essay on mathematics is a language

Why Mathematics Is a Language

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Mathematics is called the language of science. Italian astronomer and physicist Galileo Galilei is attributed with the quote, " Mathematics is the language in which God has written the universe ." Most likely this quote is a summary of his statement in  Opere Il Saggiatore:

[The universe] cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.

Yet, is mathematics truly a language, like English or Chinese? To answer the question, it helps to know what language is and how the vocabulary and grammar of mathematics are used to construct sentences.

Key Takeaways: Why Math is a Language

• In order to be considered a language, a system of communication must have vocabulary, grammar, syntax, and people who use and understand it.
• Mathematics meets this definition of a language. Linguists who don't consider math a language cite its use as a written rather than spoken form of communication.
• Math is a universal language. The symbols and organization to form equations are the same in every country of the world.

What Is a Language?

There are multiple definitions of " language ." A language may be a system of words or codes used within a discipline. Language may refer to a system of communication using symbols or sounds. Linguist Noam Chomsky defined language as a set of sentences constructed using a finite set of elements. Some linguists believe language should be able to represent events and abstract concepts.

Whichever definition is used, a language contains the following components:

• There must be a vocabulary of words or symbols.
• Meaning must be attached to the words or symbols.
• A language employs grammar , which is a set of rules that outline how vocabulary is used.
• A syntax organizes symbols into linear structures or propositions.
• A narrative or discourse consists of strings of syntactic propositions.
• There must be (or have been) a group of people who use and understand the symbols.

Mathematics meets all of these requirements. The symbols, their meanings, syntax, and grammar are the same throughout the world. Mathematicians, scientists, and others use math to communicate concepts. Mathematics describes itself (a field called meta-mathematics), real-world phenomena, and abstract concepts.

Vocabulary, Grammar, and Syntax in Mathematics

The vocabulary of math draws from many different alphabets and includes symbols unique to math. A mathematical equation may be stated in words to form a sentence that has a noun and a verb, just like a sentence in a spoken language. For example:

3 + 5 = 8

could be stated as "Three added to five equals eight."

Breaking this down, nouns in math include:

• Arabic numerals (0, 5, 123.7)
• Fractions (1⁄4, 5⁄9, 2 1⁄3)
• Variables (a, b, c, x, y, z)
• Expressions (3x, x 2 , 4 + x)
• Diagrams or visual elements (circle, angle, triangle, tensor, matrix)
• Infinity (∞)
• Imaginary numbers (i, -i)
• The speed of light (c)

Verbs include symbols including:

• Equalities or inequalities (=, <, >)
• Actions such as addition, subtraction, multiplication, and division (+, -, x or *, ÷ or /)
• Other operations (sin, cos, tan, sec)

If you try to perform a sentence diagram on a mathematical sentence, you'll find infinitives, conjunctions, adjectives, etc. As in other languages, the role played by a symbol depends on its context.

International Rules

Mathematics grammar and syntax, like vocabulary, are international. No matter what country you're from or what language you speak, the structure of the mathematical language is the same.

• Formulas are read from left to right.
• The Latin alphabet is used for parameters and variables. To some extent, the Greek alphabet is also used. Integers are usually drawn from i , j , k , l , m , n . Real numbers are represented by  a ,  b ,  c , α , β , γ. Complex numbers are indicated by w and z . Unknowns are x , y , z . Names of functions are usually f , g , h .
• The Greek alphabet is used to represent specific concepts. For example, λ is used to indicate wavelength and ρ means density.
• Parentheses and brackets indicate the order in which the symbols interact .
• The way functions, integrals, and derivatives are phrased is uniform.

Language as a Teaching Tool

Understanding how mathematical sentences work is helpful when teaching or learning math. Students often find numbers and symbols intimidating, so putting an equation into a familiar language makes the subject more approachable. Basically, it's like translating a foreign language into a known one.

While students typically dislike word problems, extracting the nouns, verbs, and modifiers from a spoken/written language and translating them into a mathematical equation is a valuable skill to have. Word problems improve comprehension and increase problem-solving skills.

Because mathematics is the same all over the world, math can act as a universal language. A phrase or formula has the same meaning, regardless of another language that accompanies it. In this way, math helps people learn and communicate, even if other communication barriers exist.

