The greatest mathematician that never lived - Pratik Aghor

翻译人员: Zining Chen 校对人员: Yolanda Zhang

When Nicolas Bourbaki applied to the American Mathematical Society

当尼古拉斯·布尔巴基（Nicolas Bourbaki） 在 1950 年代向美国数学学会

in the 1950s,

递交申请时，

he was already one of the most influential mathematicians of his time.

他已经是当时 最具影响力的数学家之一。

He’d published articles in international journals

他在国际期刊上发表了许多研究，

and his textbooks were required reading.

所攥写的教科书 也成为了教学必读物。

Yet his application was firmly rejected for one simple reason—

然而他的申请却遭到了果断的拒绝， 而原因只有一个——

Nicolas Bourbaki did not exist.

尼古拉斯·布尔巴基本人并不存在。

Two decades earlier, mathematics was in disarray.

二十年前的数学教学混乱不堪。

Many established mathematicians had lost their lives in the first World War,

许多颇有成就的数学家们 在一战时失去了性命，

and the field had become fragmented.

使得该领域变得支离破碎。

Different branches used disparate methodology to pursue their own goals.

不同分支使用不同的方法论 来追求自己的目标。

And the lack of a shared mathematical language

缺乏共同的数学语言 导致数学家们

made it difficult to share or expand their work.

很难分享自己的成就， 并拓展自己的研究。

In 1934, a group of French mathematicians were particularly fed up.

在 1934 年，一群法国的 数学家们受够了这种现状。

While studying at the prestigious École normale supérieure,

在享有声望的 巴黎高等师范学校就学期间，

they found the textbook for their calculus class so disjointed

他们发现自己所用的微积分 教科书上的内容竟然如此脱节，

因此他们决定撰写一部更好的教材。

that they decided to write a better one.

The small group quickly took on new members,

他们的小组很快有了新成员的加入，

and as the project grew, so did their ambition.

随着项目的扩大， 他们的野心也越来越大。

The result was the "Éléments de mathématique,"

他们的最终成果便是《数学要素》 （"Éléments de mathématique"），

a treatise that sought to create a consistent logical framework

一个创造了统一逻辑框架的论文合集，

unifying every branch of mathematics.

合并了每一个数学的分支。

The text began with a set of simple axioms—

该书的内容以一组简单的公理开篇——

用来支持其论点的定理和假设。

laws and assumptions it would use to build its argument.

From there, its authors derived more and more complex theorems

自此以后，该书的作者们 得出了越来越多复杂的定理，

that corresponded with work being done across the field.

与各个跨领域的结论相对应。

But to truly reveal common ground,

但为了能够真正揭示理论的共同点，

the group needed to identify consistent rules

这群人还需要制定一套

that applied to a wide range of problems.

适用于各种各样问题的统一规则。

To accomplish this, they gave new, clear definitions

为此，他们为一些 重要的数学概念

to some of the most important mathematical objects,

赋予了新颖、清晰的定义，

including the function.

包括函数。

It’s reasonable to think of functions as machines

一个普遍的解释是将函数比作机器，

that accept inputs and produce an output.

它接受输入并产生输出。

But if we think of functions as bridges between two groups,

但如果我们将函数 想像成连接两组数字的桥梁，

we can start to make claims about the logical relationships between them.

我们就可以定义 它们之间的逻辑关系。

比如，将一组设为数字， 一组设为字母，

For example, consider a group of numbers and a group of letters.

We could define a function where every numerical input corresponds

我们就可以将函数定义为：

每一个数字的输入 都有相同字母的输出。

to the same alphabetical output,

but this doesn’t establish a particularly interesting relationship.

但这并不能建立一个有趣的关系。

Alternatively, we could define a function where every numerical input

或者，我们可以定义一个函数为：

每一个数字的输入 都有不同字母的输出。

corresponds to a different alphabetical output.

This second function sets up a logical relationship

第二个函数确立了一个逻辑关系：

where performing a process on the input has corresponding effects

对输入执行一系列操作 会对其映射的输出

产生相应的影响。

on its mapped output.

The group began to define functions by how they mapped elements across domains.

小组成员开始根据 函数如何映射输出来对其进行定义。

If a function’s output came from a unique input,

如果一个函数的输出 来源于一个独有的输入，

they defined it as injective.

他们便将其定义为内射函数。

If every output can be mapped onto at least one input,

如果每个输出都可以 被映射到至少一个输入上，

the function was surjective.

那该函数就被称为满射函数。

And in bijective functions, each element had perfect one to one correspondence.

在双射函数中，每个元素 都有一一对应的输入或输出。

This allowed mathematicians to establish logic that could be translated

这就让数学家们得以构建

能够在函数域中来回转换的逻辑。

across the function’s domains in both directions.

Their systematic approach to abstract principles

他们对于抽象原理的系统性解释

was in stark contrast to the popular belief that math was an intuitive science,

与数学是一门直觉科学的普遍看法 形成了鲜明的对比，

and an over-dependence on logic constrained creativity.

而且后者认为，对逻辑的 过度依赖限制了创造力。

But this rebellious band of scholars gleefully ignored conventional wisdom.

但这组叛逆的学者 毅然拒绝了传统。

They were revolutionizing the field, and they wanted to mark the occasion

他们在为这个领域带来革命，

并想用一个噱头来纪念它。

with their biggest stunt yet.

They decided to publish "Éléments de mathématique"

他们决定将《数学要素》 （Éléments de mathématique）

和其余所有的研究成果 用一个集体的化名发表：

and all their subsequent work under a collective pseudonym:

Nicolas Bourbaki.

尼古拉斯·布尔巴基。

Over the next two decades, Bourbaki’s publications became standard references.

在接下来的二十年中，在布尔巴基名下 发表的研究变成了标准参考资料。

And the group’s members took their prank as seriously as their work.

这组数学家也像对待自己的研究一样， 一直非常认真地对待这场恶作剧。

他们凭空创造的这个数学家 声称自己是一位隐居的俄罗斯天才，

Their invented mathematician claimed to be a reclusive Russian genius

who would only meet with his selected collaborators.

只与他指定的合作人见面。

They sent telegrams in Bourbaki’s name, announced his daughter’s wedding,

他们还以布尔巴基的名义发送电报， 宣布了他女儿的婚礼，

and publicly insulted anyone who doubted his existence.

并公开羞辱了所有质疑他存在的人。

In 1968, when they could no longer maintain the ruse,

但到了 1968 年，他们无法 再继续维持这场骗局，

the group ended their joke the only way they could.

于是以唯一可行的方式 结束了这场恶作剧。

他们公布了布尔巴基的讣告， 里面包含了许多数学双关语。

They printed Bourbaki’s obituary, complete with mathematical puns.

Despite his apparent death, the group bearing Bourbaki’s name lives on today.

尽管他已经“去世”，但这个以他的名字 命名的组织至今依然存在。

Though he’s not associated with any single major discovery,

虽然他的成就并不包含 任何重大的发现，

Bourbaki’s influence informs much current research.

但布尔巴基的影响 体现在了很多现代的研究中。

And the modern emphasis on formal proofs owes a great deal to his rigorous methods.

现代对形式证明的重视 很大程度上要归功于他严谨的方法。

Nicolas Bourbaki may have been imaginary— but his legacy is very real.

尼古拉斯·布尔巴基可能是虚构的 ——但他对世人的遗赠是真实存在的。