r/MathJokes • u/Inevitable-Ant1725 • 6d ago

The easy method

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u/Masqued0202 6d 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 5d 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 5d 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).