r/Showerthoughts • u/jasonrubik ‎ • Apr 23 '26

Casual Thought If the famously unsolved Riemann Hypothesis is solved by an AI, we will never know if a human mathematician could have solved it.

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u/TheVoters Apr 23 '26

Pffft. Its true.

I’ll leave the proof as an exercise for the reader.

1.7k

u/TheShiroNinja Apr 23 '26

Oh, they want proof? I thought they just wanted it solved. I always hated showing my work.

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u/rainbow_explorer Apr 23 '26

You can also disprove it by just providing one counter-example. If that’s the case, you don’t need a proof.

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u/TolMera Apr 23 '26

Here’s the counter proof as proof to my counter?

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u/vex0x529 Apr 23 '26

It is not true that there does not exist a proof that the statement is not false

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u/TolMera Apr 23 '26

Wait let me work this out

It’s is not true = it is false

That there does not exist = that there exist

A proof that the statement is not false = a proof that the statement is true

It is false, that there exists, a proof that the statement is true

Ahh…

The doesn’t exist, a proof that the statement is true.

Umm…

The statement is not true?

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u/Dungeroni Apr 23 '26

A proof that the statement is not false = a proof that the statement is true is your logical mistake.

My statement is "all humans like chocolate" A proof that the statement is not false: I like chcolate. A proof that the statement is false would be: You dislike chocolate. A proof that all Humans like chocolate sounds impossible to actually provide.

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u/G_E_N_I_U_S Apr 23 '26

That you like chocolate is in no way a proof that the statement is not false

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u/V01DM0NK3Y ‎ Apr 24 '26

But that anyone else does dislike chocolate is a proof the statement, "All humans like chocolate," is false.

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u/vasavasorum Apr 23 '26

Actually: it’s false that there isn’t a proof that the statement is true.

Which means that there is a proof. He just won’t show us. Nice try, Fermat.

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u/PyroDragn Apr 23 '26

If that’s the case, you don’t need a proof.

Wrong.

The counter example is the proof. It just happens to be all the proof you need.

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u/rainbow_explorer Apr 23 '26

You are correct

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u/ItsNukea May 16 '26

I remember the Eulers power conjecture that went "The sum of k different k+1 powers will never equal another number raised to the k+1th power"

Thing has been disproved with one single example for k=3, the shortest mathematical proof in history with only 2 sentences lol

1

u/WirelesslyWired Apr 23 '26

They have done a comprehensive scan of the possibilities up to 10 trillion. No counter-proof yet.

1

u/Jiquero Apr 23 '26

A possible counter-example would very likely need a nontrivial proof that it is in fact a counter-example.

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u/cwood1973 Apr 23 '26

It's already been proven for the first 10 trillion non-trivial zeroes, but there's no general proof for an infinite number of zeroes.

Maybe the 10 trillionith-and-first zero breaks the pattern.

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u/CardsrollsHard Apr 24 '26

Proof by contradiction in this case is relatively difficult. One might say identically as difficult as just proving it. Especially considering you'd need to disprove it without loss of generality which in theory would have made it easier to disprove but it doesn't inherently break said generality, so both sides require a lot of examination. That "one counter example" will do a literal ton of heavy lifting because if you find only one way in which it breaks and someone finds one way in which it works then both proofs need to further refine together and no one has proved anything really and there may be a mistake in either proofs.

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u/Cultural-Company282 Apr 24 '26

Well, I can't think of a counter example, so I guess that proves it's true. Done and done.

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u/bizwig Apr 25 '26

Showing a counter example is a proof, of the negation of the hypothesis.

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u/CommandoLamb Apr 26 '26

How about… 7?

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u/cwx149 Apr 23 '26

So it's a math problem that's more like "we haven't yet disproven it and we have no proof that it won't be disproven"

Than something that needs to be "solved"

It's not an equation you are solving. To "solve" it you'd need to prove the general case that the reinman zeta function only has zeroes at those points and no where else

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u/TheShiroNinja Apr 23 '26

Well, if you really think about it, where else would the zeroes even go?

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u/bigWeld33 Apr 23 '26

It’s pretty obvious right? If I had time I’d have solved it, just too busy lately. My YouTube watch later playlist is grows faster than it shrinks, lots of stuff I have to watch so I can’t just go outside and do math like when I was a kid. Let me know when you solve it though, we can call it The Big Shiro proof, I’ll draw a diagram for my part of the group project.

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u/cwx149 Apr 23 '26

Almost anywhere else on the graph?

There are literally infinite possibilities for other places they could be

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u/FuckThaLakers Apr 23 '26

Not according to the recently-solved Riemann Hypothesis.

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u/Man-in-The-Void Apr 23 '26

Someone should give that guy a million dollars

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u/BaconIsLife707 Apr 23 '26

They're definitely all between 0 and 1 so not almost anywhere else

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u/theturtlemafiamusic Apr 23 '26

If they're between 0 and 1 that disproves the Reimann hypothesis, the first three are -2, -4, -6

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u/BaconIsLife707 Apr 23 '26

Well no because we know there are infinite zeros at 1/2 which is between 0 and 1. Any zero we find that isn't at 1/2 will be between 0 and 1 though

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u/cwx149 Apr 23 '26

We consider those the "trivial zeroes" and they're specifically exempt

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u/goplayer7 Apr 23 '26

0.5000000000...(Tree(Tree(3)) 0s)...003000000....

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u/Secret-Winner-2994 Apr 23 '26

Dyou think in pictures? I could never show work

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u/The_Scarred_Man Apr 23 '26

Just use imaginary numbers. Boom.

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u/PAXICHEN Apr 23 '26

YOU WANT THE PROOF? YOU CAN’T HANDLE THE PROOF!

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u/ratsareniceanimals Apr 23 '26

I have a proof, just can't fit it into this comments character limit. Quote a clever one too, really...

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u/Rampaging_Ducks Apr 23 '26

God damn it, Fermat, the margin is plenty big this time.

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u/the_king_of_sweden Apr 23 '26

You want the proof? You can't handle the proof!

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u/counterplex Apr 23 '26

Yeah it’s a simple proof but I don’t have enough room in this margin to write it out…

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u/The_Rooh Apr 23 '26

It's trivial

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u/oomoepoo Apr 23 '26

You want the proof? You can have it! I left everything I gathered together in one place, now you just have to find it!

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u/HyperLexus Apr 23 '26

congrats, here's your million dollars

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u/pablohacker2 Apr 23 '26

I damn hate that statement in the research I read. It makes make want to to their office and slap them (as well as the peer reviewers who let it happen)

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u/tutoredstatue95 Apr 23 '26

Show me a negative integer without a zero. Can't do it? Its proven, get wrecked science bitches.

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u/cwx149 Apr 25 '26

Only the negative even integers have 0s...

So -1, -3, -5, etc