesson worksheets, practice problem worksheets, and mini-lesson videos, organized into 12 weeks. CC BY (Creative Commons - Attribution) license.
• Adult Literacy Fundamentals Textbooks from BC Campus Open Ed Adult Literacy textbooks (available in multiple file formats) for Mathematics, English, and College Success. Most look to be CC BY licensed (Creative Commons - Attribution)
• CK-12 Math Biggest open content provider for K-12 STEM content. Look on the left column for links to Math subjects, including Grades 1-5, Arithmetic, Measurement, and more. CC BY NC 3.0 license (Creative Commons - Attribution - NonCommercial)
• ABCYA.com “ABCya is the leader in free educational computer games and mobile apps for kids. The innovation of a grade school teacher, ABCya is an award-winning destination for elementary students that offers hundreds of fun, engaging learning activities.” Free online games for Pre-K through 5th grade. Alphabet, numbers, money, geography, parts of speech, typing, technology vocabulary, skills -- INCLUDES MATH! Holiday themed games available. No charge to use on PCs. Mobile-friendly version requires a subscription more... less... Recommended by TCC AESL instructor

Any additional resources or personal recommendations to add to this guide? Please email your suggestions to your department's librarian liaison .

Related guides for faculty.

• Open Educational Resources (OER) by Laura Nagel Last Updated May 7, 2024 368 views this year

Cool Tools for Teaching with OER

• H5P "Create, share and reuse interactive HTML5 content in your browser"
• Hypothesis Free web annotation tool.
• Open Attribution Builder from Open Washington A tool to help you create attributions for openly licensed materials. "As you fill out the form, the app automatically generates the attribution for you."
• A Guide to Making Open Textbooks with Students Ed. by Elizabeth Mays. "Book Description: A handbook for faculty interested in practicing open pedagogy by involving students in the making of open textbooks, ancillary materials, or other Open Educational Resources. This is a first edition, compiled by Rebus Community, and we welcome feedback and ideas to expand the text."

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"OER by Subject: Math" by Clark College Libraries is licensed under CC BY-SA 4.0 / This guide has been adapted from content originally created by Tacoma Community College Library and shared with a CC BY SA 4.0 license.

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• URL: https://clark.libguides.com/mathoer

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Collaborative Research: Leveraging Simulations in Preservice Preparation to Improve Mathematics Teaching for Students with Disabilities

Project Number 2009939 Agency/Funding Organization NSF Funding Year 2020 View Full Project Details for Collaborative Research: Leveraging Simulations in Preservice Preparation to Improve Mathematics Teaching for Students with Disabilities

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Welcome on board Research of random dynamical systems Prof. Dr. Vitalii Konarovskyi joins the Department of Mathematics

14 May 2024, by Heiko Fuchs

Photo: privat

Every year, numerous new researchers join the University of Hamburg. In this series, we introduce them and their fields of research. This time: mathematician Prof. Dr. Vitalii Konarovskyi.

Prof. Dr. Vitalii Konarovskyi came to Hamburg from Bielefeld University in the winter semester and took up the W2 professorship for "Mathematics, in particular Stochastic Processes and their Applications" at the Department of Mathematics in the Faculty of Mathematics, Informatics and Natural Sciences.

Mr. Konarovskyi, what are your research topics?

I study stochastic processes that are the key mathematical tool for modelling complex evolving systems that appear in physics, biology, computer science and many other disciplines. They are used, for example, to describe the spread of epidemics, the diffusion of gas molecules and the training of neural networks.

What exactly are you working on?

My main research is at the intersection of four different directions that have developed over the past ten years: These are singular stochastic partial differential equations, stochastic flows, optimal transport in mathematics and the statistical non-equilibrium mechanics of materials in physics as well as engineering. Recently I also started a few projects in mathematics for machine learning and random graph theory.

Where can your work be applied?

For example, I investigate a class of random graphs, called stochastic block model, that can be used for the description of the spread of infections in the population in epidemiology or the formation of clusters in networks in computer sciences. Together with my co-authors we proposed a new type of stochastic (partial) differential equations that can be used for training and investigating neural networks in machine learning.

What are your plans at the Universität Hamburg?

My main goal at the Universität Hamburg will be to build a strong group focusing on stochastic processes and their application that would work closely with different research groups in physics, biology and computer science. In particular, I will focus on joint work with researchers from physics to construct and study mathematical models that arise in particle physics, hydrodynamics, climate research and other fields.

What do you need for your research?

For my work, I usually only need a pen and some notebooks to write down my computations. Of course, I also need a bit of luck to find the right ideas and implement them mathematically correctly.

Why did you choose the Universität Hamburg?

Hamburg is a very good place for me because of the many opportunities for cooperation. There are many excellent groups working in physics and earth system sciences, computer sciences, etc., that deal with topics that can be combined with my research, such as particle physics, climate research or machine learning. In addition, I have already worked at the Universität Hamburg as a substitute professor and find it very nice to come back and continue my work.

What are you planning for your courses?

Due to their wide range of applications, the concepts of stochastics are not only of great importance for students of mathematics, but also for other subjects. I would therefore like to offer interdisciplinary courses for students from different subject areas. I already started implementing this idea as a substitute professor at the Universität Hamburg in 2020/2021, when I offered the seminar "Application of large deviations to statistical mechanics" for students of mathematics and physics. At that time, however, it was more of an experiment. Now I would like to systematically deepen the education of students of physics, computer science, biology and other subjects in the most important concepts of stochastic processes and related fields.

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