The Argument Against Math as a Language

Not everyone agrees that mathematics is a language. Some definitions of "language" describe it as a spoken form of communication. Mathematics is a written form of communication. While it may be easy to read a simple addition statement aloud (e.g., 1 + 1 = 2), it's much harder to read other equations aloud (e.g., Maxwell's equations). Also, the spoken statements would be rendered in the speaker's native language, not a universal tongue.

However, sign language would also be disqualified based on this criterion. Most linguists accept sign language as a true language. There are a handful of dead languages that no one alive knows how to pronounce or even read anymore.

A strong case for mathematics as a language is that modern elementary-high school curricula uses techniques from language education for teaching mathematics. Educational psychologist Paul Riccomini and colleagues wrote that students learning mathematics require "a robust vocabulary knowledge base; flexibility; fluency and proficiency with numbers, symbols, words, and diagrams; and comprehension skills."

• Ford, Alan, and F. David Peat. " The Role of Language in Science ." Foundations of Physics 18.12 (1988): 1233–42. 
• Galilei, Galileo. "'The Assayer' ('Il Saggiatore' in Italian) (Rome, 1623)." The Controversy on the Comets of 1618 . Eds. Drake, Stillman and C. D. O'Malley. Philadelphia: University of Pennsylvania Press, 1960. 
• Klima, Edward S., and Ursula Bellugi. "The Signs of Language. "Cambridge, MA: Harvard University Press, 1979. 
• Riccomini, Paul J., et al. " The Language of Mathematics: The Importance of Teaching and Learning Mathematical Vocabulary ." Reading & Writing Quarterly 31.3 (2015): 235-52. Print.
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Mathematics: The only true universal language

By Martin Rees

11 February 2009

An alien’s description of the cosmos might teach us a thing or two about the nature of reality

(Image: Wolcott Henry/National Geographic/Getty)

IF WE ever establish contact with intelligent aliens living on a planet around a distant star, we would expect some problems communicating with them. As we are many light years away, our signals would take many years to reach them, so there would be no scope for snappy repartee. There could be an IQ gap and the aliens might be built from quite different chemistry.

Yet there would be much common ground too. They would be made of similar atoms to us. They could trace their origins back to the big bang 13.7 billion years ago, and they would share with us the universe’s future. However, the surest common culture would be mathematics.

Mathematics has been the language of science for thousands of years, and it is remarkably successful. In a famous essay, the great physicist Eugene Wigner wrote about the “unreasonable effectiveness of mathematics”. Most of us resonate with the perplexity expressed by Wigner, and also with Einstein’s dictum that “the most incomprehensible thing about the universe is that it is comprehensible”. We marvel at the fact that the universe is not anarchic – that atoms obey the same laws in distant galaxies as in the lab. The aliens would, like us, be astonished by the patterns in our shared cosmos and by the effectiveness of mathematics in describing those patterns.

Mathematics can point the way towards new discoveries in physics too. Most famously, British theorist Paul Dirac used pure mathematics to formulate an equation…

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We Should Teach Math Like It’s a Language

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The United States has a math problem, and, like most middle school students sitting down with their homework, we are not finding any easy solutions. Young people in this country are struggling to attain the proficiency necessary to pursue the careers our economy desperately needs. Universities bemoan students’ inability to complete college-level math. Each year thousands of newly admitted college students are placed in non-credit-bearing remedial courses in math, a path that immediately puts them at a higher risk of not completing a degree.

Maybe it’s the classics professor in me talking, but I approach this math problem from an unorthodox angle: Latin. In a 2011 article, “An Apology for Latin and Math,” high school Latin teacher Cheryl Lowe made a compelling comparison between the study of Latin and the study of math. Much like Latin, she observed, “math is hard because it builds so relentlessly year after year. Any skill not mastered one year will make work difficult the next.”

High school teachers have discovered that the unrelentingly cumulative nature of the study of Latin and the study of mathematics explains why students struggle to excel in either discipline.

A favorite lament of college and university faculty in quantitative fields is that students cannot perform college-level math. But what is college-level math?

