Another mathematician basis function from Freeman Dyson, Birds & Frogs: http://www.ams.org/notices/200902/rtx090200212p.pdf http://www.ams.org/notices/200902/r

Another mathematician basis function from Freeman Dyson, Birds & Frogs: http://www.ams.org/notices/200902/rtx090200212p.pdf http://www.ams.org/notices/200902/rtx090200212p.pdf Dyson contrasts the ADHD of the multi-disciplinary cross-fertilizing polymath, with the meticulous obsessive immersion of the specialist. There is also the Kuhnian distinction between revolutionary and ordinary progress: the leap of the system creator compared to the incremental steps of the system extender. I think it is very relevant that the intuitionist geometric thinkers are often the mathematical physicists. They have a vivid kinaesthetic imagination, where mathematical entities have a visual appearance, complete with spatial properties and forceful interaction. Sometimes these take the form of practical thought experiments, which open a problem to precise mental tests. But they can also involve more abstract explorations, like the slow precession of a mobile sculpture, such that alignments and symmetries become manifest: not yet understood, but actually there for examination. A list of the greats would include Newton, Gauss, Riemann, Poincaré himself, Einstein and Feynman. Many of these used spatial representations to inspire algebraic progress. A more recent example (although necessarily on a lower tier) would be Penrose.