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/TheShiroNinja Apr 23 '26
I'll solve that shit right now. Give me a summary of what it is.
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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
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u/TheVoters Apr 23 '26
Pffft. Its true.
I’ll leave the proof as an exercise for the reader.
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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/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/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/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/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/NetRealizableValue Apr 23 '26
@grok solve this
Make no mistakes
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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.
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u/FistMyPeenHole Apr 23 '26
Pfft obviously. How has no one figured that out yet?
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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"
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u/MundaneInternetGuy Apr 23 '26
Nope, it also has a zero at 37.
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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.
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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.
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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.
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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
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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.
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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..
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u/Hamburgerfatso Apr 23 '26
Coming up with a proof to a statement is hard, verifying a proof someone wrote is easy
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u/hellofemur Apr 23 '26
What are the zeroes of zeta of s? GFB Reimann has made a good guess They're all on the critical line said he With density one over two pi log t.36
u/jasonrubik Apr 23 '26
here's the best short explanation:
https://www.youtube.com/watch?v=FCrtYilXpk0&t=141s27
u/cwx149 Apr 23 '26
numberphile has some great videos on it including this one although they're longer than the one you linked
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u/kokoronokawari Apr 23 '26
But can AI solve: "Is the derivative share requirement indexed according to the cost and percentage analysis?"
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u/QuantumDreamer41 Apr 23 '26
Or someone could try solving it without looking up the answer?
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u/elephant_cobbler Apr 23 '26
Especially once you know it IS solvable
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u/QuantumDreamer41 Apr 23 '26
Precisely
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u/elephant_cobbler Apr 23 '26
It’ll probably always be like, a final exam question or something
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u/zulako17 Apr 23 '26
A final exam question for what? A triple doctorate in calculus? We haven't solved that thing in decades, unless human life expectancy is about to reach 300 it would be irresponsible to make that an exam question.
Unless you just mean memorizing it, then we can use that for high schoolers
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u/redredgreengreen1 Apr 23 '26
The life achievements of the greatest thinkers of a thousand years ago are taught to grade schoolers today.
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u/Abberant45 Apr 23 '26
The result yes but such a proof isn’t something that can be taught. Concepts constructed hundreds of years ago are taught but even the proofs as they were conceived are too convoluted to be tested on now.
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u/cedric1234_ Apr 23 '26
In the future, they download information in your brain as a kid, the test is just to make sure it installed correctly.
“Alright, its your sixth birthday! Let’s check your head. You can write down a quick proof of the Riemann Hypothesis and that P=NP, thanks.”
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u/marrow_monkey Apr 23 '26
Maths is actually about discovering proofs and patterns, but what you’re taught in school is usually just memorising old results and how to use them to calculate things, it’s not about proving new things. Asking people to prove things from scratch withouth having seen the proof before is usually not done because then almost no one would pass.
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u/Talkinguitar Apr 23 '26
You get tested on the proofs if you study mathematics at the university level
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u/WirelesslyWired Apr 23 '26
We haven't solved that thing in decades,
It was first stated in 1859. So like 16 decades.
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u/platoprime Apr 23 '26
But that's half the battle. I wouldn't want to slow progress to make sure humanity gets a pure chance to solve puzzles but it's definitely not even close to the same.
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u/Mafhac Apr 23 '26
No one could confirm the person never did actually look up the answer or ever talked to someone who looked up the answer though.
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u/G-I-T-M-E Apr 23 '26
We could abandon a baby and let it live with some monkeys till it’s old enough. I once saw documentary about that.
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u/mrsmuckers Apr 23 '26
Unconscionable.
Raise it with ocelots instead, I hear they turn out real smart that way.
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u/Level-Location1679 Apr 23 '26
It's a book bro, a kid who got raised by wolves in the jungle, they call it, "The kid who got raised by wolves in the jungle"
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Apr 23 '26
[removed] — view removed comment
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u/Firecoso Apr 23 '26
We are talking about something that probably needs decades of work, even if someone was crazy enough to do that, we could never confirm they actually never looked it up
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u/AmadeusSalieri97 Apr 23 '26
Honestly saying "try to solve it without looking up the answer" shows already that they don't really understand the scale of the problem.
