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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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    $\begingroup$ 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
    Commented May 6, 2010 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
    Commented May 6, 2010 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
    Commented May 6, 2010 at 7:52
  • $\begingroup$ @Victor: I'd do that, but I forgot when I asked the question. Now that people have votes on their answers, won't this be rude? $\endgroup$
    – Andrea Ferretti
    Commented May 6, 2010 at 8:04
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    $\begingroup$ Olivier, when did we start allowing historians in the common room? $\endgroup$
    – Harry Gindi
    Commented May 6, 2010 at 8:24

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Here are a few books on the history of recent mathematics that I recommend:

A History of Algebraic and Differential Topology, 1900 - 1960 by Jean Dieudonne.

History of Topology by I.M. James.

Reciprocity Laws: From Euler to Eisenstein by Franz Lemmermeyer.

The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae
by Catherine Goldstein, Norbert Schappacher, and Joachim Schwermer.

The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of its Creators by Alexander Soifer.

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    $\begingroup$ A huge +1 to Dieudonne's history of topology. I learned an enormous amount of both history and topology from reading it $\endgroup$
    – Andy Putman
    Commented May 6, 2010 at 0:36
  • $\begingroup$ there is a lot of good math in that Dieudonne book. $\endgroup$
    – Sean Tilson
    Commented Nov 20, 2010 at 3:37
  • $\begingroup$ James is probably too expensive for those of us who aren't trust fund babies or successful buisnessmen to have,but it definitely needs to be on your "must-borrow-several-times"list. Just SO much good stuff in it. $\endgroup$
    – The Mathemagician
    Commented Nov 20, 2010 at 4:50
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Jean Dieudonne's history of Algebraic Geometry is fantastic. It has been helping me put a lot of things in perspective.

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    $\begingroup$ Wouldn't a book on Projective Geometry be better for putting things in perspective? $\endgroup$
    – Gerry Myerson
    Commented Nov 20, 2010 at 11:16
  • $\begingroup$ It is partly about projective geometry. Indeed, it would be rather sad writing a book about the history of algebraic geometry without mentioning projective geometry! $\endgroup$
    – Lennart Meier
    Commented Feb 18, 2013 at 22:17
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    $\begingroup$ It's available from the MAA as a PDF: Dieudonne, The Historical Development of Algebraic Geometry $\endgroup$
    – Assad Ebrahim
    Commented May 8, 2016 at 0:01
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A very enjoyable read of modern topic is Weibel's A History of Homological Algebra (40 pages).

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    $\begingroup$ Blast, you beat me to this. I thought it was a nice read as well. His development of K-theory is also interesting: math.rutgers.edu/~weibel/papers-dir/khistory.pdf $\endgroup$
    – hypercube
    Commented May 22, 2010 at 18:43
  • $\begingroup$ The homological algebra article you mention was written for the James volume mentioned in John Stillwell's answer. $\endgroup$
    – Sean Tilson
    Commented Nov 20, 2010 at 3:38
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Other examples (just to give an idea of the choice), thematic sample, with scholarly work, popular science, and other types :

Recent theorems

Four Colours Suffice: How the Map Problem Was Solved de Robin J. Wilson

Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture de David M. Bressoud, William Watkins, Gerald L. Alexanderson, and Dipa Choudhury

Kepler's Conjecture: How Some of the Greatest Minds in History Helped Solve One of the Oldest Math Problems in the World de George G. Szpiro

20th century

The Honors Class: Hilbert's Problems and Their Solvers de Benjamin H. Yandell

Mathematical Analysis During the 20th Century de Jean-Paul Pier

Development of Mathematics 1900-1950 de Jean-Paul Pier

The Mathematical Century: The 30 Greatest Problems of the Last 100 Years de Piergiorgio Odifreddi

Biography

Ludwig Wittgenstein: The Duty of Genius de Ray Monk

Von Neumann, Morgenstern, and the Creation of Game Theory: From Chess to Social Science, 1900-1960 de Robert J. Leonard

