Einstein once made a fascinating casual remark that relativity and quantum could never be discovered inductively from observed phenomena (this is from memory, so I may be wrong)… I got the impression that when Einstein did his “thought experiments” and riding on a beam of light, that he was somehow viewing the kaleidoscopic panorama of possible axiomatic systems like Riemann, fixed-point, etc. when suddenly, serendipitously one notices a coincidence a match (sort of like Maxwell changing his equations based upon aesthetics and suddenly stumbling upon something that works) …. I am saying this with the view that some mechanical heuristic formulaic approach to grind out solutions is a consummation devoutly to be wished.. but impractical. It is sort of like Godel or Wittgenstein pointing out a fundamental recursive weakness in linguist or symbolic axiomatic systems… I suppose I am reacting to the phrase “making conclusions from knowledge of facts” … and then Euler’s simple formula sparking 30 or more years of string theory research…

http://en.wikipedia.org/wiki/Euler’s_formula

… or Galois pouring out in one night before a fatal duel material which takes a graduate student 3 months to master… (so I am told)

http://en.wikipedia.org/wiki/%C3%89variste_Galois

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