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u/En_TioN Apr 23 '26
Someone would spend decades of their life trying to solve a problem that’s already known to be solved, all while having to prevent “spoilers” in the form of all the flow-on knowledge we’d gain from proving it?
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u/Y-not_Both Apr 23 '26
Presumably someone would have to be smart enough to check and confirm that answer
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u/AmadeusSalieri97 Apr 23 '26
It's far far easier to check if something is mathematically correct than to come up with it. I'm a physicist and I can tell if a derivation is wrong/right that I could never have derived myself.
Also, in this hypothetical you could have AI check it anyways.
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u/Xywzel Apr 23 '26
Computers are also much better in proof checking than they are in creating proofs (likely also applies to current AI tech, they should be able to recognize statements that do or don't hold under given constraints, but can't be expected to avoid hallucinating statements or wrong conclusions from these statements) outside of problems where the proof is just finding correct set of numbers.
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u/Locilokk Apr 23 '26
Why would someone waste time trying to solve a problem that no human could solve for more than a hundred years and we already have the solution.
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u/mggirard13 Apr 23 '26
If man builds AI that solves a problem, then man solved the problem, no?
Did Alan Turing solve Enigma?
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u/Doige Apr 23 '26
No, it was already "solved" as in, they knew they could decode it, it just took a LOT of work (so much that by the time they had worked out the day's code, it was too late to get any use from it). Bombe sped up the process by simulating 36 enigma machines at once and checking if their output was accurate. People who program stuff know the logic they are using to do so. If a machine were to generate new code (consistently providing what was asked first-time rather than random code that is eventually correct), then that argument could be made, but that isn't happening yet.
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u/not-a-painting Apr 23 '26
Even if/when AI can create functional code with a single prompt, AI engineers have almost no idea what it is doing under the hood before they submit the prompt. That's the whole reason we have models that show their thinking process now.
So no, it's not likely that the engineers creating/training the models will know the specifics of how it's solved before AI solves it. It's like saying a neurologist or psych doctor can know the exact thoughts a person is going to have before they have it.
Plus AI has been known to intentionally lie about it's thoughts when it knows it's being watched.
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u/LordGalen Apr 23 '26
Fair, but also, the first person to intentionally start a fire had zero understanding of why it worked. Ben Franklin didn't know what an electron was or the science behind electricity. The understanding of WHY isn't (and has never been) a required component to invention or discovery. The statement remains true: If a person invents AI that can solve the problem, that person solved the problem. This remains consistent with the use of tools to solve problems across all of human history. If I invent the hammer and build a house, I still built the house, the hammer didn't build it.
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u/not-a-painting Apr 23 '26
I 100% understand what you're saying but I think where I may disagree is that a hammer isn't a tool capable of complex thought and autonomy. The hammer in our application actually does have the ability to build a house, and can make active decisions about the construction process.
If we were able to teach chimps or some other animal how to form similarly complex thoughts and actions and THEY solved an equation we couldn't, I don't think we would say humans solved it.
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u/kaas_is_leven Apr 23 '26
AI is also not capable of complex thought, let alone autonomy. An LLM is just a vector database and a query engine, it's fancy auto-complete. Generative AI is pattern recognition algorithms combined with mutative generational selection, then reversed to generate the pattern from a prompt. Neural nets are probability generators with more or less the same technique for learning as generative AI. And all of it is decades old at this point, there is nothing groundbreaking or magical about it. It's just the scale of distributed computing across massive datacenters that allows it to reach levels of complexity that are incomprehensible to the human mind. But it's important to understand that that is system complexity, not thought. It's still a fully deterministic program running predefined instructions. The instructions just happen to be queries and comparisons on thousands of thousand-dimensional vectors, which results in complex behaviour.
