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> If you want facts that won't change after 15 years, you should study Mathematics. I was just watching The Man Who Knew Infinity the other night and I would d

> If you want facts that won't change after 15 years, you should study Mathematics. I was just watching The Man Who Knew Infinity the other night and I would dispute that even Maths won't change after 15 years. Once in a generation, someone like Ramanujan comes along and manages to change something even as fundamental as Mathematics.

mcguire 10y ago
Hell, Hilbert's program, Godël, and Turing.
- philipov 10y ago
  I think a lot of mathematicians distinguish zealously between Mathematics per se, as opposed to mathematical logic/philosophy.
  - mcguire 10y ago
    True, but Hilbert was a mathematician and was expressing the general thought, that mathematics could be formalized and when that was done, it would be complete, consistent, firm, round, and fully-packed. When that was demonstrated to be false, it had no great effect on day-to-day mathematics. But still,....
    - philipov 10y ago
      Right, there are game-changing advances in mathematical logic and sea changes in mathematical philosophy. The discovery of non-euclidean geometry did not mean euclidean geometry was false, and real analysis is the same whether you found it on sets or categories, by definition. Incompleteness doesn't eliminate the possibility of consistency. Mathematics changes by becoming more expressive and growing outwards and inwards. Sometimes, a theorem is proven to be inconsistent and thrown out. My point was this happens a lot less often with mathematical theorems than it does with scientific facts because facts are based on our inductive study of the universe, whereas mathematics only makes statements about syllogisms. Unlike the real world, math is an area of study where incontrovertible facts are at least possible, because we make everything up, and just have to make sure we're consistent about it. We do not have access to such a priori knowledge about reality.

mcguire 10y ago

Hell, Hilbert's program, Godël, and Turing.

philipov 10y ago
I think a lot of mathematicians distinguish zealously between Mathematics per se, as opposed to mathematical logic/philosophy.
- mcguire 10y ago
  True, but Hilbert was a mathematician and was expressing the general thought, that mathematics could be formalized and when that was done, it would be complete, consistent, firm, round, and fully-packed. When that was demonstrated to be false, it had no great effect on day-to-day mathematics. But still,....
  - philipov 10y ago
    Right, there are game-changing advances in mathematical logic and sea changes in mathematical philosophy. The discovery of non-euclidean geometry did not mean euclidean geometry was false, and real analysis is the same whether you found it on sets or categories, by definition. Incompleteness doesn't eliminate the possibility of consistency. Mathematics changes by becoming more expressive and growing outwards and inwards. Sometimes, a theorem is proven to be inconsistent and thrown out. My point was this happens a lot less often with mathematical theorems than it does with scientific facts because facts are based on our inductive study of the universe, whereas mathematics only makes statements about syllogisms. Unlike the real world, math is an area of study where incontrovertible facts are at least possible, because we make everything up, and just have to make sure we're consistent about it. We do not have access to such a priori knowledge about reality.