Among perhaps many things common to Kuratowski's Theorem in graph theory, Reidemeister's Theorem in topology, and Cook's Theorem in theoretical com- puter science is this: all belong to the phenomenon of simultaneous discovery in math- ematics. We are interested to know whether this phenomenon, and its close cousin repeated discovery, give rise to meaningful questions regarding causes, trends, cate- gories, etc. With this in view we unearth many more examples, find some tenuous connections and draw some tentative conclusions. The characterisation by forbidden minors of graph planarity; the Reidemiester moves in knot theory; and the NP-completeness of satisfiability, are all discoveries of twentieth cen- tury mathematics which occurred twice, more or less simultaneously, on different sides of the Atlantic. One may enumerate such coincidences to one's heart's content. Michael Deakin wrote about some more 9 in his admirable magazine Function; Frank Harary remi- nisces 23 about a dozen or so in graph theory, and there are whole books on individual in- stances, such as Hall 22 on Newton-Leibniz and Roquette 42 on the Main Theorem of modern algebra. Mathematics isquintessentially aselflessjoint endeavour, in which the pursuit of knowl- edge is its own reward. This is not a polite fiction; G.H. Hardy's somewhat sour remark 24 "if a mathematician ... were to tell me that the driving force in his work had been the desire to benefit humanity, then I should not believe him (nor should I think the better of him if I did)" nevertheless allows him to rank intellectual curiosity before ambition; and this ranking is engrained in a mathematician's upbringing. So simultaneity of mathe- matical discoveries tends to be tactfully overlooked: disputes about priority or naming or respective merits are in poor taste. The infamous affair of Erdý os and Selberg's simultane- ous elementary proofs of the Prime Number Theorem, for instance, although meticulously documented, 14 is generally considered best forgotten. The topologist Joan Birman repre- sented the profession eloquently 4 in relation to another fuss, 36 over who proved Poincar´ e's Conjecture: "Reading (Nasar's biography of John Nash), I was proud of our decency as a

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关于数学中的多重发现的一些评论

图论中的Kuratowski定理，拓扑学中的Reidemeister定理和理论计算机科学中的Cook定理中可能有许多共同点：它们都属于数学同时发现的现象。我们很想知道这种现象及其近亲的重复发现是否引起了有关原因，趋势，类别等的有意义的问题。基于此，我们挖掘了更多的例子，找到了一些微妙的联系并得出了一些初步的看法。结论。禁止未成年人图形平面度的表征；Reidemiester在打结理论中前进；和可满足性的NP完全性，都是二十世纪数学的发现，该数学在大西洋的不同侧发生了两次，或多或少同时发生。可以列举这样的巧合与一个人的内心满足。迈克尔·迪金（Michael Deakin）在他令人钦佩的杂志《功能》中写了大约9本书；弗兰克·哈拉里（Frank Harary）在图论中大约使用了十二种左右的方法，并且有关于个人实例的整本书，例如牛顿-莱伯尼兹（Newton-Leibniz）的22号馆和现代代数主定理的罗克特（Roquette）42号。数学是典型的无私的共同努力，其中对知识的追求是其自身的报酬。这不是有礼貌的小说。GH Hardy的话有些酸味24：“如果一个数学家……要告诉我，他工作的原动力是渴望造福人类，那么我不应该相信他（如果我这样做，我也不应该认为他会更好。 ）”，尽管如此，他还是可以将雄心勃勃的好奇心排在雄心勃勃之前；这个排名是由数学家的成长所根深蒂固的。因此，在数学上发现的同时性往往被机智地忽略了：关于优先级或命名或各自优劣的争论不佳。例如，尽管有详尽的记载，但厄尔迪斯（Erdýos）和塞尔伯格（Selberg）的素数定理的同时基本证明的臭名昭著，通常被认为是最容易忘记的14。拓扑学家琼·伯曼（Joan Birman）口才出色地代表了该专业4，而另一个大惊小怪的人证明了庞加莱的猜想是36。例如，尽管有详尽的记载，但厄尔迪斯（Erdýos）和塞尔伯格（Selberg）的素数定理的同时基本证明的臭名昭著，通常被认为是最容易忘记的14。拓扑学家琼·伯曼（Joan Birman）雄辩地表示了该专业4的另一个大惊小怪，其中有36个证明了庞加莱的猜想：“读（纳萨尔（Nasar）约翰·纳什（John Nash）的传记），我为我们的体面而自豪 例如，尽管有详尽的记载，但厄尔迪斯（Erdýos）和塞尔伯格（Selberg）的素数定理的同时基本证明的臭名昭著，通常被认为是最容易忘记的14。拓扑学家琼·伯曼（Joan Birman）雄辩地表示了该专业4的另一个大惊小怪，其中有36个证明了庞加莱的猜想：“读（纳萨尔（Nasar）约翰·纳什（John Nash）的传记），我为我们的体面而自豪