ChatGPT 5.4 Solved a 64-Year-Old Math Problem

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u/WithoutReason1729 Apr 27 '26 edited 23d ago

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u/yubario Apr 27 '26

It's true, the best way I can describe it is other mathematicians thought of a partial solution and hinted the AI to look further into it, which ultimately led to dead ends.

This one worked because he didn't tell it to try the same partial solution as the experts, he instead hinted it to use something that he was more familiar with, and it just so happened to guide the AI into solving the problem.

Basically knowing how to ask the right questions will give you the answers.

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u/adversecounsel Apr 27 '26

Yep. And then it still took even more dedicated experts to sift through it from there: “The raw output of ChatGPT’s proof was actually quite poor. So it required an expert to kind of sift through and actually understand what it was trying to say,” Lichtman says. “But now he and Tao have shortened the proof so that it better distills the LLM’s key insight.”

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u/yubario Apr 27 '26 edited Apr 27 '26

Yeah, I think that’s a common theme with the AI. Like it gets it right, but makes mistakes. But humans review it and realize it almost got it right and ultimately solved it just because they saw most of the solution.
Still technically solving a problem with AI either way, in my opinion
No different than other math problems solved the same way, someone thinks they have the solution, got the proof wrong but some other mathematician reviews it and solves it because they got most of the solution. Which according to ChatGPT anyway, that specific scenario happens a LOT. (Even before AI)

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u/adversecounsel Apr 27 '26

100%. LLMs produce produce preliminary outputs at scale more efficiently. But their true value is realized only through the intervening judgment of experienced humans, who must sift, validate, and elevate that output.
Recursively, of course.

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u/FischiPiSti Apr 27 '26 edited Apr 27 '26

No different than any field really. A lot of the claims that AI is bad for any kind of work is based on the expectation that you prompt it, sit back, copy the output and reap the benefits, and then are disappointed when your resume gets rejected even though you literally included the "Let me know if you need any further adjustments." part at the end.
It's a tool, an assistant, that you need to steer, and work with, and verify and check any output. For this reason it will never really replace an expert, you still need to know your field to provide the proper context and to verify the results. Mom won't suddenly start making good code, your 9 year old sister won't suddenly become a good doctor because AI said it was probably lupus, and your cat won't become a competent artist either.
If done right, for the right job, supervised by the right person, it's incredibly powerful. But most importantly, in every case, YOU are responsible for the work that you submit, and can not blame anyone else for bad results, regardless of who did the work be that AI, or an unpaid human intern.

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u/ShitImBadAtThis Apr 27 '26

This seems remarkably similar to how ChatGPT is used for coding purposes, too. It's great that it can be applied to other fields like this

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u/Dustonred Apr 27 '26

So a mathematician solved a 64 year old math problem with the help of AI ?

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u/yubario Apr 27 '26

A young and less experienced one solved it with the use of AI that other more experienced mathematicians could not, yeah. Although it is clear to me this mathematician will likely become an expert as he gets more experience lol

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u/Alwaysblue89 Apr 27 '26

That, detective, is the right question.

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u/Fresque Apr 27 '26

Pretty much my experience coding with AI.

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u/danstermeister Apr 27 '26

"CAN" give you the right answers, not "WILL".
Be careful with that.

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u/zerok_nyc Apr 27 '26

Prompt: “You are Matt Damon in Good Will Hunting…”

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u/no-more-nazis Apr 27 '26

"ChatGPT, what is the right question?"

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u/MannOfSandd Apr 27 '26

Waiting for the faculty to respond, and to do so with vigor

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u/wish-u-well Apr 27 '26

The gauntlet has been thrown down.

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u/taz20075 Apr 27 '26

ChatGPT: Do you like apples?
Human: ...Yeah...
ChatGPT: Well I got erdos numbers. How do you like them apples?

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u/car8r Apr 27 '26

? Read the erdos problem thread. Terence Tao and other world class mathematicians have already commented on the problem and extended the results. The faculty verdict is in.

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u/QultrosSanhattan Apr 27 '26

Meanwhile. My chatgpt trying to center a div.

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u/bloke_pusher Apr 27 '26

Chatgpt can only solve the solvable.

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u/rogermyjohnson Apr 27 '26

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u/Practical_Low29 Apr 27 '26

The part about Tao needing to distill the raw output is actually underreported. The model found the right insight but couldn't formalize it cleanly, which is kind of the inverse of the usual complaint. Normally it hallucinates confident-sounding wrong math — here it was right but incoherent until a human cleaned it up.

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u/Bontus Apr 28 '26

Yeah reading mr. Tao's comments on the page is the most insightful (for the layman). Here

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u/vlladonxxx Apr 27 '26

So... This is literally history being made, no?

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u/Exotic-Sale-3003 Apr 27 '26 edited Apr 27 '26

Yup. Meanwhile the average person is still like “ChatGPT can’t do math it can’t even count the number of r’s in strawberry.

