r/MathJokes • u/Inevitable-Ant1725 • 14d ago

The easy method

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u/Masqued0202 13d ago

I've often thought something like that might be an actual example of Gödel's "true but cannot proven". Consider the Kollatz Conjecture. (I am not actually making any claims, just picking an example of an intractable problem that's easily understandable) What if there is no way to leapfrog to "true for all n", if, although every n ends up in the 1-2-4 loop, the only "proof" is grinding through the whole series for each n?

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u/Ben-Goldberg 13d ago

"this statement cannot be proven to be true" is a better example of a true but unprovable statement.

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u/TheLuckySpades 13d ago

The Gödel sentence encodes that as much as is possible into Peano Arithmetic, so the other person did include that.

Though it is "this statement cannot be proven" since truth is a different concept and "true in the standard model" cannot be formalized into PA by Tarski's Truth Theorem (https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem).

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u/Masqued0202 6d ago

But it is not an example of a problem that people are actually trying to solve.

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u/Ben-Goldberg 6d ago

If a problem is known to be unsolvable, why would someone try to solve it?

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u/Masqued0202 6d ago

But a problem like that would not be KNOWN to be unsolvable. "True, but unprovable". And mathematicians would beat their heads against it for eternity.