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  • When Nicolas Bourbaki applied to the American Mathematical Society

    譯者: Lilian Chiu 審譯者: Pui-Ching Siu

  • in the 1950s,

    當尼古拉·布爾巴基 在 1950 年代

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

    申請加入美國數學學會時,

  • He'd published articles in international journals

    他已經是當時最有 影響力的數學家之一了。

  • and his textbooks were required reading.

    他在國際期刊中發表文章,

  • Yet his application was firmly rejected for one simple reason

    他的教科書也被列為必讀。

  • Nicolas Bourbaki did not exist.

    但他的申請卻被堅決駁回, 理由很簡單——

  • Two decades earlier, mathematics was in disarray.

    尼古拉·布爾巴基並不存在。

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

    二十年前,數學界一片混亂。

  • and the field had become fragmented.

    許多知名的數學家 死於第一次世界大戰,

  • Different branches used disparate methodology to pursue their own goals.

    讓這個領域變得支離破碎。

  • And the lack of a shared mathematical language

    不同的分支用迥然不同的方法論 來追求他們自己的目標。

  • made it difficult to share or expand their work.

    因為缺乏共同的數學語言,

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

    他們很難分享或擴展研究。

  • While studying at the prestigious École normale supérieure,

    1934 年,一群法國數學家 特別感到忍無可忍了。

  • they found the textbook for their calculus class so disjointed

    在有聲望的巴黎 高等師範學院讀書時,

  • that they decided to write a better one.

    他們發現微積分課的 教科書實在太沒條理了,

  • The small group quickly took on new members,

    因此他們決定寫一本更好的。

  • and as the project grew, so did their ambition.

    這個小組很快就招收了新成員,

  • The result was the "Éléments de mathématique,"

    隨著計劃越做越大, 他們的野心也越來越大。

  • a treatise that sought to create a consistent logical framework

    成果就是《數學原本》,

  • unifying every branch of mathematics.

    這本專著旨在創造一致的邏輯框架,

  • The text began with a set of simple axioms

    統一數學的所有分支。

  • laws and assumptions it would use to build its argument.

    正文的一開始就是 一組簡單的公理——

  • From there, its authors derived more and more complex theorems

    該書用來建構論點的定律和假設。

  • that corresponded with work being done across the field.

    該書的作者依此導出了 更多複雜的定理,

  • But to truly reveal common ground,

    並對應到數學領域中的各種研究。

  • the group needed to identify consistent rules

    但,若要真正揭示出共同點,

  • that applied to a wide range of problems.

    這個小組就要找出一致的規則

  • To accomplish this, they gave new, clear definitions

    套用在各種問題上。

  • to some of the most important mathematical objects,

    為了完成這個目標,他們 針對一些最重要的數學物件

  • including the function.

    做出新的、清楚的定義,

  • It's reasonable to think of functions as machines

    包括「函數」。

  • that accept inputs and produce an output.

    把函數看成機器是很合理的,

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

    它能接受輸入,產生輸出。

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

    但如果我們把函數視為 兩個群組之間的橋樑,

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

    我們就可以開始主張 它們之間有某種邏輯關係。

  • We could define a function where every numerical input corresponds

    比如,有一個數字群組 和一個字母群組。

  • to the same alphabetical output,

    我們可以定義出一個函數, 讓每個輸入的數字

  • but this doesn't establish a particularly interesting relationship.

    都對應到同樣的輸出字母,

  • Alternatively, we could define a function where every numerical input

    但這樣做並不會建立出 特別有趣的關係。

  • corresponds to a different alphabetical output.

    另一個選擇是定義一個函數,

  • This second function sets up a logical relationship

    讓每個輸入數字都對應到 不同的輸出字母。

  • where performing a process on the input has corresponding effects

    這第二個函數就設立了 一種邏輯關係,

  • on its mapped output.

    針對輸入值進行一個流程,

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

    就會讓對應的輸出值 產生相應的效應。

  • If a function's output came from a unique input,

    這個小組開始這樣定義函數:

  • they defined it as injective.

    它如何對應不同定義域的元素。

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

    如果函數的輸出值 來自唯一的輸入值,

  • the function was surjective.

    他們就把它定義為單射函數。

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

    如果每個輸出值都可以 對應到至少一個輸入值,

  • This allowed mathematicians to establish logic that could be translated

    這個函數就是蓋射函數。

  • across the function's domains in both directions.

    在對射函數中,

  • Their systematic approach to abstract principles

    每個元素都剛好有一對一的對應值。

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

    這麼一來,數學家所建立的邏輯

  • and an over-dependence on logic constrained creativity.

    就能在該函教的定義域中 做雙向的轉換。

  • But this rebellious band of scholars gleefully ignored conventional wisdom.

    他們針對抽象原則所做的系統化方法

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

    與一般的想法成鮮明對比: 一般的想法認為數學是直覺式科學,

  • with their biggest stunt yet.

    且過度仰賴由邏輯限制的創意。

  • They decided to publish "Éléments de mathématique"

    但這群叛逆的學者很愉快地 無視了傳統的智慧。

  • and all their subsequent work under a collective pseudonym:

    他們想要改革這個領域,

  • Nicolas Bourbaki.

    並用他們最大的噱頭 來紀念這個時刻。

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

    他們決定要出版《數學原本》

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

    以及他們後續用共同的筆名

  • Their invented mathematician claimed to be a reclusive Russian genius

    「尼古拉·布爾巴基」所做的研究。

  • who would only meet with his selected collaborators.

    在接下來二十年,布爾巴基的 出版品成了標準的參考資料。

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

    而小組的成員對這個 惡作劇的認真程度不亞於研究。

  • and publicly insulted anyone who doubted his existence.

    他們宣稱這位捏造的數學家 是位隱居的俄國天才,

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

    只會和他選中的合作夥伴見面。

  • the group ended their joke the only way they could.

    他們以布爾巴基的名義發電報, 宣佈他女兒的婚禮,

  • They printed Bourbaki's obituary, complete with mathematical puns.

    且任何懷疑他是否存在的人 都會被公開辱罵。

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

    1968 年,他們的計謀 無法再繼續下去了,

  • Though he's not associated with any single major discovery,

    他們以唯一能用的 方式來結束這個玩笑。

  • Bourbaki's influence informs much current research.

    他們印出布爾巴基的訃告, 文中盡是數學雙關語。

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

    儘管布爾巴基表面上已故,

  • Nicolas Bourbaki may have been imaginarybut his legacy is very real.

    使用這個名字的數學家 至今仍然活著。

When Nicolas Bourbaki applied to the American Mathematical Society

譯者: Lilian Chiu 審譯者: Pui-Ching Siu

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