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There's a similar argument for why Goldbach's conjecture* might just be a statistical fluke. I remember realizing this in high school and deriving the probabili

There's a similar argument for why Goldbach's conjecture* might just be a statistical fluke. I remember realizing this in high school and deriving the probability – alas it's not a novel idea and Wikipedia has a great summary: https://en.wikipedia.org/wiki/Goldbach%27s_conjecture#Heuristic_justification https://en.wikipedia.org/wiki/Goldbach%27s_conjecture#Heuris... It's very possible that it's an unprovable true conjecture, which is kind of interesting in itself. * every even number can be written as a sum of two primes

Houshalter 10y ago
What's interesting about this argument is, if its true, it's an example of a simple conjecture that is true but unprovable. But not like Godel sentences, which can be proved under different axioms, or proved to be unprovable. This would be completely unprovable. And not because of some logical paradox, but simply because there is no mathematical reason for it to be false, it's just a coincidence. There are also probably many conjectures like this. Freeman Dyson constructed one, that no digits of powers of two, reversed, make a power of 5. The reasoning being that the digits grow big quickly, and the base 10 representation is basically random and uncorelared with it. I think other conjectures about digits of numbers are similar. E.g. Mathematicians have found it impossible to prove that any numbers are normal, or even if pi contains infinite 5's, and many similar properties. These things may only be probabilistically true.
- tgb 10y ago
  Well, any statement can be proven under different axioms. Just take that statement itself as your only axiom.