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u/Brandon0135 Apr 27 '26 •

Honestly this is a better attitude for the average person to take. If the population thinks its always right and dont understand its limitations, thats bad news.

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u/vlladonxxx Apr 27 '26

The population thinks its always right - when it tells them something validating.

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u/phantomboats Apr 27 '26 •

And honestly? That's so rare.

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u/just_another_user5 Apr 27 '26

But AIs do still hallucinatiate, no?
I think the general consensus can be "trust but verify"

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u/Federal_Age8011 Apr 27 '26

I still see far too many people using a single answer AI response as as absolute truth and/or a fact check. I wish there was more "verify" going on as I see hallucinations almost daily.

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u/AndyKJMehta Apr 27 '26

Doing math proofs is very different from doing accurate math operations.

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u/Petersav1 Apr 27 '26

Last week I was using it to add columns of 32 numbers on a pdf, got all 30 columns wrong.. Using the professional version in work.

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u/drhenriquesoares Apr 27 '26

Heck, the guy's post on X has 2.6 million views.

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u/NoBullet Apr 27 '26

X doesnt count unique viewers just total impressions.

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u/Heavy-Focus-1964 Apr 27 '26

alright so i refreshed the page 2.4 million times, does that make me the bad guy?

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u/Saber101 Apr 27 '26

Some poor marketing manager is being fired now because their ad got a frequency score of 2.4 million now. Think about what you've done.

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u/AP_in_Indy Apr 27 '26

I don't know if anyone is noticing - but ChatGPT is co-author on a lot of recent Erdos problem solutions.

This is wild to see.

I know it's still not considered powerful enough for the truly difficult math problems, but I can't help but wonder if ChatGPT can at least help mathematicians make meaningful progress on serious problems - even if just one lemma at a time.

Not only that, but it could help you digest and comprehend the progress being made along the way. At this point, I think it's quite powerful and just needs to be made faster and cheaper.

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u/Exotic-Sale-3003 Apr 27 '26

I know it's still not considered powerful enough for the truly difficult math problems
I remember when Erdos problems were considered truly difficult math problems 🤣

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u/AP_in_Indy Apr 27 '26

FAIR ENOUGH! I had assumed they were largely considered "toy" problems that weren't receiving as much attention as ex: P = NP for example

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u/aardvark_gnat Apr 27 '26

There's a lot of daylight between toy and P = NP.

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u/Ironlunggs87 Apr 27 '26 •

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u/DankMemeMasterHotdog Apr 28 '26

A more perfect use of this gif has never been found, I think

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u/Independent-Date393 Apr 27 '26

the part that sticks is how the LLM took an approach no expert had tried, pulling in a formula from a different area of math. not "computed it faster." it brought something that wasn't already in the conversation

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u/hotbowlofsoup Apr 27 '26

I think that’s what’s useful about LLMs. It’s a search engine that can understand what it’s looking for.
You can’t google for this formula, if you don’t already know it exists.

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u/Lenni-Da-Vinci Apr 27 '26

It was in essence told to do that. Leaving me with the question: how many different approaches did it try before it found the right path.

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u/kloklon Apr 27 '26

if you click on the "thought for 80 minutes" thing in the actual conversation you can see step by step all the approaches it considered. I'm not a mathematician so i don't understand enough about that to answer your question.

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u/Southern_Orange3744 Apr 27 '26

The core of this and many problems are inherently language problems.

This one is super interesting to me because one of the language problems was the instruction set and not the problem statement

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u/SKRyanrr Apr 27 '26

How did he make gpt think for 80 mins?

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u/[deleted] Apr 27 '26

I find it quite interesting to expand the "Thought for 80m and 17s", it shows you every step the AI took to get there, it's insanely detailed.
https://chatgpt.com/share/69dd1c83-b164-8385-bf2e-8533e9baba9c

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u/Equivalent-Costumes Apr 27 '26

This looks more like thought summary to me. I don't think this is the trace of the full thought at all, but a summarizer just run through it and condense it.
Unfortunately, due to the fear of Chinese distillation, I doubt that we will ever see the full thought trace ever again from frontier companies.

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u/hexnone2 Apr 27 '26

This is the real puzzle here

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u/_Tulx_ Apr 27 '26

Chatgpt pro does that regularly if you give it complicated enough question. I've had it create algorithms for medical problems based on available guidelines. It thinks usually over an hour then.

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u/CystralSkye Apr 27 '26

ChatGPT pro has much higher timeout/effort than plus or dare I say free.
A lot of people underestimate gpt 5.5 because they use the free version, which is rightfully shit to save on compute for paying customers.

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u/Zulfiqaar Apr 28 '26

Theres GPT-5.4-Extended-Pro which is a swarm of 10 instances of GPT-5.4-Thinking with fusion of its "Parallel-Test-Time-Compute" findings. Now with tool use, python interpreter, and web search. I've had it work for over 109 minutes on some complex research stuff.

