most recent 30 from http://mathoverflow.net 2013-05-18T23:55:27Z http://mathoverflow.net/feeds/question/40330 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/40330/examples-of-theorems-arising-from-many-authors-work Colin Reid 2010-09-28T15:45:13Z 2010-09-29T05:51:20Z

<p>(Old question: How much of mathematics is or could be done by the 'geniuses'?)</p> <p>A lot of important theorems or even theories end up being named after or otherwise attributed to one person or a small group of people. This is often fair, but taken as an overall trend it can give the (hopefully false!) impression that the most important mathematics is being done by a small minority of mathematicians. What I'm wondering is, how much does the opposite phenomenon occur, where it's very clear that a result is a large team effort and that no small group of authors deserves the lion's share of the credit? The most obvious example I can think of is the Classification of Finite Simple Groups, but I'm sure there are others from different areas of maths.</p>

http://mathoverflow.net/questions/40330/examples-of-theorems-arising-from-many-authors-work/40396#40396 Tony Huynh 2010-09-29T00:39:20Z 2010-09-29T00:39:20Z

<p>One possible answer (and hopefully the source of many future answers) is Tim Gowers' <a href="http://polymathprojects.org/" rel="nofollow">polymath experiment</a>. In short, the idea of the project is to test if massively collaborative mathematics over the internet is possible. </p>

http://mathoverflow.net/questions/40330/examples-of-theorems-arising-from-many-authors-work/40402#40402 Felipe Voloch 2010-09-29T02:03:38Z 2010-09-29T02:03:38Z

<p>Most theorems in Mathematics build upon the work of many people. Maybe a good recent example is the proof of Serre's conjecture by Khare and Winterberger. They contributed a decisive, fundamental piece of the puzzle, but it depends on the work of e.g. Serre, Tate, Ribet, Mazur, Taylor, Wiles, Kisin, Dieulefait and many others.</p>

http://mathoverflow.net/questions/40330/examples-of-theorems-arising-from-many-authors-work/40424#40424 Andy Putman 2010-09-29T05:42:32Z 2010-09-29T05:51:20Z

<p>Aside from the Geometrization Theorem/Poincare conjecture, probably the deepest theorem in low-dimensional topology in the last 10 years is the classification of hyperbolic structures on 3-manifolds with finitely generated fundamental group. Aside from the topological type, it turns out they they are classified by certain invariants "at infinity" (either Riemann surfaces at infinity or so-called "ending laminations"). The proof of this uses work of an enormous number of people : Agol, Alhfors, Bers, Brock, Calegari, Canary, Gabai, Namazi, Kleineidam, Kra, Lecuire, Marden, Maskit, Masur, Minsky, Mostow, Ohshika, Prasad, Rees, Souto, Sullivan, Thurston, and probably people I'm forgetting.</p>