The Random Walks of George Polya de Gerald L. Alexanderson

Logic's Lost Genius: The Life of Gerhard Gentzen de Eckart Menzler-Trott

Auto biography

Indiscrete Thoughts de Gian-Carlo Rota et Fabrizio Palombi

Discrete Thoughts: Essays on Mathematics, Science, and Philosophy de M. Kac

A Mathematician Grappling With His Century de Laurent Schwartz = "Un mathematicien aux prises avec le siecle" original french title

Photographs

Mathematical People: Profiles and Interviews de Donald J. Albers

Source books

(because it is invaluable to read the original articles)

From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931 de Jean van Heijenoort

Yearly compilation

What's Happening in the Mathematical Sciences 200x-200x+1 de Barry Cipra

Math and society

The Rise of Statistical Thinking 1820-1900 de Theodore M. Porter

other

Abrégé d'histoire des mathématiques, 1700-1900

6000 Jahre Mathematik: Eine Kulturgeschichtliche Zeitreise - 2. Von Euler Bis Zur Gegenwart de Hans Wussing

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    $\begingroup$ "Mathematical people" and its sequel were great! In a related vein, there's "I have a photographic memory" by Paul Halmos. Haven't looked at them in a while, but I think the latter book is photos only. $\endgroup$
    – Victor Protsak
    Commented May 6, 2010 at 4:08
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    $\begingroup$ Indiscrete Thoughts is fantastic; I cannot recommend it (indeed, most of Rota's writing) highly enough. $\endgroup$
    – Qiaochu Yuan
    Commented May 6, 2010 at 5:03
  • $\begingroup$ As you mention Jean van Heijenoort, I can also recommend his biography: "From Trotsky to Gödel: The Life of Jean Van Heijenoort" by Feferman. It has not much mathematics in it, but his life was simply remarkable! $\endgroup$
    – Lennart Meier
    Commented Jul 11, 2012 at 9:55
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I don't think that there is a shortage of books on "recent" history of mathematics - if anything, the growth has been exponential here as well! There are many recent books dealing with more specialized areas written by eminent scholars, e.g.

Charles Curtis, Pioneers of representation theory: Frobenius, Burnside, Schur, and Brauer
Armand Borel, Essays in the history of Lie groups and algebraic groups
Thomas Hawkins, Emergence of the theory of Lie groups. An essay in the history of mathematics 1869–1926

and, although this is not a book on history of mathematics as such, the erudite

Marcel Berger, A panoramic view of Riemannian geometry

Among broader views, I enjoyed reading

Piergiorgio Oddifreddi, The mathematical century. 30 greatest problems of the last 100 years

The four-color problem, Kepler's conjecture, and the Monster have all been featured in popular mathematics books.

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Monastyrsky's Modern Mathematics in the Light of the Fields Medals. For a review see here.

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These have already been mentioned in comments, but I wanted to put them here explicitly:

I Want To Be a Mathematician: An Automathography by Paul Halmos

I Have a Photographic Memory by Paul Halmos

And as for photographs, the recent Mathematicians: An Outer View of the Inner World is another good one.

There's some good historical material in the Princeton Companion to Mathematics as well.

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Surprised the Grothendieck-Serre letters haven't been mentioned yet. As historical primary sources go, they don't get much better than that.

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  • $\begingroup$ It is interesting indeed, but hardly a book on history of mathematics. $\endgroup$
    – Andrea Ferretti
    Commented May 10, 2010 at 12:54
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Mark Ronan's book, Symmetry and the Monster, deserves a mention. It is a very well-written, popular account of the classification of finite simple groups which even the experts can learn from.

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Andre Weil wrote an autobiography, The Apprenticeship of a Mathematician.

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    $\begingroup$ This is a highly readable and fascinating view of Weil's early life from his own later perspective, translated (quite well it seems) from the French original and published by Birkhauser. In the absence of a full biography of Weil this is worthwhile for those who have been influenced by his mathematical legacy. Where else can one learn that Trotsky once slept in Weil's bed in Paris while Weil himself was away? $\endgroup$
    – Jim Humphreys
    Commented May 6, 2010 at 15:45
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I am shocked that Carol Parikh's "The Unreal Life of Oscar Zariski" hasn't been mentioned.

