On Wednesday, September 12, 2012 1:03:16 AM UTC-6, Andrzej Kozlowski wrote: > On 11 Sep 2012, at 08:34, John Doty wrote: > > > > >> So what > > >> exactly is the evolutionary path from a near "laboratory animal" to > > >> Riemann or Perelman? > > > > > > I think it's similar to the evolutionary path from laboratory animal > > to elite athelete. Sports like ice skating are not really like anything > > humans evolved to do, but involve physical and cognitive "modules" > > evolved for other purposes, combined in novel ways. Scientific > > understanding of this has made it possible to teach atheletes to perform > > feats once thought impossible, like "quadruple jumps". I see no reason > > this shouldn't also apply to mathematics. > > > > Oh, so presumably you have now explained the "mystery of Ramanujan"
Hardy, who was in a better position than either of us to judge, did not appear to find Ramanujan particularly mysterious. According to Hardy, Ramanujan ombined a power of generalization, a feeling for form, and a capacity for rapid modification of his hypotheses". That even sounds like the kind of things we say about athletes ("hand quickness", "peripheral vision", ..., and also sounds like the sort of cognitive modules Nunez talks about. Ramanujan did not obtain his mathematical knowledge by magic: he studied for years, but without conventional direction. So, he became a very unconventional mathematician.