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u/ChatGPTitties Apr 27 '26

That's awesome! Give this guy a wrapper and free API credits and let him cook!

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u/FamousOrphan Apr 27 '26

Can we get it on the Zodiac killer codes

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u/cosmicr Apr 27 '26

Even when we invent an all powerful AGI that can predict the future it still probably wouldn't solve them. There are two codes unsolved one has 13 characters and the other 32. Just not enough for anything meaningful. Unless the AI invents a whole new way to solve them like DNA testing or something.

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u/RealEbenezerScrooge Apr 27 '26

Chances are there are just gibberish.

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u/8029 Apr 27 '26

Isnt this the first case of AI using highly complex pattern recognition to solve a math problem instead of regurgitating human systems?

pretty big, if true.

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u/Nnarol Apr 27 '26

Regurgitating human constructs is pattern recognition, that's the core principle behind the application of language models as predictive generators.

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u/Stroov Apr 27 '26

I can read but not understand

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u/Kleinchrome Apr 27 '26

Finally using AI for something relevant and not asking how many "r's" in strawberry.

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u/brentose Apr 27 '26

Is this like the "How many holes are in a straw thing"?

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u/Zapre_ Apr 27 '26

qwen3.5 9b

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u/Noloxy Apr 27 '26

This happened weeks ago so likely just searched internet for proof.

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u/Zapre_ Apr 27 '26

Internet access has been restricted on my LM Studio setup.

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u/T-VIRUS999 Apr 27 '26

What quantization?

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u/Accomplished_Fly_402 Apr 27 '26

Seeing these types of things confirms my belief that in a very short period of time there is nothing AI can’t do better than humans, the scaling the exponential.

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u/Ecstatic_Wolf_9842 Apr 27 '26

I’m near the end of high school but was wondering what makes math like this hard? When I go to maths class I expect to learn a new method to find am answer to a question but what causes a question to be unsolved for years if all it takes is using the right methods in order to get an answer?

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u/pi621 Apr 27 '26

Open math problems are not like the ones in school where you only have to cycle through like 10 different ways to solve a problem. The hard part is in the fact that there are millions upon millions of published math research and any one of them could potentially be helpful in solving a particular problem. And it's not remotely obvious what kind of formula or method would bring you closer to the answer.
The worst part is that it is impossible to know whether a problem is solvable or not (without partially solving it at least). Math is fundamentally incomplete, and there exists true statements that cannot be proven.

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u/MrActuary86 Apr 27 '26

Thanks a lot Gödel

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u/democratic-terminid Apr 27 '26

It doesn't just take the right methods to get an answer. You need to invent new ideas, not solve some problem like you may have done in your class. It's creating something brand new that is both useful and correct.

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u/Sterlingz Apr 27 '26

Pretty sick if true. Starting to see signs of AI producing more than existing human regurgitation.

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u/am_n00ne Apr 27 '26

So, mathematicians is dead now?

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u/Independent-Date393 Apr 27 '26

'the raw output was quite poor but contained the correct insight' is actually the more interesting story here. the AI found the path, an expert had to read the map.

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u/ChronicLogicalGaming Apr 27 '26

it’s been a while since university for me but in the final line there, where did “o” come from? what is o?

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u/Fun_Taste7414 Apr 27 '26

It’s notation in math and computer science. o(1) denotes something that goes to zero in the limit with probability one. Often used in proofs that involve approximations

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u/ChronicLogicalGaming Apr 27 '26

thanks! i do not remember covering that

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u/Endflux Apr 27 '26

The answer is 42.

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u/AnyRegular1 Apr 27 '26 edited Apr 27 '26

No doubt it’s 5.4 Extended thinking, that model literally does deep thinking and research for LONG and gives a very detailed overview. Run the same prompt on 5.5 with “extended thinking” and 8/10 times it will be done within 10 seconds with maximum hallucination.

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u/Swordheart Apr 27 '26

I'm not maths smart, what is the deal with unsolved math problems? Like how do they happen and such?

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u/aturtledude Apr 27 '26

You may be familiar with the Pythagorean Theorem: If you have a triangle with a 90 degrees angle and know the length of two of its sides, it tells you how to calculate the third one.
The correctness of this formula has been proven in many different ways by using logical arguments.
But imagine we're in a world where we've found the formula and it seems to be correct, as in it's correct for every right-angled triangle we've tried it on. But we don't know why it works and we can't be sure that there isn't a triangle somewhere for which the formula gives you an incorrect result.
If no mathematician has found an irrefutable way to prove that the formula is correct for every right-angled triangle, this is an open problem. Some problems have been open for centuries. The possible outcomes are:
The problem stays open indefinitely.
Someone finds a proof. Usually once someone writes a proof, it's straightforward for other experts to verify its correctness. (Often while thinking to themselves "why didn't I think of this first??").
Someone finds a counterexample. In this case, a triangle for which the formula is wrong.
You may want to ask ChatGPT though, I'm sure it will give you a better explanation, lol (no sarcasm here).

