most recent 30 from http://mathoverflow.net 2013-05-20T03:52:58Z http://mathoverflow.net/feeds/question/28008 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/28008/at-what-point-in-history-did-it-become-impossible-for-a-person-to-understand-most Harry Gindi 2010-06-13T09:27:13Z 2010-06-13T17:23:05Z

<h2>Disclaimer:</h2> <p>I am asking this question as an improvement to <a href="http://mathoverflow.net/questions/27881/who-is-the-last-mathematician-that-understood-all-of-mathematics" rel="nofollow">this question</a>, which should be community wiki. This is in line with the actions taken by Andy Putman in a similar case (cf. <a href="http://meta.mathoverflow.net/discussion/399/i-hope-that-people-will-do-this-in-the-future/" rel="nofollow">meta</a>).</p> <p>See the relevant <a href="http://meta.mathoverflow.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/" rel="nofollow">meta thread</a> about the previous question. </p> <p>Edit: If it wasn't already obvious, I only asked this question to prevent the other one (which was not made community wiki) from being reopened. </p> <h2>Question:</h2> <p>The scope of mathematics has grown immensely since ancient times. At what point in time did it become impossible for a single person to understand the majority of mathematics enough to keep current with contemporary research? </p> <p>Edit: Clarified the wording.</p>

http://mathoverflow.net/questions/28008/at-what-point-in-history-did-it-become-impossible-for-a-person-to-understand-most/28012#28012 Charles Matthews 2010-06-13T09:59:53Z 2010-06-13T09:59:53Z

<p>At some point between Harald Bohr's foundation of the theory of almost periodic functions, and the major paper of van der Corput that J. E. Littlewood regarded as the most technical paper in the whole of mathematics so far. In other words some time round 1915, or when <em>classical analysis</em> ceased to be a comfortable unifying and central area of graduate mathematical education (so that reading a good <em>Cours d'Analyse</em> would set you up for research), and became a bunch of technically-refined areas for specialists. This is also the period when the Lebesgue integral became a necessity, and when Brouwer had first provided needed foundations for topology (e.g. simplicial approximation). The generation of universalist wannabes that followed Poincaré and Hilbert would include names such as Weyl, von Neumann, Weil and Kolmogorov. But you can see from that list that such great talents have already "spread out", not trying to comment on everything.</p>

http://mathoverflow.net/questions/28008/at-what-point-in-history-did-it-become-impossible-for-a-person-to-understand-most/28033#28033 Tim Perutz 2010-06-13T15:35:12Z 2010-06-13T15:35:12Z

<p>The world's output of scientific papers increased exponentially from 1700 to 1950. </p> <p>One online source is <a href="http://www.its.caltech.edu/~dg/crunch_art.html" rel="nofollow">this article</a> (which is concerned with what has happened since then). The author displays a graph (whose source is a 1961 book entitled "Science since Babylon" by Derek da Solla Price) showing exponential increase in the cumulative number of scientific journals founded; an increase by a factor of 10 every 50 years or so, with around 10 journals recorded in 1750.</p> <p>Perhaps someone can locate similar statistics specific to mathematics, but it's reasonable to expect the same pattern. If so, it is a long time since any individual could follow the primary mathematical literature in anything close to its entirety. </p> <p>But then, gobbling papers is not how leading mathematicians (or scientists) actually operate. </p> <p>By making judicious choices of what to pursue when, and with sufficient brilliance and vision, it is possible even today to make decisive contributions to many fields. Serre has done so in, and between, algebraic topology, complex analytic geometry, algebraic geometry, commutative algebra and group theory, and continues to do so in algebraic number theory/representation theory/modular forms.</p>