It paints a very charming picture of the man and casts new light onto luminaries like Weil, Lefschetz and Birkhoff.

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  • $\begingroup$ Agreed; this is a real gem. $\endgroup$
    – Qiaochu Yuan
    Commented Feb 18, 2011 at 21:05
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I didn't see this mentioned elsewhere: the AMS has a whole series devoted to the history of mathematics, much of it fairly recent.

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I found the book "The Genesis of the Abstract Group Concept", by Hans Wussing (I have the Dover reprint) very interesting.

It covers the development of group theory from its precursors in pre-19th century mathematics, and then traces the development of the concept of an abstract group through to the end of the 19th century. It makes (what seems to me to be) a detailed study of primary sources, and the fact that the author has a good command of the mathematics helps lend credence to his assessment of the various historical trends and developments.

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"A Panorama of Pure Mathematics", written by Jean Dieudonne, a book depicts a general picture of various branches of pure mathematics.

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    $\begingroup$ … although I think Dieudonné's claim that it's suitable for a 2nd-year honours undergraduate student is perhaps a bit of a stretch. :-) (Somehow, I also find “Le choix bourbachique” a tremendously funny subtitle. It reminds me of an article of Gel'fand where he advances the hope that some theory will eventually undergo “a suitable Bourbakisation”.) $\endgroup$
    – LSpice
    Commented Feb 19, 2011 at 15:41
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The degree to which you like this answer is very dependent on the degree to which you find physics even in its own right of interest to mathematicians, but Abraham Pais is a wonderful historian of (relatively) recent physics; I'm most familiar with his biography of Einstein (Subtle is the Lord) and his history of particle physics (Inward Bound), but I understand he has many more books as well.

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It is rare to have a history of the modern field:

Bruce Chandler and Wilhelm Magnus. The history of combinatorial group theory. A case study in the history of ideas. Studies in the History of Mathematics and Physical Sciences, vol. 9. Springer, New York, 1982.

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For Banach space theory and linear operators, Albrecht Pietch's book History of Banach spaces and linear operators is very interesting and well-researched, and only a couple of years old.

There is also Jean Dieudonne's History of Functional Analysis.

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  • $\begingroup$ Ah, you beat me to it. Yes, obviously Pietsch's book only focuses on one subject area, but it's very good. $\endgroup$
    – Matthew Daws
    Commented May 6, 2010 at 7:56
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    $\begingroup$ @Matt: GMT+10 FTW! :-) $\endgroup$
    – Philip Brooker
    Commented May 6, 2010 at 9:00
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I thought this book was terrific.

Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics: Jose Ferreiros Dominguez

I'm finding this useful in my research on a philosophy of mathematics dissertation:

Tool and object: a history and philosophy of category theory: Ralf Krömer

Others have mentioned Dieudonne's "A History of Algebraic and Differential Topology". As a philosopher (albeit one with some graduate math training) I found it very difficult to follow. Maybe I need to really commit to it, however.

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    $\begingroup$ Dieudonne's book is fantastic, but its target audience is really research mathematicians. You really need to know at least the contents of a first year graduate course in topology (homology, cohomology, the fundamental group, and the basics of the higher homotopy groups) to follow it. $\endgroup$
    – Andy Putman
    Commented May 6, 2010 at 2:56
  • $\begingroup$ (...if not more...) $\endgroup$
    – Kevin H. Lin
    Commented May 6, 2010 at 15:58
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    $\begingroup$ The other day, I happened to be wondering just how mathematics came to be the study of "sets with structure" and "structure-preserving maps". Dominguez is a really great source for this information. I had thought that this was a 20th century phenomenon, but a quick perusal seems to indicate that Dedekind played a very prominent role in getting it started. Anyway, +1 for a great reference. $\endgroup$
    – castal
    Commented May 6, 2010 at 17:51
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    $\begingroup$ By the way, I wonder if you might not also be interested in "From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory" By Jean-Pierre Marquis. Here is a link to it on Google books: <books.google.com/…> $\endgroup$
    – castal
    Commented May 7, 2010 at 1:49
  • $\begingroup$ Dedekind was the real precursor on the idea of structure. It is remarkable that he was influenced by the less formal ideas of Riemann. Ferreirós explain this in great detail. A very nice lecture for the roots of present-day mathematics. The book by Krömer is a very nice complement getting into the waters of category theory. $\endgroup$
    – Leo Alonso
    Commented Jul 11, 2012 at 15:29
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Bit of a different direction: autobiographies or tributes written by mathematicians that favor mathematical events over personal ones, at least to some degree. So:

