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Why Mathematics Is a Language
by
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 is used to construct sentences.
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 defines 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 syntatic 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 metamathematics), 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 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, x2, 4 + x)
· Diagrams or visual elements (circle, angle, triangle,
tensor, matrix)
· Infinity (∞)
· Pi (π)
· 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.
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 other 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.
Key Points
· 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.
Anne Marie Helmenstine, Ph.D.
· Ph.D. in biomedical sciences from the University of Tennessee at Knoxville - Oak Ridge National Laboratory.
· Science educator with experience teaching chemistry, biology, astronomy, and physics at the high school, college, and graduate levels.
· ThoughtCo and About Education chemistry expert since 2001.
· Widely-published graphic artist, responsible for printable periodic tables and other illustrations used in science.
Experience
Anne Helmenstine, Ph.D. has covered chemistry for ThoughtCo and About Education since 2001, and other sciences since 2013. She taught chemistry, biology, astronomy, and physics at the high school, college, and graduate levels. She has worked as a research scientist and also abstracting and indexing diverse scientific literature for the Department of Energy.
In addition to her work as a science writer, Dr. Helmenstine currently serves as a scientific consultant, specializing in problems requiring an interdisciplinary approach. Previously, she worked as a research scientist and college professor.
Education
Dr. Helmenstine holds a Ph.D. in biomedical sciences from the University of Tennessee at Knoxville and a B.A. in physics and mathematics with a minor in chemistry from Hastings College. In her doctoral work, Dr. Helmenstine developed ultra-sensitive chemical detection and medical diagnostic tests.
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