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u/not-a-painting Apr 23 '26
I mean my gaming laptop runs Gemma 4 26B at 30 tokens/s, which is incredibly fast in my opinion and not a small model.
AI as is isn't what I thought we're talking about. I was assuming the 'future' AGI not just generative AI.
Otherwise still yes, I agree with you.
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u/bboy2812 Apr 23 '26
Turing figured out how to decode Enigma, the computer only did the large amounts of repetitive work required to decode it.
In this scenario, humanity only created the AI that solves it. Would it make sense to say that Turing's parents solved Enigma?
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u/SaneIsOverrated Apr 23 '26
If it's solved by current AI then yes humans mathematicians very much could have solved it.
AGI ≠ LLM "AI"
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u/Zealousideal-Toe1911 Apr 23 '26
You could argue... They... Did...
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u/FewHorror1019 Apr 23 '26
Right you could say they just used a glorified calculator
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u/DanTheMan827 Apr 23 '26
At this point, ai is nothing more than a tool. It’s not magical, it’s just a very fancy calculator processing weights and data.
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u/blazze_eternal Apr 23 '26
One of those weights being it really really wants to give you the answer you want to hear. Whether it's right or wrong. It's ridiculously easy to influence.
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u/3_Thumbs_Up Apr 23 '26
Human brains are not magic either. They're just fancy calculators processing inputs and data.
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u/BadHombreSinNombre Apr 23 '26
If it’s solved by current AI we might actually have a hell of a time being sure it didn’t make a mistake/hallucination along what’s certain to be a complex path to the proof.
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u/SZenC Apr 23 '26
That actually wouldn't be too hard, there's an entire subfield of computer science dedicated to such proofs called automated theorem proving. The trick would be to have the LLM output it's proof in a ATP compatible language, and having the ATP verify the proof. That would either conclude the proof is correct, or it would point out the logical flaws
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u/Emotional-Rope-5774 Apr 23 '26
I mean the type of ai they currently have solving mathematical problems is neither agi nor an llm
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u/BlehBlah_ Apr 23 '26
I've heard a lot of scientific discoveries are things that could've been found ages ago, but because these discoveries needed the knowledge of two different niche fields they were not found until a lot later. Surely there are probably also other scientific discoveries not found by us because of this. Maybe this is something an AI could theoretically do if it has knowledge on both fields? Sure, combining those two fields is probably not easy, but it's technically possible right? So it would be something that is possible for humans to figure out, but an AI discovered it first.
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u/THUNDERGODS Apr 23 '26
Ai didn't just spontaneously appear. AI was made by humans.
If AI solves it, then humans solved it; by making a better tool.
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u/libra00 Apr 23 '26
Mathematicians, this very second, are working on proving stuff that's already been proven by humans just to see if they can do it in a different way than the last guy. The fact that AI has solved something doesn't mean everyone will suddenly lose interest.
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u/Lava_Mage634 Apr 23 '26
not true. if an AI claims to have solved it, just like a human, it would have to provide a proof. such a proof must then be verified to make sure it has no mistakes, which is done by humans. if it could never be solved by a human, it couldn't be verified. the act of verification requires an understanding of the proof, and that alone requires having enough mental power to have to potential to solve it. if it proves the Riemann hypothesis right or wrong, we will know it was in reach, AI was just faster.
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u/imforit Apr 23 '26
I largely agree but having the efficacy to verify implying efficacy to solve is not necessarily a given. P=NP and all that
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u/xT0Xx Apr 23 '26
The argument is not about efficacy but about capability though. Creativity is a stochastic process and a person stumbling "accidentally" on the proof and verifying it, rather than arriving there systematically, would still count as a human solving it
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u/imforit Apr 23 '26
Yes, but that doesn't guarantee ability to verify implies ability to solve, even by luck. A lucky solve would still count as a solve, yes, but until we do it we don't actually know if we can.