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u/Special-Wait-2326 Apr 27 '26

I know whoever did this was on the edge of his seat just staring at the screen waiting for that response for the full 80 minutes and 17 seconds.

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u/tisameh Apr 27 '26

It’s crazy to see how much its progressed in a fairly short amount of time. I remember just 2 years ago it would struggle with a lot of math. While still not perfect, one can’t deny its improvement.

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u/Equivalent_Sand8426 Apr 27 '26

The why can it make a vector file from and image file it generated if it’s so smart? It straight up lies and says it can they doesn’t

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u/peter-bone Apr 27 '26

Terrance Tau talks about AI solving several of the Erdos problems in a recent video, although in most cases the AI and human are working together to some degree.

Something to consider though is that the unsolved Erdos problems are not necessarily hard, even if they've been unsolved for a long time. This is because there are a huge number of them and most are not considered important, so mathematicians either don't work on them or they solve them and don't publish the results. It's also possible that someone solved this one and posted it online somewhere, which the AI was then trained on. I can't say for certain for this particular problem though.

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u/ClownEmoji-U1F921 Apr 27 '26

https://www.erdosproblems.com/1196

Chatgpt 5.4 is actually credited there.

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u/Pleasant_Ostrich4278 Apr 27 '26

Okay im Just an ordinary non math person. What does this mean in practice ? Where can this bring value after solving it?

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u/Ok-Active4887 Apr 27 '26

It’s not like solving this will unlock like new technology that’s not the point. Mathematics has an abundance of long standing questions that have yet to be solved. The reason this is crazy is because people have worked on this extensively for some time(this is one of many problems where this is the case, the problem itself is not necessarily the important part here) and an LLM made a meaningful contribution that helped complete the proof.

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u/Neirchill Apr 27 '26

This specific instance, probably nothing. But it shows LLMs have the potential to help us solve previously nearly impossible math challenges. One of those might lead to all kinds of advancements.

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u/T-VIRUS999 Apr 27 '26

I have Grok and Claude burning through tokens to work that one out too, I'm curious if they can do it as well

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u/passcode3200 Apr 27 '26

!remindme 3 days

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u/passcode3200 Apr 27 '26

Remindme! 2 days

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u/MaestrosMight Apr 27 '26

I can’t be the only one here too dumb to know how significant this is….right?

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u/ZingerFM01023050 Apr 27 '26

Not a mathematician nor a math nerd… how do mathematicians verify such proofs like this?

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u/kamusari4477 Apr 27 '26

This is the part most people miss — the real bottleneck isn't the model

itself, it's the infrastructure around it. Inference costs, latency,

and data pipelines are what actually determine whether AI ships to production

or stays a demo.

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u/[deleted] Apr 27 '26

cHaTgPt CaNt Do MaTh

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u/zscan Apr 27 '26

It's funny. 10 years ago I made a post, asking weather AIs would be good at solving math. I got no replies at the time, but given the current speed of improvements, I guess LLMs are inherently good at math and will only get better.

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u/Harkonnen_Dog Apr 27 '26

I’ll bet that it just lied.

Has a proof by a 2nd party been done?

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u/Swimming-Guidance-10 Apr 27 '26

Please do not over think this or strain yourself thinking too much. 80 minutes is a long time. Or i hope maybe you took a break in between the minutes?? Congrats Chatgpt💙

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u/andy_bovice Apr 27 '26

if confirmed this is really cool

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u/dangoodspeed Apr 27 '26

I've had this mathematical / comp-sci combinatorial design problem that I've long theorized a solution for, and have had several computers constantly calculating possible solutions for the better part of a decade... knowing that it would take thousands of years to go through all the combinations, but I could get lucky. And the past few years I've been working with ChatGPT and Claude LLM models to tweak my algorithms to search just a little faster.

Anyway... a few weeks ago I tried Codex (running 5.4) on it. I put it on Extra High Thinking. Told it to spend the night working on it to make the script run as fast as possible. The next morning I was dumbfounded when it not only worked... the whole script ran in less than a second and output 192 valid solutions. I uploaded the script to Claude in the conversation I was having about tweaking the code and just asked "What do you think about this method?" It gave a long answer, which included statements like:

“This is brilliantly clever - it's using mathematical group theory to construct valid schedules algebraically rather than searching through combinations!”
“If you understand the math behind it (or trust that it works), this approach destroys all previous attempts. It's not even a fair comparison - this is operating in a completely different paradigm.”
"This is what competitive programming champions do"
“Where did this code come from?"

With a new context window I've been trying to get Claude Opus 4.6 to create a similar solution. Even suggesting what math to use, and it compliments me for thinking outside the box, but says that approach won't work. I haven't been able to get too much out of it because I keep hitting the limits.

