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In the 16th century, the mathematician Robert Recorde wrote a book called "The Whetstone of Witte" to teach English students algebra.
十六世纪的时候，数学家罗伯特·雷考德写了一本叫做《砺智石》的书，以教授英国学生代数。
But he was getting tired of writing the words "is equal to" over and over. His solution?
但是他为一遍遍写“等于”两个字而感到疲惫。他的解决方法是什么呢？
He replaced those words with two parallel horizontal line segments because the way he saw it, no two things can be more equal.
他用两个平行的水平线段替代了“等于”这个词，因为在他的眼中，没有更相等的两个事物了。
Could he have used four line segments instead of two? Of course.
他可以用四条而非两条线段吗？当然。
Could he have used vertical line segments? In fact, some people did.
他可以用两条竖线吗？实际上，的确有人用了。
There's no reason why the equals sign had to look the way it does today.
等号并非一定要长成今天这样。
At some point, it just caught on, sort of like a meme.
某个时间起，它突然就火了起来，有点像流行用语。
More and more mathematicians began to use it, and eventually, it became a standard symbol for equality.
越来越多的数学家开始使用它，最终，它成为了“等于”的标准符号。
Math is full of symbols. Lines, dots, arrows, English letters, Greek letters, superscripts, subscripts.
数学里到处都是符号。线，点，箭头，英语字母，希腊字母，上标，下标。
It can look like an illegible jumble.
有时候看起来杂乱无章。
It's normal to find this wealth of symbols a little intimidating and to wonder where they all came from.
觉得这么大量的符号有点恐怖很正常，也自然想知道它们都从哪来。
Sometimes, as Recorde himself noted about his equals sign, there's an apt conformity between the symbol and what it represents.
有时候，就像雷考得注意到关于他的等号一样，这个符号和它所代表的东西之间有恰当的一致性。
Another example of that is the plus sign for addition, which originated from a condensing of the Latin word et meaning and.
另一个例子就是加法的加号，起源于拉丁et，这是“和”的缩写。
Sometimes, however, the choice of symbol is more arbitrary,
有些时候，符号的选择就随性一点，
such as when a mathematician named Christian Kramp introduced the exclamation mark for factorials
例如当数学家基斯顿·卡曼推行用感叹号来表示阶乘，
just because he needed a shorthand for expressions like this.
仅因为他需要一个这种表达式的简写。
In fact, all of these symbols were invented or adopted by mathematicians
实际上，所有这些符号都是由数学家发明或选用的，
who wanted to avoid repeating themselves or having to use a lot of words to write out mathematical ideas.
他们不想总是重复或写很多词来描述数学思想。
Many of the symbols used in mathematics are letters, usually from the Latin alphabet or Greek.
数学中使用的许多符号都是字母、拉丁字母或是希腊字母。
Characters are often found representing quantities that are unknown, and the relationships between variables.
符号一般用于表达未知数，以及变量之间的关系。
They also stand in for specific numbers that show up frequently but would be cumbersome or impossible to fully write out in decimal form.
它们也表示某些经常出现的、但是用十进制形式不可能或者很难写的特定数字。
Sets of numbers and whole equations can be represented with letters, too.
数集以及整个式子也可以用字母表示。
Other symbols are used to represent operations.
其他符号被用来表示运算。
Some of these are especially valuable as shorthand because they condense repeated operations into a single expression.
其中有一些作为缩写尤为重要，因为他们能把重复的运算浓缩到一个简单的表达式。
The repeated addition of the same number is abbreviated with a multiplication sign so it doesn't take up more space than it has to.
同一个数字的重复相加被缩写成乘法，所以不会占用不必要的位置。
A number multiplied by itself is indicated with an exponent that tells you how many times to repeat the operation.
数字自乘用指数来表示重复操作了多少次。
And a long string of sequential terms added together is collapsed into a capital sigma.
一连串的连续加法浓缩成大写的Σ（sigma）。
These symbols shorten lengthy calculations to smaller terms that are much easier to manipulate.
这些符号把冗长的计算过程简化成较小的、更容易处理的项。
Symbols can also provide succinct instructions about how to perform calculations.
符号也可以提供关于计算的简明指导。
Consider the following set of operations on a number.
想象接下来的一系列运算。
Take some number that you're thinking of, multiply it by two, subtract one from the result,
在脑海中选一个数字，乘以二，结果减一，
multiply the result of that by itself, divide the result of that by three, and then add one to get the final output.
结果和自己相乘，结果除以三，然后再加一以得到最终答案。
Without our symbols and conventions, we'd be faced with this block of text.
如果没有符号，我们就要面对这样的大块文字。
With them, we have a compact, elegant expression. Sometimes, as with equals, these symbols communicate meaning through form.
有了符号，我们就有了简洁、优雅的表达方式。有时候，就像等号一样，这些符号通过形式传达意义。
Many, however, are arbitrary. Understanding them is a matter of memorizing what they mean
然而，许多符号是很随意的。要了解它们，记住它们的意思就好了，
and applying them in different contexts until they stick, as with any language.
并在不同的场景下使用，直到把它们牢牢得记住，就像任何其他语言一样。
If we were to encounter an alien civilization, they'd probably have a totally different set of symbols.
如果我们遇到了外星文明，他们很有可能有完全不同的符号。
But if they think anything like us, they'd probably have symbols.
可是如果他们像我们一样得思考，他们很有可能也有许多符号。
And their symbols may even correspond directly to ours.
这些符号或许和我们的相呼应。
They'd have their own multiplication sign, symbol for pi, and, of course, equals.
他们也会有自己的乘号，代表圆周率的π，当然还有等于号。