Saunders Mac Lane A Mathematical Autobiography
http://www.akpeters.com/product.asp?ProdCode=1500

Kadison's article on Kaplansky in: http://www.ams.org/notices/200802/index.html

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    $\begingroup$ "I want to be a mathematician" by Paul Halmos was phantastic! $\endgroup$
    – Victor Protsak
    Commented May 6, 2010 at 3:53
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    $\begingroup$ "I Want To Be A Mathematician" by Halmos is one of the all time classic books PERIOD.Any young student thinking about majoring in math needs to read it. I also find it very telling-and very disappointing-that the feud between he and Mac Lane that led to Halmos leaving the University of Chicago is never even mentioned in MacLane's book. You'd think he'd want to tell his side of it. Unless it happened exactly as Halmos said and MacLane thought he was above reproach for it. $\endgroup$
    – The Mathemagician
    Commented May 7, 2010 at 2:07
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The correspondence between Cartan and Weil edited by Michele Audin contains a lot of interesting history (Bourbaki, Riemann hypothesis for curves, algebraic topology and various political topics related to mathematics).

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The Nature and Growth of Modern Mathematics written in 1970 by Edna E. Kramer is a good book that touches on a wide selection of topics - very similar to Kolmogorov, Aleksandrov, and Lavrent'ev's Mathematics: its Content, Methods, and Meaning.

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My favorite parts of Sylvia Nasar's A Beautiful Mind (the book, not the movie) were the parts which described the Princeton math department in the 40s and 50s.

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    $\begingroup$ I read some of that on google books (the parts about Artin, Lang, Milnor, Tate, etc.), which were pretty good, but the book is written from a very "journalistic" perspective, which I found a bit off-putting. $\endgroup$
    – Harry Gindi
    Commented May 6, 2010 at 7:27
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    $\begingroup$ I liked those bits when I read the book (which has been a while ago now) but got a sense of deja vu when I read certain parts of Rota's Indiscrete Thoughts $\endgroup$
    – Yemon Choi
    Commented May 6, 2010 at 8:14
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    $\begingroup$ Nasar approached Nash's life and work from her background as an economics reporter, so some mathematical details get out of focus. She did a good job of talking with relevant people in Princeton and elsewhere about the period involved, though Nash himself didn't cooperate and therefore much of his life story is filtered through his ex-wife/wife. There are minor errors of detail in the book, such as misidentifications of people, but Nasar did a reasonable job with the materials she had. Unlike the movie version, she included even Nash's arrest and loss of security clearance. $\endgroup$
    – Jim Humphreys
    Commented May 6, 2010 at 14:43
  • $\begingroup$ @HarryGindi Yes. But it is fantastic journalism. The coverage of the Rand Corporation, and of the economics prize often mistakenly called a Nobel Prize, do a great job of providing context, though not themselves history of math. $\endgroup$
    – Colin McLarty
    Commented Sep 21, 2013 at 0:24
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Nicolas Bourbaki's Elements of the History of Mathematics covers the history of mathematics, and is a nearly unaltered reproduction of the historical notes from Bourbaki's Elements of Mathematics. The historical notes themselves are a great source for this type of information, and this book collects them in a nice readable format. It is pretty funny the way Bourbaki writes about the contributions of members of the group (from the chapter on uniform spaces: "Uniform spaces have only been defined in a general way recently by A. Weil...". He also plays up the importance of filters, in classic Bourbaki style.).