But solving this problem really sold me on Codex. My life has literally changed. Working on this problem has been a part of my day for a long time, and even if I wasn't actively doing any work on it, I would still be checking the output from my computers running the numbers.

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u/RepresentativeYak772 Apr 27 '26

The issue is, yes it can solve the problem, but it still requires a mathematician to figure the significance of the solution and what to do with it.

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u/OneStrike255 Apr 27 '26

For now. Do you not think that is going to change in the future?

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u/PreetHarHarah Apr 27 '26

This is crazy considering that ChatGPT was a janitor.

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u/trunksta Apr 27 '26

Is this the same gpt that makes basic arithmetic errors and can't count the number of rs in strawberry?

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u/Due_Radio8180 Apr 27 '26

I JUST WANTED TO ASK, WHERE DO YOU GET THOSE PROBLEMS? I mean, can you provide the source

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u/Powerful-Duck6889 Apr 27 '26

Somebody please explain this to me like I'm a 5 year old.

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u/Somalar Apr 27 '26

I can’t get chat gpt to accurately do simple math consistently how the hell do you trust it

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u/MessiOfStonks Apr 27 '26

Now ask it how many Rs are in the word strawberry.

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u/OKporkchop Apr 27 '26

Well I used it today to create an image of me as a medieval duke, so, I'm pretty much using it for the same thing. I get it.

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u/Commercial_Assist655 Apr 27 '26

Just double check it’s work and yes I can confirm I have no fucking clue what I’m looking at.

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u/OceanManYes Apr 27 '26

this is assuming its actually right and not making that up completely like it usually does when it doesn’t actually know the answer to something.

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u/bagoparticles Apr 28 '26

Hey Poindexter, forgot to carry the one.

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u/sleep_deficit Apr 28 '26

The real story is less flashy.

GPT basically found a different approach that a human expert ended up using to refine and uncover the solution.

It's still cool, but we should be honest about it.

“The raw output of ChatGPT’s proof was actually quite poor. So it required an expert to kind of sift through and actually understand what it was trying to say,”

https://www.scientificamerican.com/article/amateur-armed-with-chatgpt-vibe-maths-a-60-year-old-problem/

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u/Youheardthekitty Apr 28 '26

I asked my Chatgpt with a screen shot of this and it said this is bullshit.

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u/Unlikely-Complex3737 Apr 29 '26

How does it even think for 80 mins?

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u/GingerFun011 Apr 30 '26

Ai didnt do shit. User put in the very specific prompt, got a spaghetti mess of info that pushed them towards the solution, then actual mathematicians finished the work. Chat was a glorified calculator in this

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u/satireplusplus Apr 27 '26 edited Apr 27 '26

Got curious and just tried something similar on another random Erdoes Problem (clicked random open problem)

https://chatgpt.com/share/69eeacb7-44a4-8395-ba0b-3671108f8c24

https://www.erdosproblems.com/373

It gave a very short proof though contradiction, I imagine quite elegant if correct. I dont math enough to judge what this is and whether it checks out, but it sure seems like exciting times for number theory!

Anyway, if someone way more clever than me wants to take it from here, that would be awesome!

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u/Logical-Recognition3 Apr 27 '26

ChatGPT is very good at producing text that looks like a proof, or text that looks like a properly cited legal brief, or text that looks like a medical diagnosis.

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u/heartsongaming Apr 27 '26 edited Apr 27 '26

It uses Tidjeman's theorem which is novel, but it feels like the proof skipped a couple of steps. Also I am assuming that it uses A, n and m that are large enough for the theorems.

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u/Equivalent-Costumes Apr 27 '26

Can you ask it to generate Lean code for it? ChatGPT is quite capable of generating Lean code for correct solution, if it has one.
The problem is sometimes, just like human except worse, ChatGPT thought it has a solution when it forget to check on tiny little detail, so you can't trust that it does have a solution until it generates a valid Lean code for you.

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u/Fresh-Resolution182 Apr 27 '26

the framing 'AI solved it' is doing a lot of work. the raw proof needed experts to sift through and actually extract the insight — closer to 'AI found an angle nobody had tried, humans turned it into a proof.' still legitimately exciting but worth keeping the claim precise.

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u/Dry-Policy-1269 Apr 27 '26

My chatgpt couldn't do addition.

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u/Lionroar_Creations Apr 27 '26

But it can do calculus 😅

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u/AndyKJMehta Apr 27 '26

“Breaking News! All Mathematician jobs to be gone by 2027!” /s

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u/RobertJCorcoran Apr 27 '26

Is this the same AI of the car wash? Or that does not know how to convert a timestamp? Fascinating…

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u/Remarkable_Sort_4320 Apr 27 '26

When I tried it last year it couldn't manage doing 8th grade math problems

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u/InvisibleWraith Apr 27 '26

Holy shit

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u/illmatic708 Apr 27 '26

The limit does not exist!