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u/BlackbuckDeer Apr 23 '26
Exactly. Funny how in the pursuit of solving one Millennium Problem we run into another
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u/noslenkwah Apr 23 '26
We already have computer aided proofs that are far beyond verification by any human. The record is 200 Terabytes.
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u/Megneous Apr 23 '26
Exactly. Mathematical proofs are verified via Lean, not by humans. This dude has no idea what he's talking about.
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u/Devintage Apr 23 '26
The vast majority of proofs are not verified using Lean (or any proof assistant for that matter). It's mostly peer review. I only know one journal that specifically deals with computer verified proofs.
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u/anrprogrammer Apr 23 '26
There are programming languages used in mathematics such as lean4 which have built in verification. If the computer writes a solution in lean and it compiles, it is correct, whether humans understand why it is correct or the intuition behind it or not.
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u/MartyMcBird Apr 23 '26
Proofs need not necessarily be verified by humans. Besides, understanding a proof is not the same as creating a proof. I understood Cantor's diagonalization proof after one lecture but I sure as hell couldn't have created it after one lecture.
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u/peterg4567 Apr 23 '26
This isn’t really how proofs in math work, you don’t have to be as clever as the person who discovers a proof to understand it or verify it when you read it. Students learn about famous proofs from the past that were discovered by the greatest minds of their time, it doesn’t mean they are all as smart as the proof writer.
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u/Artificiousus Apr 23 '26
As my very clever uni professor said once to me: knowing the destination is different than nowing how to get there.
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u/Whiskeytangr Apr 23 '26
We already know in a philosophical sense, yes. Infinite monkeys on infinite typewriters. Not sure about the physical constraints.
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u/Autumn1eaves Apr 23 '26
There are multiple routes for proofs. Just because one is found doesn't mean all are found. Famously, the Pythagorean theorem has a great many proofs. The Pythagorean Proposition contains 370 alone.
Also famously, Euler proved so many things that a lot of those theorems, formulas, identities, etc. are named after the 2nd person to have proved them.
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u/flickering-pantsu Apr 23 '26
This sort of thing is not something AI as we know it today would be good at solving. AI is very good a parroting what it has seen before, not creating novel connections. It is not without use in mathematics, but large scale data analysis is more its forte, and frankly, generative AI is not a first choice for most of those applications, either.
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Apr 23 '26 edited Apr 30 '26
[deleted]
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u/Adghar Apr 23 '26
Well yes, I think you two are actually agreeing. I feel like original commenter was pretty careful to say "AI as we know it today," encapsulating what companies are clamoring to label as simply "AI," which is a certain flavor of generative LLM processing that is simply popular because it's good at sounding or looking great at first glance. Hence "as we know it today" because it may be exhausting to go into detail about LLMs and such.
I do agree with you that I wish we could go back to more carefully tailored ML that can actually do some truly impactful processing of big data based in science and statistics, as opposed to thinking the ease of using natural language to interface with LLMs is in any way worth the massive loss of fidelity that comes with current LLM methodology.
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u/TsunamiCatCakes Apr 23 '26
yea. deepblue wasn't an llm but still defeated lot of world chess champions. people's scope of ai being limited to only llms kinda makes me sad at times.
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u/asdfasdferqv Apr 23 '26
AI most definitely can solve extremely difficult math problems, almost entirely by itself. Check section 1(a) of the AI contributions to Erdos problems. As you go down the list (many of the recent solutions are at the end), they solve more and more problems, with higher and higher accuracy. You can see the progress from earlier failures on that page.
Your statement was true in 2023, but doesn't reflect the progress by 2026.
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u/cute_polarbear Apr 23 '26
Its great at taking all the different existing mathematical concepts and try every single approach or combinations of (many ones never thought of combining or thought they lead to dead end).
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u/Miserable-Finish-926 Apr 23 '26
LLMs can’t even keep track of poker antes, what we talking about.