In the world of classics, there is no such thing as college-level Latin. My daughter’s high school Latin teacher uses the same textbook for her class that I have used to teach Latin at Duke University, Whitman College in Washington state, and the University of Southern Maine. It turns out that there are only two differences between high school Latin and college Latin. The first is pace. I tell students that one year of college Latin is the approximate equivalent of three years of high school Latin.

The other difference is the developmental level of the student. A high school student is often not as prepared as a college student to confront demanding theoretical material, and therefore college classes might incorporate more theory than would a high school class.

The United States has been sucked into the myth of college-level math."

Like Latin, algebra is a language; and like Latin, algebra is taught to students of different developmental levels at different paces and with different levels of theoretical grounding across the K-16 landscape. The crucial difference between Latin and math education is that classicists understand that Latin is Latin, no matter the level.

Students who took Latin in high school are often encouraged to begin Latin anew when they get to college. The review students receive in an introductory college course reinforces their learning in preparation for more advanced work. This is precisely what I did when I got to college, and no one suggested that mine was not college-level study, quite the opposite: I became a classical languages major and nine years later finished a doctorate in classical studies.

In contrast, the United States has been sucked into the myth of college-level math. If students need a review of algebra, instead of encouraging them to start anew in order to reinforce their skills, we test them, label that review “remedial,” and withhold college credit from them. This message is jarring and discouraging to new college students, many of whom already have significant doubts about whether they belong in college or whether college is worth the investment.

I point out the discrepancy between our approaches to these subjects not to downplay the national crisis in quantitative reasoning but to suggest that the deficiency is in our attitude toward teaching math.

We know how to teach Latin, and we do it well. Year after year we teach the same challenging skills, facts, and concepts in different ways from middle school through college, never complaining that students are not doing college-level work. Once students have enough facility to read unabridged ancient texts, whether that happens in 8th grade or their junior year of college, we move on to translation and critical reading appropriate to the developmental level of the student.

Our approach to teaching Latin can inform better practices in math education. No one would deny that students wishing to become physicists must master calculus, but we must shift our narrative from one that labels students “deficient” on the basis of arbitrary grade-level designations. Instead, we should embrace a reverse-engineering model in which we establish clear, carefully constructed pathways to the things students must do.

Our lamentations about student deficiencies and our focus on what constitutes college-level work have been an unfortunate distraction from the salient challenge of how to help students reach the careers or paths of study to which they aspire. Meeting this challenge may require blurring the lines even further between high school and college curricula. It may require courses of different paces and configurations from the familiar K-16 standards. It will certainly require better partnerships between high schools and universities.

As is so common in the academy, we have focused on faculty-centric, content-based questions (“What constitutes college-level math?”) rather than student-centric, learning-based questions (“What do students need to reach their goals?”). Solving our math problem will require unorthodox strategies for increasing student success in math rather than trying to quantify what “counts” at the college level.

A version of this article appeared in the May 30, 2018 edition of Education Week as Math Is a Language. Let’s Teach It That Way

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Mathematics Is a Language

The notion that Mathematics is a language is held by many mathematicians and is being expressed on frequent occasions. Below, I am going to collect quotes I occasionally come across that uphold that point.

R. L. E. Schwarzenberger, The Language of Geometry , in A Mathematical Spectrum Miscellany , Applied Probability Trust, 2000, p. 112:

My own attitude, which I share with many of my colleagues, is simply that mathematics is a language. Like English, or Latin, or Chinese, there are certain concepts for which mathematics is particularly well suited: it would be as foolish to attempt to write a love poem in the language of mathematics as to prove the Fundamental Theorem of Algebra using the English language.

Yu. Manin, Mathematics as profession and vocation , in Mathematics: Frontiers and Perspectives , (V. Arnold et al, ed), AMS, 200, p. 154:

The basis of all human culture is language, and mathematics is a special kind of linguistic activity.

A. Adler, Mathematics and Creativity , in The World Treasury of Physics, Astronomy and Mathematics , (T. Ferris, ed), Little, Brown and Co, 1991, p. 435:

Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. (In a spoken language, there exist words, like "happiness", that defy definition.) It is also an art - the most intellectual and classical of the arts.

