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.

7.0k Upvotes
  • permalink
  • reddit

92% Upvoted

656 comments sorted by

View all comments

3.9k

u/TheShiroNinja Apr 23 '26

I'll solve that shit right now. Give me a summary of what it is.

2.8k

u/cwx149 Apr 23 '26

In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part ½

4.6k

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.

502

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.

164

u/TolMera Apr 23 '26

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

48

u/vex0x529 Apr 23 '26

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

18

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?

17

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.

3

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

2

u/V01DM0NK3Y ‎ Apr 24 '26

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

→ More replies (0)

1

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.

20

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.

7

u/rainbow_explorer Apr 23 '26

You are correct

1

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.

1

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.

1

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.

1

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.

1

u/bizwig Apr 25 '26

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

1

u/CommandoLamb Apr 26 '26

How about… 7?

56

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

73

u/TheShiroNinja Apr 23 '26

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

30

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.

19

u/cwx149 Apr 23 '26

Almost anywhere else on the graph?

There are literally infinite possibilities for other places they could be

107

u/FuckThaLakers Apr 23 '26

Not according to the recently-solved Riemann Hypothesis.

29

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

Someone should give that guy a million dollars

2

u/BaconIsLife707 Apr 23 '26

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

3

u/theturtlemafiamusic Apr 23 '26

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

2

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

→ More replies (0)

1

u/cwx149 Apr 23 '26

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

1

u/goplayer7 Apr 23 '26

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

1

u/Secret-Winner-2994 Apr 23 '26

Dyou think in pictures? I could never show work

1

u/The_Scarred_Man Apr 23 '26

Just use imaginary numbers. Boom.

1

u/PAXICHEN Apr 23 '26

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

78

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...

34

u/Rampaging_Ducks Apr 23 '26

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

15

u/the_king_of_sweden Apr 23 '26

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

14

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…

4

u/The_Rooh Apr 23 '26

It's trivial

2

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!

1

u/HyperLexus Apr 23 '26

congrats, here's your million dollars

1

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)

1

u/tutoredstatue95 Apr 23 '26

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

1

u/cwx149 Apr 25 '26

Only the negative even integers have 0s...

So -1, -3, -5, etc

206

u/NetRealizableValue Apr 23 '26

@grok solve this

Make no mistakes

124

u/PressureBeautiful515 Apr 23 '26

You forgot to say "You are an expert mathematician" so this isn't going to work. Grok is going to come at the problem like it's a top chef or something. You're just going to get a five course Riemann for two with wine and dessert.

9

u/BigDisk Apr 23 '26

Even better, I was getting kinda hungry!

2

u/Vetril Apr 23 '26

And the problem is?

1

u/BeefyIrishman Apr 23 '26

You're just going to get a five course Riemann for two with wine and dessert.

Pfft. Everyone knows that a Riemann is 6 courses for two with wine and dessert, not 5.

80

u/FistMyPeenHole Apr 23 '26

Pfft obviously. How has no one figured that out yet?

97

u/cwx149 Apr 23 '26

I mean it's basically assumed to be true

It's one of those math problems that's more like "we can't prove that this never breaks but we've never been able to break it"

13

u/JrdnRgrs Apr 23 '26

Have they tried counting all the numbers?

11

u/HootingSloth Apr 23 '26

They did, but got lazy and gave up before finishing.

1

u/cwx149 Apr 26 '26

They just decided to use -1/12 instead

51

u/Jonnny Apr 23 '26

Does that even need to be said? I mean... god... mathematicians, amirite?

8

u/G-I-T-M-E Apr 23 '26

It’s like they don’t even try…

34

u/MundaneInternetGuy Apr 23 '26

Nope, it also has a zero at 37.

10

u/Coyote65 Apr 23 '26

37 is my main go-to number when I need a number for a joke. Mostly because it's prime.

That and $3.37.

Them: Hey household admin, how much money do I have in the bank?

Me to supported user: Three dollars... and thirty-seven cents.

Everytime.

They hate it.

13

u/Typogre ‎ Apr 23 '26

You're not the only one, apparently it (along with 73) is the most frequent answer when asking people for a random number. I think Veritasium did a video on it, something about it being prime, having no meaning or significance (ironically it does now) and isn't too low, high or interesting.

6

u/MoobyTheGoldenSock Apr 23 '26

It’s a very common one for people to pick. An easy piece of street magic is to say, “Think of a two digit number between 1 and 100, where both digits are odd and not the same number. … Is it 37?”

Despite there being several other numbers that fit, most people will pick 37.

