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I really love Godel and logic, but it seems to me that most books are heavy on theory and light on problems. It also seems to me that this isn't just a fluke -- there really is something about logic that makes it tougher to approach via problems, rather than reading theory.

What I'm wondering is: is it true? Do some areas of math really have worse problems? Why would that be, and what areas of math are most afflicted with this plight?

MBP
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  • I think obviously, yes, some areas of mathematics (e.g. calculus, combinatorics) yield themselves much more readily to computational problems than others (e.g. topology). – user7530 Oct 11 '17 at 04:01
  • But problems need not be computational, right? For example regular old plane geometry contains a wealth of non-computational proof problems. – MBP Oct 11 '17 at 04:02
  • true, though if you count proofs as problems, it's not clear to me why logic shouldn't have as many as other subjects – user7530 Oct 11 '17 at 04:07

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I suppose it depends on what you mean "worse problems." Number theory has something as simple as Goldbach's conjecture, which you could state to a grade school child, but has yet to be proven. Again, topology has the "inscribed square problem," which is almost equally easy to state, again, has an illusive proof. https://en.wikipedia.org/wiki/Inscribed_square_problem

Chickenmancer
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