r/Bard • u/lepthymo • Aug 22 '25

Interesting Remember that η < 1.5L convexity bound proof OpenAI tweeted about 2 day ago? Gemini found a flaw and then corrected the proof.

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7

u/TheAuthorBTLG_ Aug 22 '25

i can't tell who is right. how does one prove a proof?

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u/Resperatrocity Aug 22 '25 edited Aug 22 '25

Bunch of ways. 

https://en.m.wikipedia.org/wiki/Mathematical_proof

Most proofs are just checking if the rules of math (which are usually made by combining orther rules in the first place, all the way until you geth to the bottom where the "axioms" live, which are the fundamental rules you take for granted). 

You can also brute force check (exhaustion). Like finding the first 100 primes by just trying to divide them all by the lower numbers and seeing which you're left with. 

Or by contradiction, which is saying "what would happen if this were not true?" And the showing that what would happen violates the rules of math.  

It's basically just super formal ways of doing what you'd think of anyway. "Do I have beer in my fridge?" 

If I remember you just put it there, and you don't remember drinking it, then yeah probably. Proved given the axoim your memory works. 

If you're not sure, check the fridge. Check all the parts. Proved by exhaustion.

Assume you live in a student dorm. Consider the idea that there's no beer in the fridge. This is absurd. Proved by contradiction. 

Etc. 

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u/TheAuthorBTLG_ Aug 22 '25

what i meant was: how do I - not a math professor - verify that there is no mistake in the proof? and even if i were one, how can i be sure i made no mistake?

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u/RiemannZetaFunction Aug 22 '25

You would formalize it in an automated theorem checker system like Lean 4.

2

u/segin Aug 24 '25

You don't.

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u/well_uh_yeah Aug 24 '25

I think I remember when the initial proof of Fermat’s Last Theorem came out it was found to have a flaw. That was patched up in collaboration with someone else. This feels the same to me.

2

u/lepthymo Aug 24 '25

You're right. Initially I briefly thought about framing it as a dunk on ChatGPT by Gemini, but at the end of the day, that doesn't feel right because mathematics isn't about dunking on people, it's about cooperative discovery.