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An interesting piece to read which tells the story of a dream leading, not to a single result, but a fundamental shift in a mathematician's work (leading to the proof, with collaborators, of Local Lan …

Uncle Petros proved Goldbach's conjecture just minutes before his death, when he was more than sixty.

All questions of the form 'Why was such a mathematician interested in such a subject?' are difficult, and have a tendency to become metaphysical ('why are we doing mathematics in general?", and then " …

The question is interesting, but presupposes that we understand and accept Amir's conclusion, namely that "we owe Definition by abstraction (taking equivalence classes as new objects) to the the abstr …

Hopefully at some point, GRH will be proved, and then the Siegel zeros of Zeta functions will disappear. There are currently thousands of papers on them.

I think you are misinterpreting the quote. In the last sentence, the word "source" does not mean "source of these theories (K-theory, categories, group representations", but "source of the theory of s …

After having read Katz' article, I must say I am not convinced and find that the standard interpretation, namely that of Cauchy making a mistake in 1821 and failing to acknowledging it or correcting i …

I recommend the reading of a wonderful 15-page text of Imre Lakatos, "Another case study of the method of proofs and refutations", which discuss precisely what Cauchy knew and didn't know and did and …

I propose Edward Nelson's "conjecture" that Peano's arithmetic is inconsistent. First, to be honest, I am not aware that he stated it as "conjecture", using that word, but this is something he said …

(Edited to correct mistakes signaled in comments below). I don't know much about the first steps on the theory, Krein and Tannaka. I can just say their works answer a question that seems very natural …

The point (5) is at most doubtful. It was made by Mahoney in his book on Fermat, but Mahoney's interpretation of what Digby writes to Wallis does not correspond to what Digby actually writes, as quote …

The way the question is written seems a little weird to me. At first, a phenomenon is described and presented as a fact: many very important papers are published in journals much less well-ranked than …

This is not an answer but a longish comment, which moreover is certainly "subjective and argumentative". Reading all the stories given in the 12 answers, I find I can classify them in three categories …

Grassmann made his most important contribution in Linguistics. Poincaré, besides his enormous work in mathematic, also add very important contribution to physics, and his work in philosophy of scienc …

To complete Carlo's answer, I think that one thing that can explain the long gap (in addition of the amount of difficult material in Weil II) is that Deligne felt the need to consolidate his result of …