J.-P. Changeux, A. Connes, Conversations on Mind, Matter and Mathematics , Princeton University Press, 1995, p. 10:

Connes : It is unquestionably the only universal language.

Language of Mathematics, Language of Science and Plain Language

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Mathematics as Language

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Mathematics: The Language of Nature Essay

Reaction 1: The importance attached to mathematics as a science, and a collaborator for physics has fast gained credibility and recognition, especially in the context of its logical reasoning and scientific principles that supports its theories and practices. It is also seen as claiming to be the fountainhead of thoughts that have been generated through interpretations of surreal mathematics.

Reaction 2: The success gained by mathematics could be largely attributed to the fact that it is a language that has quantitative utility value; it does not relate itself with mundane business applications, but is more concerned with abstract relationships and also in terms of seeking relations within relationships, in order to critically examine the principles or theories themselves, rather than the empirical application of such tenets. (Peat & Mickens, 1990).

Reaction 3: The language of mathematics, especially in its pristine form, has been popularized because it is the only quantitative method that could possibly address theories of physics, more so, in contemporary times. The Cartesian grid, for instance, has been a striking illustration of mathematical suzerainty over physics. (Peat & Mickens, 1990).

Reaction 4: The debate whether mathematics could be treated as a language needs to be seen in the context of the fact that in certain cases, it deals with codified quantitative data which has very little to do with the abstract and conceptual thinking attributed to languages. The fact remains that mathematics may not be treated more than a technical language due to absence of conveyance of human emotions and feelings.

Reaction 5: Drawing comparison between mathematics and music, it could be said that while both follow logical order and precision, music is a sense experience that transcend normal senses, and “seeks a harmony between the four basic human functions; thought balanced by feeling and intuition by sensation.“ (Peat & Mickens, 1990).

Reaction 6: In reaching a nexus between mathematics and functioning of the human brain, it is seen that both have patterned hierarchical level of thinking and logical functioning. As a matter of fact, the brain needs to seek assimilate and correlate data in a structured and orderly manner in order to solve a mathematical problem. It is also seen that the science of mathematics also lends itself for structural integrity and coherence.

Reaction 7: The aspect of archetype cannot also be ruled out, in that scientific arguments and validations of many great mathematics have originated not from rigorous pursuit of study but from their intuitions, or gut feelings. It would also not be improbable to surmise that these hunches could form the premise of major mathematical breakthroughs in future, too. (Peat & Mickens, 1990).

Reaction 8 : It may be concluded that theories that mathematics as a precursor to physics may be valid, sustainable, and may lent credence to the reality of our very existence on earth, but it is essential that a wider perspective be taken in order to ake stock of the goals and objectives of scientific studies. It also needs to be assessed and judged in order to be able to make critical appreciation of the various empirical and scholarly treatise of mathematics as a major quantitative and value based subject amenable to interpretations and future studies.

Peat, F. David., & Mickens, Ronald E (Ed.). (1990). Mathematics and the Language of Nature . Mathematics and Sciences. (Word Scientific, 1990). (provided by the customer).

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Please note you do not have access to teaching notes, mathematics as a universal language: transcending cultural lines.

Journal for Multicultural Education

ISSN : 2053-535X

Article publication date: 8 August 2016

Universal language can be viewed as a conjectural or antique dialogue that is understood by a great deal, if not all, of the world’s population. In this paper, a sound argument is presented that mathematical language exudes characteristics of worldwide understanding. The purpose of this paper is to explore mathematical language as a tool that transcends cultural lines.

Design/methodology/approach

This study has used a case study approach. The data relevant to the study were collected using participant observations, video recordings of classroom interactions and field notes.

Researchers found that mathematics communication and understanding were mutual among both groups whose languages were foreign to each other. Findings from this study stand to contribute to the ongoing discussion and debates about the universality of mathematics and to influence the teaching and learning of mathematics around the world.

Originality/value

Mathematics is composed of definitions, theorems, axioms, postulates, numbers and concepts that can all generally be expressed as symbols and that have been proven to be true across many nations. Through the symbolic representation of mathematical ideas, communication may occur that stands to break cultural barriers and unite all people using one common language.