Edit: Fixed.

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    $\begingroup$ I am reasonably certain that "Elements of the history of mathematics" is precisely the collection of historical notes from various volumes of the main treatise: "Cet ouvrage rassemble, sans modification substantielle, la plupart des Notes historiques dans mes Elementes de Mathematique". $\endgroup$
    – Victor Protsak
    Commented May 6, 2010 at 4:04
  • $\begingroup$ Note, however, that Elements was translated by a different person than the individual volumes, and in my opinion the translations in the individual volumes are better. $\endgroup$
    – Marcus Johnson
    Commented Aug 20, 2014 at 14:42
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History, biography, and memoir are quite different genres for mathematics. But as long as some of the latter are being recommended, I'd have to add G.H. Hardy's short memoir A Mathematician's Apology. Like most memoirs this falls short of giving a full picture of Hardy's life and work. His life is by now impossible to document anyway, though the somewhat fictionalized account of his years in Cambridge during Ramanujan's visit given recently by David Leavitt in The Indian Clerk is quite readable. Leavitt's mathematics is weak at times, though corrections were made in the softcover reprint. But he has explored the documentary evidence thoroughly, including the detailed biography of Ramanujan by Kanigel (which however has been criticized by some Indian mathematicians for its portrayal of Indian culture and religion).

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  • Number theory:

"Rational Number Theory in the 20th Century: From Pnt to Flt", Wladyslaw Narkiewicz, Springer, 2011

  • Category Theory:

"Tool And Object: A History And Philosophy of Category Theory", Ralf Krömer, Springer, 2007

and

"From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory", Jean-Pierre Marquis, Springer, 2008

  • Numerical Analysis:

"A history of numerical analysis from the 16th through the 19th century", Herman Heine Goldstine, Springer, 1977

followed by

"Numerical Analysis: Historical Developments in the 20th Century", Claude Brezinski, Luc Wuytack, Gulf Professional Publishing, 2001

  • Operations Research

"An Annotated Timeline Of Operations Research: An Informal History", Saul I. Gass, Arjang Assad, Springer, 2005

  • General

"Mathematical Events Of The Twentieth Century", A. A. Bolibrukh, I͡Uriĭ Sergeevich Osipov, Springer, 2006

and

"Development of Mathematics 1950-2000", Jean-Paul Pier, Birkhäuser, 2000

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    $\begingroup$ The Narkiewicz book "From PNT to FLT" is a heroic attempt to extend Dickson's history of number theory through the 20th century. It is telegraphic in style and has thousands of references. $\endgroup$
    – John Stillwell
    Commented Jul 8, 2012 at 7:21
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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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Two (very recent) books on (at least selected aspects of) the history of complex (holomorphic) dynamics, in the years >1850:

Audin, Michèle: Fatou, Julia, Montel. The great prize of mathematical sciences of 1918, and beyond. Translated from the 2009 French original by the author. Lecture Notes in Mathematics, 2014. History of Mathematics Subseries. Springer, Heidelberg, 2011. viii+332 pp. ISBN: 978-3-642-17853-5 (the French original is from 2009)

Alexander, Daniel S.; Iavernaro, Felice; Rosa, Alessandro: Early days in complex dynamics. A history of complex dynamics in one variable during 1906–1942. History of Mathematics, 38. American Mathematical Society, Providence, RI; London Mathematical Society, London, 2012. xviii+454 pp. ISBN: 978-0-8218-4464-9

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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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The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions (2010) by Shing-Tung Yau and science writer Steve Nadis. It is an interesting mixture of autobiography, history of a slice of mathematics (largely surrounding Calabi-Yau manifolds), and popular-science tutorial. Here is Witten's endorsement:

"Shing-Tung Yau and Steve Nadis take the reader on a fascinating tour of many contemporary topics in geometry and physics. Readers will find many challenging ideas to explore in this book, and even specialists will enjoy Yau’s reminiscences about his education and work."

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