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Daniel Moskovich's user avatar
Daniel Moskovich's user avatar
Daniel Moskovich's user avatar
Daniel Moskovich
  • Member for 15 years
  • Last seen more than a month ago
  • Israel
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Pseudonyms of famous mathematicians
@LSpice The quotation mark "gershayim" indicates an acronym. en.wikipedia.org/wiki/Gershayim
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What is the high-concept explanation on why real numbers are useful in number theory?
I'm happy with theorems in $Z_2$ that are provably (or conceptually "obviously") harder to prove in $PA$. I would therefore agree with your restatement... and wish for some sort of "speedup theorem", or at least a plausible heuristic argument for such, for a "useful" theorem in number theory...
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What is the high-concept explanation on why real numbers are useful in number theory?
So are you saying that many techniques were originally developed for complete fields, after which completeness could be dropped and we were still left with useful techniques?
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Where can square roots come from when they are not distances?
How is this different from Noam Elkies' answer?
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Books you would like to read (if somebody would just write them…)
@ThomasRot This is very nice!! My peeve is that it doesn't seem to treat Cerf's work at all and merely outlines Hatcher's proof of the Smale Conjecture- but it looks wonderful nonetheless!
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