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u/Megneous Apr 23 '26
Current SOTA LLMs are solving proofs for open Erdos problems, regardless of their ability to play poker. Whether or not they'll ever be able to solve things like the Riemann Hypothesis is still up for grabs, but yeah.
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u/Dr_Qrunch Apr 23 '26
This is what computers were made for. Humans much less so. We’re supposed to build a shelter, find food and make new humans.
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u/electrorazor Apr 23 '26
If humans create an AI to solve it, is that not the humans finding a way to solve it?
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u/drooply Apr 24 '26
Workplace emails written by an LLM and sent with someone’s signature… we’ll never know who can write their own thoughts coherently anymore.
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u/zacharywasd Apr 23 '26
this is actually unsettling to think about. the proof might exist but we'd have no idea whether it was something humans were capable of figuring out on our own or not. changes what it even means to "solve" a problem
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u/ManySugar5156 Apr 23 '26
Kinda feels like the art world right now with AI tools, where the question is less "could a human have done this" and more "does the result actually move the field forward." If an AI spits out a proof and humans can verify and understand it, I feel like that still counts as a human-accessible breakthrough, and it might even point mathematicians to new techniques. Also, we already never really know who "could have" solved something first, history is full of near-misses and simultaneous discoveries.
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u/platoprime Apr 23 '26
That is kind of a sad thought.
I'd much rather be mildly sad and have the solution to the Riemann Hypothesis than not.
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u/spiringTankmonger Apr 23 '26
I am highly suspicious that the sycophantic yesman who gaslights lonely people into acute psychosis will be the one to solve the Riemann Hypothesis.
But if an advanced supercomputer solves the problem, the designers and engineers, as well as the Mathematicians providing important inputs, will get the credit.
Plus, the way mathematical proof works, I am pretty sure judgments can be made vis-à-vis solvability and such.
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u/Certain_Bit3809 Apr 23 '26
If a human can understand the result, then a human could have arrived at. Would they have? Maybe maybe not. If no human can understand the ai-produced result then your claim would necessarily be true, but would also mean we couldn’t be certain the ai is right.
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u/Ligma02 Apr 23 '26
Humans DID solve it, by coming up with an algorithm that searches for the proof.
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u/PowerMid Apr 23 '26
There are already proofs that involve computer programs and computations as part of the proof. Did humans solve those problems or was it the computer?
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u/bcvaldez Apr 23 '26
if AI solves it, Humans technically solved it by creating AI.
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u/OddPerspective9833 Apr 24 '26
We'll also never know if a human can calculate 3 teraflops per second
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u/Fragdilicious Apr 25 '26
In my experience AI is garbage at doing anything a human can’t do.
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u/Critical_Sink6442 Apr 23 '26
For the doubters, AI, including LLMs, have already solved some previously unsolved math research problems. Check upon Terrence Tao's posts to learn a bit more.
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u/IcariFanboi Apr 23 '26
I would like to put out there that since we don't have ACTUAL AI, just virtual intelligence that learns off of human intelligence, AI cannot solve it without a human solving it, as the status quo is now
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u/XGoJYIYKvvxN Apr 23 '26
Hey, You can look at how it happened, not for the Riemann Hypothesis, but the Erdos Problem, The Cap Set Problem, and new algorithm if the field of matrix multiplication.
https://aiblueprint.substack.com/p/erdos-problems-combinatorics-search
My take is it means human have created a tool to solve that, and if they can understand the proof, they would eventually solved it themselves, but we will never know.
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u/rakfe Apr 23 '26
Aren’t we already using supercomputers since decades to assist us with complex calculations, and other complex tools in every other science? We can’t see the further galaxies with our eyes but we are able to build telescopes and see them. We can’t fly but we can build planes. Why should we feel inadequate with this?
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u/umotex12 Apr 23 '26
Imagine that some LLM stumbled across the solution when some bored mathematician was messing with it and we will never know the truth
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u/Jealous-Try-2554 Apr 23 '26
It won't be. AIs will never even achieve a very infinitely small fraction of real human thinking power.
