Is math discovered or invented? - Jeff Dekofsky

翻译人员: Yuanqing Edberg 校对人员: Cissy Yun

Would mathematics exist if people didn't?

如果没有人的存在还会有数学吗？

Since ancient times, mankind has hotly debated

在古时侯，人类就为此热烈地争辩

whether mathematics was discovered or invented.

数学到底是被发明的或是被发现的

Did we create mathematical concepts to help us understand the universe around us,

人们创造数学概念是为了 更好得了解周围的世界呢

or is math the native language of the universe itself,

还是数学本就是宇宙的语言，

existing whether we find its truths or not?

一直存在于这世界上 不管人类的介入或不

Are numbers, polygons and equations truly real,

数字，多边形和对等是真的吗？

or merely ethereal representations of some theoretical ideal?

或只是些空洞的理论概念？

The independent reality of math has some ancient advocates.

数学的独立存在有很多古代支持者

The Pythagoreans of 5th Century Greece believed numbers were both

五世纪希腊的毕达哥拉斯相信数字既是

living entities and universal principles.

存活的实体又是宇宙的规则。

They called the number one, "the monad," the generator of all other numbers

他们把数字1唤作 ”单子，“ 是所有其它数字的启动器

and source of all creation.

是所有东西的来源

Numbers were active agents in nature.

数字是大自然的活性剂

Plato argued mathematical concepts were concrete

柏拉图认为 数学概念是具体的

and as real as the universe itself, regardless of our knowledge of them.

数学概念就像宇宙自身一样真实， 不管我们是否意识到它们的存在

Euclid, the father of geometry, believed nature itself

欧几里德，几何之父， 相信自然本身

was the physical manifestation of mathematical laws.

就是数学定律的物理表现。

Others argue that while numbers may or may not exist physically,

而有些人却说因为数字并非一定有实体，

mathematical statements definitely don't.

所以数学的命题绝对不会有

Their truth values are based on rules that humans created.

它们的真实价值是 基于人类所创立的规则

Mathematics is thus an invented logic exercise,

数学是一种 被发明的逻辑练习，

with no existence outside mankind's conscious thought,

在人类的理性的思想之外， 并不会存在

a language of abstract relationships based on patterns discerned by brains,

它是一种能被大脑识别的 基于某种格式的抽象语言，

built to use those patterns to invent useful but artificial order from chaos.

利用这些模式 在混乱中来发明有用的人为秩序

One proponent of this sort of idea was Leopold Kronecker,

这种理论的支持者 是Leopold Kronecker

a professor of mathematics in 19th century Germany.

一位十九世纪德国的数学教授

His belief is summed up in his famous statement:

他的信条可在他著名的宣言 中总结如下：

"God created the natural numbers, all else is the work of man."

“上帝创造了自然数， 除此而外都是人类的工作。“

During mathematician David Hilbert's lifetime,

在数学家David Hilbert的一生中，

there was a push to establish mathematics as a logical construct.

对将数学看做一种逻辑的建树 有很大的推动

Hilbert attempted to axiomatize all of mathematics,

Hibert曾尝试将所有的数学公理化

as Euclid had done with geometry.

就像欧几里德在几何上所做的

He and others who attempted this saw mathematics as a deeply philosophical game

他和其他尝试这件事的数学家把数学 看成是一场深奥的哲学游戏

but a game nonetheless.

但依旧只是一个游戏。

Henri Poincaré, one of the father's of non-Euclidean geometry,

Henri Poincaré,，是 非欧几里德几何之父，

believed that the existence of non-Euclidean geometry,

他相信非欧几里德几何的存在

dealing with the non-flat surfaces of hyperbolic and elliptical curvatures,

用于处理非平面的 双曲线和椭圆曲率

proved that Euclidean geometry, the long standing geometry of flat surfaces,

从而证明欧几里德了的平面几何 这一长时间被认同的理论

was not a universal truth,

并不是全部的宇宙真相，

but rather one outcome of using one particular set of game rules.

只是遵从了游戏规则的一种的结果

But in 1960, Nobel Physics laureate Eugene Wigner

但在1960年，诺贝尔物理学奖得主 Eugene Wigner

coined the phrase, "the unreasonable effectiveness of mathematics,"

创造了名言，“无理的 数学效率，”

pushing strongly for the idea that mathematics is real

强烈得灌输了数学得真实存在

and discovered by people.

并且是由人们发现的

Wigner pointed out that many purely mathematical theories

Wigner指出很多纯粹的数学理论

developed in a vacuum, often with no view towards describing any physical phenomena,

是在真空里发展出来的，常常 无视任何物理现象，

have proven decades or even centuries later,

这些理论在几十年或几个世纪 后被证明

to be the framework necessary to explain

它们仅仅是空空的骨架， 需要进一步地阐述

how the universe has been working all along.

整个宇宙是如何 一直维持运行的。

For instance, the number theory of British mathematician Gottfried Hardy,

比如，英国数学家 Gottfried Hardy的数字理论，

who had boasted that none of his work would ever be found useful

他曾自嘲说， 他的作品

in describing any phenomena in the real world,

在描述实用现象上的价值 没有一件是有用的

helped establish cryptography.

但是他帮助建立密码学

Another piece of his purely theoretical work

这是他的另一个纯理论成果

became known as the Hardy-Weinberg law in genetics,

也变成了著名的遗传学上的 Hardy-Weinberg定律

and won a Nobel prize.

并且赢得了诺贝尔奖。

And Fibonacci stumbled upon his famous sequence

费伯纳齐突破至他最有名的序列是

while looking at the growth of an idealized rabbit population.

在观察假设的兔群增长时

Mankind later found the sequence everywhere in nature,

而人类后来发现自然中到处都存在序列，

from sunflower seeds and flower petal arrangements,

从葵花籽到葵花花瓣的排列

to the structure of a pineapple,

以及菠萝的结构，

even the branching of bronchi in the lungs.

甚至肺中的支气管分支。

Or there's the non-Euclidean work of Bernhard Riemann in the 1850s,

另外在1850年，伯奈德瑞曼的非欧几里德 成果

which Einstein used in the model for general relativity a century later.

在一个世纪后， 爱因斯坦用此为模版创立了广义相对论。

Here's an even bigger jump:

这儿甚至有着更大的飞跃：

mathematical knot theory, first developed around 1771

数学结的理论，开创的时候是1771年

to describe the geometry of position,

用以描述几何形状的方位，

was used in the late 20th century to explain how DNA unravels itself

这在二十世纪的后期用来解释DNA，

during the replication process.

在复制的过程中，如何解开它的螺旋结构

It may even provide key explanations for string theory.

这甚至为弦理论提供了关键的解释

Some of the most influential mathematicians and scientists

人类史上一些最有影响力的 数学和科学家们

of all of human history have chimed in on the issue as well,

都以令人吃惊的方式

often in surprising ways.

倾向于这个说法。

So, is mathematics an invention or a discovery?

所以，数学是一种发明 还是一种发现？

Artificial construct or universal truth?

是人工的构建或是宇宙的真相？

Human product or natural, possibly divine, creation?

是人类的产物或是自然或 神圣的创造？

These questions are so deep the debate often becomes spiritual in nature.

这些问题让争辩更为深入， 而成为自然的精髓。

The answer might depend on the specific concept being looked at,

问题的答案也许在于审视数学时的一个具体概念，

but it can all feel like a distorted zen koan.

但它让所有人都感到像 扭曲的禅宗公案。

If there's a number of trees in a forest, but no one's there to count them,

如果在森林中有很多树， 但没有人去数它们，

does that number exist?

那么数字会存在吗？