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I draw on this question to ask something that has always been a pet peeve of mine. It is very easy to find books about the history of mathematics, much less so if one wants books about the recent (say > 1850) one.

Of course I know that this is difficult because not so many people would understand what's going on; to learn about the history of a subject, one should better know the subject beforehand. On the other hand, my feeling is that more or less all mathematics I know has been developed after 1850, and the growth, like in many other sciences, has been exponential. So the amount of mathematics which appears in history book seems negligible to me.

Can you point me to any good resources about the recent history of maths?

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Community wiki, please! –  Victor Protsak May 6 '10 at 4:14
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The Notices of the AMS (ams.org/notices/201005) often have historical articles; you could look at those or at their sources. –  Qiaochu Yuan May 6 '10 at 4:31
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To write the history of a subject, one should better know how to do good history beforehand. Precious few people master both the technical historical knowledge and the technical mathematical knowledge required to write good recent mathematical history. For this reason, many (but not all) books mentioned in answers might be excellent books, but I wouldn't characterize them as historical, in the sense that they wouldn't (and by far) pass the standard requirement for a scholarly publication in the field of history. –  Olivier May 6 '10 at 7:49
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Or to put it in the form of the famous joke: a famous retiring algebraic topologist ends her retiring speech saying "Now that I am 65 and retiring, I want to spend my free time doing history". "And a good thing too", a historian in the room says "because now that I am 65 and retiring, I want to spend my free time doing algebraic topology". –  Olivier May 6 '10 at 7:52
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Olivier, when did we start allowing historians in the common room? –  Harry Gindi May 6 '10 at 8:24
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34 Answers 34

Multiple answers have mentioned books by Dieudonne. I can recommend one more: Mathematics- The Musics of Reason (Springer, 1992) or the French original Pour l'honneur de l'esprit humain: les mathématiques aujourd'huis (Hachette, 1987). Its stated purpose is to give a generally accessible account of major mathematical developments after 1800, of which it does a remarkably good job.

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I would recommend "The Mathematician Sophus Lie: It was the Audacity of My Thinking" by Arild Stubhaug and R. Daly (original in Norwegian, there is also a German translation).

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The ICM website records all the addresses given at the Fields Medal conferences, and they always begin with a short paper by a distinguished mathematician describing to a "broad" audience why that medallist has deserved the award. This is often very interesting, containing recent historical remarks.

You can read Katz' description of Deligne's work in 1978, for instance: I find it delightful. Funny enough, the very same conference saw a contribution by André Weil http://www.mathunion.org/ICM/ICM1978.1/Main/icm1978.1.0227.0236.ocr.pdf entitled "History of Mathematics: Why an How" which addresses many of your questions – and answers them, I think. For example, he discusses "why" is a mathematician interested in the history of "which" mathematics, and "how" this should be pursued. And the very last paragraph begins: "What, then, separates the historian from the mathematician when both are studying the work of the past?" Besides all, extremely enjoyable!

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Michèle Audin's book on the history of complex iteration has already been mentioned. But "Remembering Sofya Kovalevskaya" should be mentioned also.

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