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Sort of. As t approaches infinity, more and more of the simple parts of math will have been discovered. Therefore the only parts left to discover will be thos

Sort of. As t approaches infinity, more and more of the simple parts of math will have been discovered. Therefore the only parts left to discover will be those which are more complicated; hence the overall idea is necessarily correct.

PurplePanda 13y ago
This would seem to be true as long as mathematics is discovered rather than invented. Otherwise I beleive that one may be able to invent generalisations that result in a simplification of mathematics.
j2kun 13y ago
You are misled to believe that mathematics has simple parts and not simple parts, and that simple parts are easier to "discover" than the complex parts. In fact, the simple parts are usually the most difficult to discover. Why? Precisely because it takes extreme genius to give simple answers to mathematical questions. Over time complicated proofs and definitions get simplified and clarified (such it was with calculus, set theory, logic, group theory, and countless other topics). So there's no precedent to believe that current mathematics won't be simplified in the future (unless, of course, you believe that all mathematics is complicated; but then you seem to be trying to make an objective point about complexity, so we'll ignore that possibility).
siddboots 13y ago
It could instead be the case that all of maths is simple, but that complexity tends to appear whenever we have an incomplete understanding of a domain.
dkural 13y ago
This assumes that the purpose of math is to prove things, whereas another worthy goal for me at least is enabling humans to truly understand why things are true, and not just what things are true.
- pavpanchekha 13y ago
  No disrespect, but your purpose for math is entirely irrelevant unless you speak for the majority of research mathematicians.
  - gjm11 13y ago
    No disrespect, but dkural's idea of what mathematics is about is no more irrelevant than sillysaurus2's or yours, and dkural's view is quite well represented among research mathematicians, first-rate ones included. For a famous example, see William Thurston's "On proof and progress in mathematics" at http://arxiv.org/pdf/math/9404236v1.pdf http://arxiv.org/pdf/math/9404236v1.pdf .
  - dkural 13y ago
    I have a mathematics degree from Harvard, though I haven't taken a poll of research mathematicians. I do think algorithmic theorem proving is a great field of inquiry!

PurplePanda 13y ago

This would seem to be true as long as mathematics is discovered rather than invented. Otherwise I beleive that one may be able to invent generalisations that result in a simplification of mathematics.

j2kun 13y ago

You are misled to believe that mathematics has simple parts and not simple parts, and that simple parts are easier to "discover" than the complex parts. In fact, the simple parts are usually the most difficult to discover. Why? Precisely because it takes extreme genius to give simple answers to mathematical questions. Over time complicated proofs and definitions get simplified and clarified (such it was with calculus, set theory, logic, group theory, and countless other topics). So there's no precedent to believe that current mathematics won't be simplified in the future (unless, of course, you believe that all mathematics is complicated; but then you seem to be trying to make an objective point about complexity, so we'll ignore that possibility).

siddboots 13y ago

It could instead be the case that all of maths is simple, but that complexity tends to appear whenever we have an incomplete understanding of a domain.

dkural 13y ago

This assumes that the purpose of math is to prove things, whereas another worthy goal for me at least is enabling humans to truly understand why things are true, and not just what things are true.

pavpanchekha 13y ago
No disrespect, but your purpose for math is entirely irrelevant unless you speak for the majority of research mathematicians.
- gjm11 13y ago
  No disrespect, but dkural's idea of what mathematics is about is no more irrelevant than sillysaurus2's or yours, and dkural's view is quite well represented among research mathematicians, first-rate ones included. For a famous example, see William Thurston's "On proof and progress in mathematics" at http://arxiv.org/pdf/math/9404236v1.pdf http://arxiv.org/pdf/math/9404236v1.pdf .
- dkural 13y ago
  I have a mathematics degree from Harvard, though I haven't taken a poll of research mathematicians. I do think algorithmic theorem proving is a great field of inquiry!