By Anne Marie Helmenstine, Ph.D.
Updated on June 27, 2019 更新于 2019 年 6 月 27 日
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:
数学被称为科学的语言。意大利天文学家和物理学家伽利略·伽利莱 (Galileo Galilei) 被引述为“数学是上帝书写宇宙的语言”。这句话很可能是他在 Opere Il Saggiatore 中的陈述的总结：
[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.
[宇宙]在我们学会了语言并熟悉了它所写的字符之前是无法阅读的。它是用数学语言写成的，字母是三角形、圆形和其他几何图形，没有它意味着人类无法理解一个单词。
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.
然而，数学真的像英语或汉语一样是一门语言吗？要回答这个问题，了解什么是语言以及如何使用数学词汇和语法来构造句子会有所帮助。
Key Takeaways: Why Math is a Language
要点：为什么数学是一门语言
In order to be considered a language, a system of communication must have vocabulary, grammar, syntax, and people who use and understand it.为了被认为是一种语言，一个交流系统必须有词汇、语法、句法，以及使用和理解它的人。
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.数学符合语言的这个定义。不认为数学是一种语言的语言学家引用它作为一种书面而不是口头交流形式的用途。
Math is a universal language. The symbols and organization to form equations are the same in every country of the world.数学是一种通用语言。构成方程式的符号和组织在世界上每个国家都是相同的。
What Is a Language? 什么是语言？
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.
“语言”有多种定义。语言可以是一门学科中使用的单词或代码系统。语言可以指使用符号或声音进行交流的系统。语言学家诺姆乔姆斯基将语言定义为一组使用有限元素集构造的句子。一些语言学家认为语言应该能够代表事件和抽象概念。
Whichever definition is used, a language contains the following components:
无论使用哪种定义，语言都包含以下组件：
There must be a vocabulary of words or symbols.必须有一个单词或符号的词汇表。
Meaning must be attached to the words or symbols.必须将含义附加到单词或符号上。
A language employs grammar, which is a set of rules that outline how vocabulary is used.语言使用语法，语法是概述词汇使用方式的一组规则。
A syntax organizes symbols into linear structures or propositions.句法将符号组织成线性结构或命题。
A narrative or discourse consists of strings of syntactic propositions.叙述或话语由句法命题串组成。
There must be (or have been) a group of people who use and understand the symbols.一定有（或曾经）有一群人在使用和理解这些符号。
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.
数学满足所有这些要求。这些符号、它们的含义、句法和文法在全世界都是相同的。数学家、科学家和其他人使用数学来交流概念。数学描述自身（一个称为元数学的领域）、现实世界的现象和抽象概念。
Vocabulary, Grammar, and Syntax in Mathematics
数学中的词汇、语法和句法
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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:
数学词汇来自许多不同的字母表，包括数学特有的符号。一个数学方程式可以用单词来表达，形成一个有名词和动词的句子，就像口语中的句子一样。例如：
3 + 5 = 8
could be stated as "Three added to five equals eight."
可以表述为“三加五等于八”。
Breaking this down, nouns in math include:
分解一下，数学中的名词包括：
Arabic numerals (0, 5, 123.7) 阿拉伯数字（0、5、123.7）
Fractions (1⁄4, 5⁄9, 2 1⁄3) 分数（1⁄4、5⁄9、2 1⁄3）
Variables (a, b, c, x, y, z)变量（a、b、c、x、y、z）
Expressions (3x, x2, 4 + x)表达式 (3x, x 2 , 4 + x)
Diagrams or visual elements (circle, angle, triangle, tensor, matrix)图表或视觉元素（圆形、角度、三角形、张量、矩阵）
Infinity (∞) 无穷大 (∞)
Pi (π) 圆周率 (π)
Imaginary numbers (i, -i) 虚数 (i, -i)
The speed of light (c)
Verbs include symbols including: 动词包括以下符号：
Equalities or inequalities (=, <, >)等式或不等式（=、<、>）
Actions such as addition, subtraction, multiplication, and division (+, -, x or *, ÷ or /)加法、减法、乘法和除法（+、-、x 或 *、÷ 或 /）等操作
Other operations (sin, cos, tan, sec)其他运算（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.
如果您尝试对数学句子进行句子图解，您会发现不定式、连词、形容词等。与其他语言一样，符号所扮演的角色取决于其上下文。
International Rules 国际规则
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.
数学语法和句法，就像词汇一样，是国际化的。无论您来自哪个国家或说什么语言，数学语言的结构都是相同的。
Formulas are read from left to right.公式从左到右阅读。
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.拉丁字母用于参数和变量。在某种程度上，希腊字母表也被使用。整数通常取自 i、j、k、l、m、n。实数由 a、b、c、α、β、γ 表示。复数由 w 和 z 表示。未知数是 x、y、z。函数的名称通常是 f、g、h。
The Greek alphabet is used to represent specific concepts. For example, λ is used to indicate wavelength and ρ means density.希腊字母用于表示特定的概念。例如，λ 用于表示波长，而 ρ 表示密度。
Parentheses and brackets indicate the order in which the symbols interact.圆括号和方括号表示符号交互的顺序。
The way functions, integrals, and derivatives are phrased is uniform.函数、积分和导数的表达方式是统一的。
Language as a Teaching Tool
语言作为教学工具
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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.
在教或学数学时，了解数学句子的工作原理很有帮助。学生们常常觉得数字和符号令人生畏，因此将方程式用熟悉的语言表达会使这门学科更容易上手。基本上，这就像将外语翻译成已知语言。
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.
虽然学生通常不喜欢单词问题，但从口头/书面语言中提取名词、动词和修饰语并将它们翻译成数学方程式是一项宝贵的技能。单词问题可以提高理解力并提高解决问题的能力。
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.
因为数学在全世界都是一样的，所以数学可以作为一种通用语言。短语或公式具有相同的含义，而不管伴随它的是另一种语言。通过这种方式，即使存在其他交流障碍，数学也可以帮助人们学习和交流。
The Argument Against Math as a Language
反对数学作为一种语言的争论
Anne Helmenstine 安妮赫尔门斯汀
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.
并不是每个人都同意数学是一种语言。 “语言”的一些定义将其描述为一种口头交流形式。数学是一种书面交流形式。虽然大声朗读一个简单的加法语句（例如 1 + 1 = 2）可能很容易，但大声朗读其他方程式（例如麦克斯韦方程组）就难多了。此外，口头陈述将以说话者的母语而不是通用语言呈现。
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.
但是，根据此标准，手语也将被取消资格。大多数语言学家认为手语是一种真正的语言。有一些死去的语言，没有人知道如何发音甚至阅读。
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."
数学作为一门语言的一个强有力的例子是，现代中小学课程使用语言教育中的技术来教授数学。教育心理学家保罗·里科米尼 (Paul Riccomini) 及其同事写道，学习数学的学生需要“强大的词汇知识基础；灵活性；对数字、符号、单词和图表的流利和熟练；以及理解能力。”
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