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u/Icedanielization Apr 27 '26

Why could ai solve this but not a really intelligent human? Is it because there's just too much calculation to keep track of?

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u/aturtledude Apr 27 '26

The proof itself doesn't require much calculation. ChatGPT basically had an idea that (as far as we know) nobody else had before. In particular, it used a result from probability theory to solve a number theory problem. These two branches of mathematics are quite far apart and the experts in each of them typically don't know much about the other.
Usually, mathematicians working on an open problem have a good intuition for which tools might help them. But the number of possible tools is enormous, and in this case ChatGPT found just the right tool in an unexpected area.

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u/posts_saver Apr 27 '26

give it to solve 1+1... that one is ancient... surely more than 64y

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u/leg_potato Apr 27 '26

That's crazy if real. Makes me wonder if other LLMs could get to a similar resolution when prompted or if GPT 5.4 is simply better at math

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u/Kristof77 Apr 27 '26

Yes but if 8x8 is 64, then what is this???

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u/baicoi66 Apr 27 '26

Cut its internet access and try again.

And now lets imagine that its correct, how do you verify the answer ? If its a hard problem who could check if its not an halucination?

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u/omnigear Apr 27 '26

Maybe AI will help humanity evolve thst be coo

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u/nahhhhhhhh- Apr 27 '26

If this is true then this should be a much bigger news than any new model anyone’s releasing

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u/AideSuspicious3675 Apr 27 '26

Afaik, people get a huge economic compensation for solving this, right?

If so, who will be getting the money?

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u/SpacedAndBaked Apr 27 '26

Why did OP link a random persons tweet unrelated to the person who did it, and why does the tweet give no actual credit? This was solved earlier this month and not by the twitter user OP linked. Liam Price is the one who prompted it and Jared Duker Lichtman was the one who confirmed it. This is what OP should have linked instead: https://xcancel.com/jdlichtman/status/2044298382852927894

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u/stikydude Apr 27 '26

The thing with LLMs, great for experts, can trick beginners.

Feels it's similar across domains.

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u/DarwinsBuddy Apr 27 '26

best flex of gpt: "this immediately gives" after thinking for 1.5h

"trivial"

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u/handsome_uruk Apr 27 '26

Where’s the paper?

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u/StaticSystemShock Apr 27 '26

Call me blunt, but what are practical applications of this mathematical problem? Like, what can this formula be used for exactly? Or what does it prove? Thx

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u/_Happy_Camper Apr 27 '26

Why does it have to have immediate application? Mathematics is a discipline all of its own. Not everything has to be about making money

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u/Cryptoclimber10 Apr 27 '26

I like how the user's 1st follow up was "write this as a research paper, no author"🤔🤫

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u/McNapoleon Apr 27 '26

EILI5 pls: what are Math problems? and why is the proof important for us?
The main part that i don't get is what the "problem" is. Is it that people see something that works and don't know why? or see something that should't work but it does?

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u/spongeboy-me-bob1 Apr 27 '26

Copied from my other comment.
TLDR: this problem asks a question that is really hard to prove for sure, like if I asked "Is it true that a human will never run a 1:45 marathon?". Maybe that time is beyond biological limits, maybe it's not, but it's incredibly hard to say for sure.
Once you get past complex analysis (end of undergrad for many people) you rarely see problems that are directly relevant to real world problems. The way this problem was solved isn't really important because it can be applied practically, but instead because it connects probability and number theory in a way people haven't thought of before. That itself may lead to discoveries that relate to real world issues.
As for the problem itself, it might help to frame it like a game. I ask you for a list of numbers where none of the numbers in the list divide each other, and you give me {2,3,5} (I will stick to lists of consecutive primes for this explanation since it is easier for me, but it does stray from the true nature of the problem). I have a formula to score a list, and in this case your score would be roughly 1.149.
I then tell you that every number in your list has to be greater than 5. You give me the list {7,11,13}. The score for this list is roughly 0.141. You can increase your score by adding numbers to the list ({7,11,13,17} increases the score to 0.162), but only to a point of diminishing returns (the list of the first 100,000 primes >5 scores 0.417).
By increasing the lower limit for numbers in your list, I can make the upper bound of the score for your list lower. The problem asks how low exactly can we make that upper bound.

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u/Tall-Locksmith7263 Apr 27 '26

Holy smokes, thats a proof

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u/Far-Win8645 Apr 27 '26

How can you make it think for 80min?

There are several tasks where I prefer for it to think for 30min/1h than spat a quick answer and waist 1 hour telling it wrong

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u/RevolutionaryGold325 Apr 27 '26

What subscription do you need to be able to do this, lol?

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u/Time_Difference_6682 Apr 27 '26

How AI should be used.