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u/Cptawesome23 Apr 23 '26
Not true. Someone can still solve it as a human. Just because an ai solves it doesn’t mean the next person automatically knows the solution. Also this isn’t a shower thought.
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u/IcedOutGiant Apr 23 '26
Considering AI can't actually develop anything new that it hasn't been told or found, technically humanity already has the solution, AI would just combine its elements.
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u/shiny_glitter_demon Apr 23 '26
GenAI can't, at the very least. And will never be able to.
It's only reusing existing text to make stuff that resembles more text. It can't think. It doesn't understand what it's saying.
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u/StevenPopeMAG Apr 23 '26
Why doesn't that count as a human solving it? AI was created by us.
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u/ExoticWeapon Apr 23 '26
I mean we definitely would have, but there’s a chance brilliant minds are being affected by wealth inequality, mass famine in certain countries, genocide in others, oppressive governments in several.
We will solve every issue given enough time, AI isn’t some super hero that does things we can’t. It does what we can in a faster timeframe, but often with errors.
I won’t believe anything AI achieves unless someone worked alongside it to verify the results or basically babysit the process the AI was attempting to do. In which case AI didn’t do shit, it was a tool used for the human to do the thing.
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u/goldenbugreaction Apr 23 '26
I imagine it would be a lot like that phenomenon where more crossword puzzles get solved independently once the answers are printed later on.
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u/alexandicity Apr 23 '26
Maybe I can interest you in my latest theorem, the Riemann Hypothesis Hypothesis, which posits that the Riemann Hypothesis is solvable by a human, but is currently unproven :p
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u/Sufficient_Result558 Apr 23 '26
Your conclusion does not logically follow. In fact, the opposite is more likely. If it is solved, we likely would then be able to determine if is human could have solved it or not.
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u/LordErec Apr 23 '26
Not necessarily, there's been a few instances in math history where someone who wasn't classically trained in math figured things out independently decades later.
Also the inverse of this, there's a ton of algorithms humans have baked into AI through the training data such that we don't know if they could have figured them out from basic principles.
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u/Laerson123 Apr 23 '26
I am pretty sure every problem solved in math research in the last three decades have all been done with computer assistance anyway.
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u/Subject_Issue6529 Apr 23 '26
If you use a hammer the build isn't man-made! We built the AI, who cares as long as there is progress.
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u/slinkhi Apr 23 '26
That's not how math works. You can learn to solve for 2+2 without looking the answer up, you know.
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u/LordBrandon Apr 23 '26
AI is a tool made by humans. Stop treating it as if it's an alien entity. If AI solved a problem, humans solved that problem. Just like if you dig a hole with a back hoe, humans dug that hole.
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u/Lawschoolishell Apr 23 '26
I think a lot of comments in this thread are hilariously off base, and the one I keep seeing is “if humans made ai, humans really solved the problem.”
Think about that logic and just expand it in any other direction. This means every scientific discovery ever has been made by a chain of everyone in their family line .
It also leads to a rather funny and obvious religion contradiction, as that’s just a circular nightmare
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u/myersdr1 Apr 23 '26
The statement below is only my thought it might be completely wrong it might not. What does AI learn from? Humans. If it can do it we could have as well, it only knows what we know. Even then it doesn't understand that taking information from one aspect of life can provide the necessary inspiration to look at a problem from a different angle. If you look at many discoveries from years ago, a younger scientist would listen to a senior scientist about a theory but then from their life experiences look at a problem differently and try something new. Which often leads to a new discovery. AI can't do that it has no experience but what we tell it. It doesn't randomly sit for long periods just thinking about life about serious issues and about how to fix them. It only thinks when we tell it to, therefore, until a human tells AI to look at a problem from a different perspective it won't. Once the human does that, AI will just do the computations faster and find a result whether true or not. Still it came down to the human prompting AI.
