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I was reading Stillwell's book, Mathematics and its History, and it got me thinking about how research developments in the last two decades (i.e. history for us too, except recent) would be "narrated".

Here's the sort of stuff that makes a period in history memorable:

  • period of (intense) debate: e.g. the late 1800s and the development of set theory

  • period of consternation: e.g. the developments of real analysis after Fourier's "disturbing" approach to solving the heat equation in the first two or three decades of the 1800s

  • period of (initial) unification: Klein's "Erlangen" program, Hilbert's efforts with geometry and logic -- again, late 1800s

  • period of solidification/modernization: Kolmogorov, Feller and others (and many others) working to axiomatize and develop probability theory in the mid 20th century

A period can have one or more of these labels, and likely there are more labels than the ones I have listed. I know a lot more about the history of the 19th century than the history of the last 50 years. This is understandably because historians haven't yet had the time to chew through recent history, but could current mathematicians at the frontlines be able to do what historians can't yet, and perhaps "narrate" some of the "label worthy" themes of the last half-centry?

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    $\begingroup$ In my opinion, this depends less on 1960-2010 and more on the culture during the time when the history books are written. (History isn't completely subjective, but writing about history is shaped very strongly by when it is written) $\endgroup$ – Yemon Choi Feb 19 '15 at 15:39
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I think the question you propose to ask ("In the math history books of the future, what will be written about the years 1960-2010?") would be more appropriate for History of Science and Mathematics Stack Exchange.

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  • $\begingroup$ I am not sure it'd be appropriate there; maybe if 2010 was at least something a little more in the past. $\endgroup$ – user9072 Feb 18 '15 at 13:58
  • $\begingroup$ @quid: That's up for debate meta.hsm.stackexchange.com/questions/167/… $\endgroup$ – Zack Wolske Feb 18 '15 at 15:59
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    $\begingroup$ @ZackWolske well, yes, which is why I said that I am not sure. To ask for an evaluation of math that was done in 2010 on a historical scale seems in any case premature to me. I think I would vote to close as primarily opinion based (there and here). $\endgroup$ – user9072 Feb 18 '15 at 16:06
  • $\begingroup$ @quid: I think that 2010 is a very interesting year, since it was the year I started my M.Sc. and began taking interest in the axiom of choice. If that is not a seminal event in mathematical history, I don't know what is. :-) $\endgroup$ – Asaf Karagila Feb 19 '15 at 14:01
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    $\begingroup$ @Asaf I agree completely. However, arguably this fact is not yet well-known. It will take some years until this is generally recognized, which is why I think the question is premature and the history cannot yet be written. $\endgroup$ – user9072 Feb 19 '15 at 14:03
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Case I: The answer is currently known. Then there is no obstruction to those "books of the future" being written today, and therefore they'd be books of the present. Contradiction.

Case II: The answer is not currently known. In that case, this question is opinion-based and hence off-topic.

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    $\begingroup$ This assumes the law of excluded middle. $\endgroup$ – Asaf Karagila Feb 22 '15 at 0:17
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    $\begingroup$ Actually, it just assumes that either the answer is currently known or the answer is not currently known. The law of excluded middle is more general. Also, he hasn't said QED; he may present Case III later. $\endgroup$ – The Masked Avenger Feb 22 '15 at 6:30
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    $\begingroup$ Actually, the assumption that books of the future are disjoint from books of the present worries me much more that the law of excluded middle. $\endgroup$ – Emil Jeřábek Feb 23 '15 at 10:39
  • $\begingroup$ @Emil: I am sure that in a million years nobody will read Jech, or Kunen or even Grothendieck. Their books will be disjoint from ours, probably in language as well. I doubt French or English will survive that long. $\endgroup$ – Asaf Karagila Feb 24 '15 at 0:07
  • $\begingroup$ @Asaf: I see. So, in your opinion, there's present, then a million years of nameless void, and only then a future? That considerably simplifies the OP's question. $\endgroup$ – Emil Jeřábek Feb 24 '15 at 10:54
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    $\begingroup$ @Emil: No, of course not, but being naturally interested almost entirely in the transfinite, I am allowing some finitely many years of chaos, as long as eventually things will stabilize. Here I even gave an upper bound for the finite period of problematic future! And it's quite small too, smaller than the number of molecules in your average drop of water! :-) $\endgroup$ – Asaf Karagila Feb 24 '15 at 11:23

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