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A lot of mathematicians I've known feel a kind of awe for Hilbert that they don't feel even for history-makers like Euler or Gauss. I think little stories like
by mnemonicsloth 17y ago
A lot of mathematicians I've known feel a kind of awe for Hilbert that they don't feel even for history-makers like Euler or Gauss. I think little stories like this one are part of the reason why. Hilbert always makes it look easy, even when his results are weirdly counter-intuitive.
Technically, though, there aren't any paradoxes here. It's for the purpose of avoiding paradox that we're willing to talk about infinities in the first place.
- slackenerny 17y agoTechnically, though, there aren't any paradoxes here. The real reason why it is a paradox doesn't have much to do with notion of infinity per se, but with problem of infinite decision aka Supertask. Which reminds me of an article on physics of supertasks that among other things somewhat outlines how classical theory is more paradoxical before than after quantization http://th-www.if.uj.edu.pl/acta/vol36/pdf/v36p2887.pdf http://th-www.if.uj.edu.pl/acta/vol36/pdf/v36p2887.pdf (43pp but easy reading).
- Luc 17y agoI really wanted to like this PDF, but the grammar is at times so bad it is often quite hard to parse.
- deleted 17y ago[deleted]