• Multicultural
• Global education
• Mathematical language

Parker Waller, P. and Flood, C.T. (2016), "Mathematics as a universal language: transcending cultural lines", Journal for Multicultural Education , Vol. 10 No. 3, pp. 294-306. https://doi.org/10.1108/JME-01-2016-0004

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Mathematics and Language and Literature

• First Online: 20 December 2022

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• Claus Michelsen 23  

Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 19))

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The relations between mathematics, language and literature have been a recurring theme at MACAS symposia. The contributions to the MACAS proceedings remind us that the disciplines, including mathematics, are man-made creations, and standing alone the single discipline has only limited usefulness and underscores the vision of MACAS to develop a humanistic approach to education, which combines various disciplines in a single curriculum. Articles in the MACAS proceedings offer different approaches and views on the relations between mathematics, literature and language, and the articles in this chapter by former participants in the MACAS symposia follow up and expand on the themes of mathematics, literature and language addressed in the MACAS proceedings.

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Michelsen, C. (2022). Mathematics and Language and Literature. In: Michelsen, C., Beckmann, A., Freiman, V., Jankvist, U.T., Savard, A. (eds) Mathematics and Its Connections to the Arts and Sciences (MACAS). Mathematics Education in the Digital Era, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-031-10518-0_28

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Is Maths a Language?

“Is maths a language?”  There are thousands of languages across the world – English, Spanish, German, French… all taught across schools and reinforced as being important to succeed in later life with jobs. So why is this attitude not portrayed with maths?

Math is a language that has been used thousands of years. It is spoken universally, and can be understood by all no matter the age, religion or culture. Sure, different countries may have different symbols or words for aspects of it, but the profound fundamental understanding of maths is the same no matter where you go. Paying for your shopping in a supermarket uses the same knowledge of maths whether you’re paying in pounds, rupees, yen or euros.

Some anthropologists suggest that the global language of maths was needed in order to trade. Many different countries were trading, and were not able to communicate with each other as there was such a wide variety of languages, so a universal language that could be understood by all needed to be implemented. Roman numerals were the most dominant number system used in trade. It was created on the base 10 system but was not directly position and did not include a value for zero (Mastin, 2010). The base 10 system is a system used today in every country, and our understanding of place value is based on this. It is thought that this system was introduced at least as early at 2700 BCE by the Egyptians (Mastin, 2010). This system is used widely and is an understood language across the world, even though it appears to have begun in Egypt.

Europeans were still using Roman numerals in the 13 th Century, but found that they were difficult to work with when trying to divide or multiply. This is when Italian mathematician Fibonacci introduced Arabic numerals into Europe. These are the numerals that we know and use today to represent values of numbers. The difficulty of the Roman numerals led to merchants and bankers embracing the simpler Arabic system (Maths Careers, n.d.). This number system eventually spread across the globe, as the inclusion of zero meant that so much more could be done.

Here is a great video from Dr. Randy Palisoc, talking about maths as a language. This video also touches on maths anxiety, and how looking at maths as a language can help to eradicate the anxiety and fear around maths.

References:

Mastin, L. (2010). Egyptian Mathematics. [Online]. Available at: http://www.storyofmathematics.com/egyptian.html [Accessed 23rd October 2017]

  Mastin, L. (2010). Roman Mathematics. [Online]. Available at: http://www.storyofmathematics.com/roman.html [Accessed 23rd October 2017]

Maths Careers. (No Date). A Universal Language. [Online] Available at: http://www.mathscareers.org.uk/article/universal-language/ [Accessed 23rd October 2017]

TEDx Talks (2014) Math isn’t hard, it’s a language | Randy Palisoc | TEDxManhattanBeach [Online].  YouTube. Available at:  https://www.youtube.com/watch?v=V6yixyiJcos [Accessed 23rd October 2017]

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2 thoughts on “ is maths a language ”.

A really interesting post – I loved the video and haven’t seen it before. Perhaps you can make links in your next post to PUFM? I’m looking forward to seeing what you write about next. Cheers!

I truly appreciate this post. I have been looking everywhere for this! Thank goodness I found it on Bing. You’ve made my day! Thx again!

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Why Math is the "Language of the Universe:"