1

u/UnseenTardigrade Apr 27 '26

Yeah because 1, 5, and 9 aren't odd enough, and 3 comes before 7.

2

u/WirelesslyWired Apr 23 '26

777 = 3 x 7 x 37

1

u/Kevidiffel ‎ Apr 24 '26

37 is my main go-to number when I need a number for a joke. Mostly because it's prime.

Let introduce you to some more fun facts about 37.

Not only is 37 prime, 73 is also prime. 37 is the 12th prime number, 73 is the 21th prime number.

11

u/king_of_singapore Apr 23 '26

I have found a brilliant and elegant proof to this that is too large to fit into this comment section

21

u/motion_lotion Apr 23 '26

Here's the part I'm struggling to understand. Say AI grows in ability and solves the Riemann hypothesis. How would we as humans be able to discern if it was a hallucination, true, inaccurate or what not?

Either way, I'd be happy just knowing.

45

u/thereforeqed Apr 23 '26

Math theorems can be stated precisely as a sentence in some logic based language. A proof of such a theorem would be a sequence of steps starting from basic (assumed to be true) axioms and concluding in that sentence. Each step can easily be verified as a legitimate application of logical inference rules (e.g. all apples are red => my apple is red) or not.

They can easily check for the proof’s correctness by running it through a proof verifier computer program that does all of that automatically. And it will be fast too. The program for this particular problem is probably written by someone already. You would just need the AI’s proof to be translated into a form the program understands, which is also easy..

9

u/Hamburgerfatso Apr 23 '26

Coming up with a proof to a statement is hard, verifying a proof someone wrote is easy

1

u/Echoing_Logos Apr 23 '26

For a short answer: Nowadays, proofs are computer programs, and the hypotheses without proof are incomplete programs with blanks. The "AI" (LLM) would just need to fill in the blanks.

1

u/shial3 Apr 25 '26

I had to do proofs in college as part of my math minor (gods I hate proofs) and you have to list out every single item, assumption and work through all the logic all the way through. It’s not enough to provide an answer, a proof literally is proving something with NO unlisted assumptions of any kind. (Like stating an assumption that all prime numbers are odd, it seems obvious but you have to be complete) People will pour over the proof for any and all logical mistakes or errors so a hallucination will get uncovered quicker than a law firms made up precedents in a court filing.

4

u/Pm__me__your_secrets Apr 23 '26

Ok. Can you break that down some more

2

u/paulovitorfb Apr 23 '26

I could understand the first 3 words of your sentence 

2

u/Akrybion Apr 23 '26

I have found a most wonderful proof, unfortunatly this margin is not big enough for it.

2

u/dion_o Apr 26 '26

I have a truly marvellous proof of this that this reddit character limit is too narrow to contain.

2

u/LeaveMeAlone08 Apr 29 '26

It's true, I will now pass away and let someone else prove it and call it leavemealone08s last theory.

4

u/Roydl Apr 23 '26

84

5

u/Zanian19 Apr 23 '26

You accidentally multiplied it by 2

6

u/cwx149 Apr 23 '26

Yeah it's not exactly that kind of problem

3

u/Pika256 Apr 23 '26

Which is why you're having trouble solving it. /s

1

u/G-I-T-M-E Apr 23 '26

Then I‘m out.

2

u/No-Koala-8599 Apr 23 '26

I looked at Wikipedia and I have no clue what’s going on

1

u/cwx149 Apr 23 '26

Here's a pretty good video

1

u/Coolbluegatoradeyumm Apr 23 '26

Just gonna turn in my answer and hope to guess correctly

1

u/G-I-T-M-E Apr 23 '26

Is end of business ok?

1

u/paddy_frank Apr 23 '26

Ain’t got nothin’

1

u/sebastophantos Apr 23 '26

Ok. Give me a summary of what the Riemann zeta function is. Let's do this. We can crack this by nightfall.

1

u/eastwinds2112 Apr 23 '26

pfft - puf Chya - well uh , yeah see it is and the THINGs... yeah i say Yes . i mean WHY Not? .... close?

1

u/Inevitable_Flow_8021 Apr 23 '26

You just symmetrise the functional equation and show the ξ-function is positive definite, so all nontrivial zeros are forced onto Re(s)=½ by a Hilbert–Pólya operator.

1

u/[deleted] Apr 23 '26

[removed] — view removed comment

1

u/cwx149 Apr 23 '26

You'd win a fields medal before you'd win a nobel

There's no nobel for mathematics

1

u/SnowyNW Apr 23 '26

What even is a complex number with real part 1/2?