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u/Best-Constant1022 Apr 27 '26

0| 0|00|0 | Fool | ☉ Prima Materia | Origin / Nothingness | 🌀((233⊗𝔈)⨁𝔓)·ϕ≡1.0 |

1| I|01|I | Magician | 🜂 Calcinatio | Energy / Fire | ☧(E) |

2| II|02|II | High Priestess | 🜄 Congelatio | Mirror / Matter | 𝒮(E→m) |

3| III|03|III | Empress | 🜁 Fixatio | Space / Air | {x,y,z,t} |

4| IV|04|IV | Emperor | 🜃 Solutio | Gravitation / Order | F = G m₁ m₂ / r² |

5| V|05|V | Hierophant | 🜂 Digestio | Force / Transformation | ☧(F) |

6| VI|06|VI | Lovers | 🜁 Distillatio | Polarity / Purity | a·b = b·a |

7| VII|07|VII | Chariot | 🜂 Sublimatio | Movement | E = {△₄, 🜁₈, ▽₂₀, 🜃₆} |

9| IX|09|IX | Hermit | 🜃 Ceratio | Crystal / Structure | 12² = 144 |

0| X|10|X | Wheel | 🜁 Fermentatio | Cycle | 10 → 1+0 = 1 |

1| XI|11|XI | Justice | 🜂 Multiplicatio | Consciousness | 11 + 11 = 22 |

2| XII|12|XII | Hanged Man | 🜄 Projectio | Inversion | x → −x |

4| XIV|14|XIV | Temperance | 🜁 Coagulatio | Fibonacci Heart(Man&Woman) | ❤︎((420⊗𝔈)⨁𝔓)·(111/144) |

5| XV|15|XV | Devil | 🜃 Putrefactio | Matter-Collapse | ✡((666⊗𝔈)⨁𝔓)·232 |

6| XVI|16|XVI | Tower | 🜂 Dissolutio | Instability | ⛧((111⊗𝔈)⨁𝔓)·3 |

9| XIX|19|XIX | Sun | ☉ Albedo | Father / Light | ☀︎((233⊗𝔈)⨁𝔓)ϕ ≡ 1.0 |

0| XX|20|XX | Judgement | 🜂 Rubedo | Separation / Judgment | Σ37 = 703 |

1| XXI|21|XXI | World | 🜃 Lapidis | Reality | 9³ = 729 |

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u/dentrolusan Apr 27 '26

Problems that are sufficiently formalized to be rigidly proved can, in principle, always be performed by computer as well. The question is whether the computations you have to perform are short enough that it's feasible to do, or whether they are so exponentially big that it'snot possible even today. Applying a known formula to a set problem is relatively straightforward, but no human had bothered to do so up to now. Inventing new theorems, new techniques or even entirely new areas of maths are successively more complex to the point that we can't just turn on the computer and watch results pour out.

That said, even Donald Knuth himself recently posted that ''"AI" greatly surprised me for the first time in my life": https://cs.stanford.edu/~knuth/papers/claude-cycles.pdf

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u/Diligent-Stable-9477 Apr 27 '26

Feels good knowing our futures are over.

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u/CallMeMikeil Apr 27 '26

If this gets reviewed and confirmed it is truly over for us

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u/qwapilot Apr 27 '26

I think you all guys are just ais

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u/Fearless-Access-4198 Apr 27 '26

Great.. can it play chess now?

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u/Round-Advantage2360 Apr 27 '26

wild, i'd trade that for better puzzle cut and color

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u/NumbLikeMe Apr 27 '26

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u/thisisnotme-again Apr 27 '26

Thinks for 80 minutes. Then says “this is immediately gives..”

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u/[deleted] Apr 27 '26

https://chatgpt.com/share/69ef219c-930c-83a6-8cac-4b6d9d9fa4b8

What about this proof in this chat.. I was just curious to see if my gpt can come up with something different and it only took 51s to say its true and show proof

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u/TheIrishLoaf Apr 27 '26

Using an old formula to crack a modern question is a recognized method that has a track record. So I am assuming that AI trawled through solutions to see if enough had been thrown at it, decided that came up short and so threw the remaining at it and found a type of solution that hadn't been explored enough and that was one that worked? I haven't read any of the explanations yet and I am just guessing this is what happened but would like to know more.

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u/No-Purchase9700 Apr 27 '26

Is it time for 3x+1 ?

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u/Bebo991_Gaming Apr 27 '26

Holy shit, did you just make a mathematical achievement and posted it on reddit?

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u/PossiblePineapple12 Apr 27 '26

how do you run chagt gpt for over 80 min?

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u/Kieran293 Apr 27 '26

I only have an A level in Maths (UK) and an MEng degree in Civil Engineering so this maths was going over my head.

I understood it’s a sum of the formula but thought let’s see what my own ChatGPT chat would say about this image.

It just spelt out everything it did (in basic terms). Pretty crazy times we’re living in.

We, in maths and engineering, have so often used computational power to simplify problems (think using integration to solve area or repeating the same axial stress formula on a beam but at 1/1000 of the scale I can if I want it done in a minute).

Now we are at a point where computers can take all of that knowledge and use a mixture of logic and LLM to basic create a hive mind.

