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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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    $\begingroup$ Community wiki, please! $\endgroup$ – Victor Protsak May 6 '10 at 4:14
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    $\begingroup$ The Notices of the AMS (ams.org/notices/201005) often have historical articles; you could look at those or at their sources. $\endgroup$ – Qiaochu Yuan May 6 '10 at 4:31
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    $\begingroup$ 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. $\endgroup$ – Olivier May 6 '10 at 7:49
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    $\begingroup$ 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". $\endgroup$ – Olivier May 6 '10 at 7:52
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    $\begingroup$ Olivier, when did we start allowing historians in the common room? $\endgroup$ – Harry Gindi May 6 '10 at 8:24

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I enjoyed the book "Remarkable Mathematicians: From Euler to von Neumann" by Ioan James. It gives a good account of what the mathematicians were doing (in their personal lives and professional) and how their interactions shaped mathematics. It is fairly light on the mathematical content but an enjoyable read nonetheless.

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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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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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Jeremy Gray, Plato's Ghost: the modernist transformation of mathematics, Princeton 2008 discusses the changes in mathematical thinking and views of mathematics between 1890 and about 1930.

Dennis E. Hesseling, Gnomes in the Fog: The Reception of Brouwer’s Intuitionism in the 1920s, Birkhauser 2012 (reprint of the 2003 edition). I haven't read this one, but it deserves a look on the basis of the title alone.

(Forthcoming in Nov 2017) Alberto Cogliati, Writing Small Omegas: Elie Cartan's Contributions to the Theory of Continuous Groups 1894-1926 (Studies in the History of Mathematical Inquiry) looks as though it could be very interesting.

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Jean-Pierre Marquis and Gonzalo E. Reyes The History of Categorical Logic 1963–1977

The above article discusses the history of the development of categorical logic starting from a brief historical sketch of the birth of Category Theory and its early developments.

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Another book which covers some recent history in its last chapters is The Queen of Mathematics: A Historically Motivated Guide to Number Theory. Also look at

A History of Abstract Algebra by Israel Kleiner

Episodes in the History of Modern Algebra (1800-1950)

You do not have to restrict yourself to books, there also articles that touch on the history of a particular area of mathematics.

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  • $\begingroup$ I wasn't all that impressed by "A history of abstract algebra". If biographies are removed, the remaining 100 pages or so are inferior to Bourbaki's "Elements of history of mathematics" $\endgroup$ – Victor Protsak May 6 '10 at 3:58
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For a well-written historical presentation of the mathematical physics underlying basic quantum mechanics

The Rise of the New Physics by A. D'Abro

A detailed, fascinating presentation on some aspects of the evolution of mathematical physics is the book

Masters of Theory: Cambridge and the Rise of Mathematical Physics by A. Warwick

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