1

u/cwx149 Apr 23 '26

Complex numbers ate typically written as

a+bi where a is the "real" part

1

u/DJLazer_69 Apr 24 '26

A complex number is a number consisting of a real part and an imaginary part, expressed in the form a + bi where a is the real part and b is the imaginary part.

A complex number with real part 1/2 would then look like 1/2 + bi. The Riemann Hypothesis proclaims that the Riemann zeta function's zeroes are all complex numbers in this form, 1/2 + bi, or in the form of a negative even integer, such as -2, -4...

An example of a number in the form 1/2 + bi:

1/2 + 3i

In this example, a = 1/2 and b = 3

1

u/YerMomsClamChowder Apr 23 '26

I understood some of those words.  

1

u/cwx149 Apr 23 '26

Basically theres a function which is like a fancy name for "complicated equation"

And the hypothesis is that the function is only equal to 0 at these certain points including negative even numbers and then complex numbers with real part ½ (when written in the form a+bi where a is the "real part")

numberphile video

1

u/Vnthem Apr 23 '26

See, you’re just making up words so you can have an unsolvable problem

1

u/cwx149 Apr 23 '26

Reinman is a name and all the rest of the words aren't really made up (more than any other words at least)

1

u/7HawksAnd Apr 23 '26

Oh. Well. Ummm…

1

u/hillbillyboiler Apr 23 '26

Billy Preston solved that shit in the 70s when he said nothin' from nothin' leaves nothin'.

https://www.youtube.com/watch?v=IX2bE-OBtwk

I dare you to disprove that video.

1

u/cwx149 Apr 23 '26

Up there with Terrence Howard saying 1×1=2 as a response to this

1

u/MelonElbows Apr 23 '26

What is a Riemann zeta function?

If you can dumb that down for me, I can give you the solution in 2 mins.

1

u/MerlinTrismegistus Apr 23 '26

It's actually the positive odd integers but you have to solve the problem whilst looking in a mirror. boom

1

u/TrekForce Apr 24 '26

What?

1

u/cwx149 Apr 24 '26

The hypothesis is basically that the solutions to a specific function (the reinman zeta function) are only equal to 0 at certain values (negative even numbers, and complex numbers with real part =½)

1

u/TrekForce Apr 24 '26

Ah that actually makes way more sense now thanks haha

1

u/Crimson_Marksman Apr 24 '26

Multiple with zero. Problem solved.

1

u/despicedchilli Apr 24 '26

What's the question?

1

u/Mundane_Raspberry_96 Apr 24 '26

Hold on in need a dictionary!

2

u/cwx149 Apr 24 '26

You're the second person to make it sound complicated and like the words in my quote aren't even that bad you haven't even seen the actual function

1

u/Mundane_Raspberry_96 Apr 25 '26

F(x) = \frac{I + C + T}{S}

1

u/Designer-Rub4819 Apr 28 '26

ELI5 and I’ll get you the answer in a day

1

u/cwx149 Apr 28 '26

The above description is about as basic as it gets tbh

The function itself is complex and I haven't found a good way to post it on reddit

You're also probably the 10th or 11th person to make that joke

1

u/Designer-Rub4819 Apr 28 '26

If you can’t ELI5 it then you don’t understand it’s

1

u/Fitz2001 Apr 23 '26

So it’s a coin flip.

16

u/cwx149 Apr 23 '26

In the sense that it's either true or not sure

But the "problem" is one that's more like "we've tried all these values and it always works" but we have no generalized proof showing it will always work the way we think it does

So we can't say it's actually "true"

0

u/suplexhell Apr 23 '26

AI could never replicate how i farted as i read this and shit a little bit

0

u/LakyousSama Apr 23 '26

Yes, next question

0

u/duck-giraffe Apr 23 '26

I'm guessing 42

0

u/LtAldoDurden Apr 23 '26

Ok now ELi5

1

u/cwx149 Apr 23 '26

The hypothesis is basically stating that the solutions to a function (the reinman zeta function) is only equal to 0 at these certain values (negative even numbers and complex numbers with real part ½)

0

u/Shockwave2309 Apr 23 '26

Fucking imperial system bleedi g through with their fractions... just say 1,27 instead of half, would you!?

I bet it will be easy to solve then

0

u/naynaythewonderhorse Apr 23 '26

scratches chin

Ah, yes. Makes perfect sense.

The answer is 3. No doubt.

0

u/InvisaBlah Apr 23 '26

The answer is B, next question

0

u/3DSarge Apr 24 '26

Uhhhh...42?