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I've read Marcus Du Sautoy's "The Music of Primes" recently and, although I'm not so much interested in number theory, I really liked it for the global perspective on the subject, though at an "educational", "popular " level.

I'm also goig to read Aczel and Singh's Fermat Last Theorem. Now, I am wondering wether there are similar books that a fourth-year student of Mathematics like me could appreciate. In particular I would like to have an insight in the recent history of the subjects, let's say from 1940-50 until now. Of course Du Sautoy's level is a bit low, so a little "higher-level" references are also welcome.

So, are there such books for algebraic topology, modern set theory, or other abstract issues? I'm asking because there doesn't seem to be a way to have a perspective on recent history of some topics, on the important and challenging theoretical problems and approaches, also - I must say - in order to choose my career.

I hope the question is not off-topic. (Perhaps I should have posted it in the Math StackExchange?) Thank you in advance.

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Princeton companion to mathematics, Gowers, ed. http://press.princeton.edu/titles/8350.html is perhaps what you want. It tries to cover the whole mathematics (and of course fails). But parts of it it could be an interesting reading.

Now in most areas of mathematics there are introductory undergraduate-level books. Not on "history" but just introducing to the area. But you have to specify the area, of course because otherwise the list will be too long.

Usually mathematics after 1950 is not qualified as "history": the main participants can be still alive. What really belongs to "history" will be decided by next generations. So they do not write "history books" but write surveys on various level. There is a nice collection

Development of mathematics 1900–1950 (Luxembourg, 1992), 369–384, Birkhäuser, Basel, 1994,

but this is probably the latest period "history of mathematics" deals with.

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  • $\begingroup$ Thank you very much indeed. I will read the Princeton Companion with interest. I have edited the title changing the word "history". Referring to the second paragraph in your answer, a survey on algebraic topology and -eventually- related topics (modern algebraic geometry, category theory, differential topology) would be perhaps the most compelling reading for me at the moment. $\endgroup$ – W. Rether May 13 '17 at 19:26
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    $\begingroup$ @W.Rether Dieudonné may have what you want on topology, algebraic and differential topology, algebraic geometry, functional analysis,... $\endgroup$ – Francois Ziegler May 13 '17 at 22:29
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Have a look at Zalamea, Synththetic Philosophy of Contemporary Mathematics.

https://www.amazon.com/Synthetic-Philosophy-Contemporary-Mathematics-Fernando/dp/0956775012

This is a book of philosophy, since as others noted it's too soon to write the history of post-1950's math. Zalamea's book gives an overview of the Grothendieck revolution in math and its philosophical relevance. It brings the philosophy of math out of its Russell-Frege-Gödel phase and into the present.

Very well written and easy to read. If you're interested in the modern history of algebraic topology, you'll find plenty here to enjoy.

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