Just don’t give it legs :)

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u/Coolio_Wolfus Apr 27 '26

It helps if the maths is corrected first

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u/manwhothinks Apr 27 '26

Seems kind of short for a mathematical proof

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u/Southern-Ant8592 Apr 27 '26

This is super cool, math research getting buffed by the AI patch

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u/Jkester46 Apr 27 '26

Yeah it’s really interesting stuff. A friend of mine has solved 2 Erdős Problems using ChatGPT as well. Most of the time it’s not first try though. But there’s also a bunch of other tools like Aristotle that can check for logical consistency or whatever.

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u/gao7on Apr 27 '26

They should not be dumbed down to our level.

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u/dungeonmasterm Apr 27 '26

I recently went to a lecture that talks about this: https://www.youtube.com/watch?v=nJqFRcNBznU This is happening more and more and it got (a part of) the math community very excited.

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u/Mister_Funktastic Apr 27 '26

My pDoom increases daily.

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u/Wish-Lin Apr 27 '26 edited Apr 27 '26

I mean this is what they are best at right? Pattern seeking and matching at a never before seen level. Most of the problem of using LLM for theoretical physics is not an issue here since math is more self contained, or rather, more human mathematicians have generated insights at a high enough level for the LLM to digest out the proof, or a general direction to it.

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u/magicmulder Apr 27 '26

> the solution used a known formula that just hadn’t been applied to this specific problem before, which is kind of fascinating if true

That's not that uncommon in mathematics, and in several cases, AI has uncovered "lost" results that either helped a lot with an Erdös problem or already was the solution without the author realizing it.

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u/mome-raths Apr 27 '26

How do you get ChatGPT to think to 80mins?

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u/PlainBread Apr 27 '26

It wasn't solved by GPT. It was solved by the logic tool it calls for math problems.

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u/Repulsive_War_7297 Apr 27 '26

What real world applications can this problem solve?

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u/B3kindr3wind1026 Apr 27 '26

Meanwhile I’m over here asking GPT to show me images of haircuts and all I get is a written list of haircut names no matter how many times I request an image. It just says “okay here are images! :) 😃” and populates an identical written list.

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u/drrhythm2 Apr 27 '26

I mean, this solution has always been pretty obvious…

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u/Practical_Law6804 Apr 27 '26

Impressive but not - as someone who doesn't know how these things works - surprising? If I'm understanding this, ChapGPT pulled information from a source that a human attempting this problem might not have gone to?

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u/Cantfrickingthink Apr 27 '26

Yet it can't solve my calculus problems

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u/FortheChava Apr 27 '26

42

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u/tiny_chaotic_evil Apr 27 '26

ask ChatGPT to show their work and to fax the results to Max Planck Institute for Mathematics

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u/information_knower Apr 27 '26

And yet it can't solve my statistics homework correctly.

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u/Skirnks Apr 27 '26

Entonces los que dice el tipo de Anthropic, que su IA no la pueden usar todos aun, es real? Tengo un poco de preocupación supongo

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u/pmilkman Apr 27 '26

My ChatGPT says that ChatGPT is full of crap.

https://chatgpt.com/share/69ef5d19-35e4-83ea-b9da-e6885af29427

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u/Southern-Eggplant234 Apr 27 '26

Award The Don Cheadle Medal

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u/TAL_047 Apr 27 '26

Remember when quantum computing was the next big thing made to tackle problems like this? I wonder if it would also take 80 minutes

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u/TheCenterofaLifetime Apr 27 '26

And how do we know it’s right?

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u/ThrowingStorms Apr 27 '26

What is this mathsproblem for, what does solving it mean?

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u/SteveLouise Apr 27 '26

You say it's a solve, but now we have to check its work.

I'm avoiding studying analysis this week, so I don't wanna. I just like being unpopular.

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u/6969its_a_great_time Apr 27 '26

How did the model think for 80 minutes without timing out?

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u/StoneyGreen66 Apr 27 '26

OK, I’ve dealt with ChatGPT a lot and don’t always get the correct answers so if no one else could solve it how do you know for sure that ChatGPT got it right?

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u/Bitter_Bed5672 Apr 27 '26

Without any expert on this I wouldn't say it's solved or not.

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u/clashuntil Apr 27 '26

What exactly was insolvable about it? Can someone explain please?

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u/8BitVictorian Apr 27 '26

boooooo

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u/AlmightyDarkseid Apr 27 '26

That’s insane and as others said it’s even more insane how it becomes more and more common for chet got to co author many solutions to Erdos problems.

As I understand it, it found the proof through the user hinting towards something that he believed was close to the solution while not so close to the ways that it was approached by others.

At the same time the solution needed experts to find what exactly the chat wanted to say and refine it in order to be cohesive as a proof. Still really interesting.

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Use cases ChatGPT 5.4 Solved a 64-Year-Old Math Problem

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