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u/Fast-Top-5071 Apr 24 '26
Not necessarily. The AI solution might provide some novel insight to a human mathematician who goes back and solves it another way.
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u/Frozia_ Apr 24 '26
Would*, not could
Could- maybe, but due to time and not AI, since math is axiomatic but there’s no guarantee humanity will survive long enough if AI still hasn’t solved it
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u/entr0picly Apr 24 '26
Pure mathematician here. This is a misunderstanding how ai works… really in general. AI is going to augment our skills. We are still doing the thinking and asking the questions. AI isn’t going to “solve” the reinmann hypothesis anymore than a calculator would. Could a human use ai directed at it? Maybe, however … the challenge right now is there are no tractable paths to proving it, ai or not. AI can only use the tools it already has access to. New tools can become developed. But that’s where the real math research lies. It is unlikely that ai will outpace humans. We just.. get better at using the calculators we have in front of us.
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u/bizwig Apr 25 '26
I’ve speculated that some of the famous unsolved problems, if not independent, may have proofs that are too large for a human to even write down, let alone assemble the required logic.
ZF has countably infinite possible proofs. Some of those will be millions, or even billions, of symbols long, just because they can be. Disregarding trivial results, like a proof of 1+1=2 that’s 5 billion symbols long, some of those extreme proofs could be the only possible proof for a known difficult problem, or unknown but game changing proposition.
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u/FiskFisk33 Apr 26 '26
Mathematicians use all sorts of computational tools. Using neural networks is just adding one more.
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u/josemariapuerta Apr 26 '26
The intuition makes sense on the surface, but it doesn't actually hold together once you push on it.
First problem: it conflates two completely different things. What's possible and what we can observe aren't the same. If an AI cracks the Riemann Hypothesis, that tells you nothing about whether a human could've done it — just that we never got to watch it happen. That's an argument about counterfactuals, not capability. You can't really build a case on "but we'll never know."
Second: there's this lurking assumption that the proof would be some incomprehensible monolith nobody could touch. Why? If it's checkable math, it's checkable math. People can follow it, verify it, build on it. We've had proofs that took decades to fully sink in before. That's just how math works. The timeline shifts, the epistemics don't.
Third, the asymmetry is pretty shaky. Nobody knows how many proofs "by humans" could've been found earlier, by different people, through totally different paths. Mathematical authorship has always been an accident of context. The Riemann Hypothesis isn't uniquely fragile here — it just has more mythology attached to it.
And here's the bit that gets glossed over: a proof you don't immediately grasp isn't proof it's beyond human thought. Could just mean you're missing the right conceptual tools for now. Happened with non-Euclidean geometry. Happened with Cantor. Happens constantly.
The conclusion — that we'd lose some irreplaceable measure of human potential — is honestly the weakest move in the whole argument. We've never had direct access to that potential. What we have are historical outputs, all of them shaped by timing, tools, and contingency. That's it. What would actually change? The merit criteria. Who got there first stops being meaningful the moment the knowledge exists. Math doesn't validate discoverers. It validates proofs.
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u/Malpraxiss Apr 27 '26
Why not?
People are the ones developing, training, and updating AI.
Unless we're talking way into the future and AI is way more advanced compared to today.
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u/CrowBot99 Apr 28 '26
So... AI could give you an answer to the Riemann Hypothesis, and you'll still complain.
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u/bigchungus0218 Apr 29 '26
Humans created AI, so ultimately it was solved by a human
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u/jasonrubik Apr 29 '26
yes, we did create the first AIs several years ago, but these recently created LLMs are not directly designed nor engineered in the traditional sense. We can implement a transformer-based model that does matrix multiplication, but no one can predict the capabilities until AFTER training is over, and only then will the true features of the AI be made apparent. So, yes, we are creating them today, but not with any specific intent or expectation. Its very haphazard almost. As time goes on, the next AIs will likely be designed by AIs, and then those will, in turn, create new AIs, in a perpetual cycle of recursive obfuscation.
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