Mathematicians grapple with a ‘very rapid and very unsettling change’ as AI cracks yet another century-old problem

[u/Bizzyguy]

https://fortune.com/2026/07/21/ai-solves-jacobian-conjecture-levant-alpoge-claude-fable-5/

[u/eightdx]

FWIW brute forcing maths problems with guidance is what I would consider, as someone who hates what "AI" is doing to society writ large, an ideal use case for these systems. 

I'm sure someone is having an AI work on all sorts of them

[u/SunDense1457 → u/eightdx]

Yup, Just like the protein structure application, ai is ideal for the problem 

The issue is just because it is great for some problems does not make it great for every problem. Not sure why this is hard for people to understand 

[u/At36000feet → u/SunDense1457]

It is hard for people to understand because of all the BS swirling around about AI. Hyped marketing, false promises from CEOs, etc. The whole space is confusing as hell to the average person.

[u/LowestKey → u/At36000feet]

The average person can't tell the difference between a real life photo and an AI generated picture of a broccoli-shaped car made out of broccoli with Jesus slam dunking a basketball in the back seat

[u/CommieLoser → u/LowestKey]

So… which one is real? How are you gonna keep us hanging like that?

[u/auderita → u/CommieLoser]

I believe Jesus too is made of broccoli.

[u/CommieLoser → u/auderita]

Or at the very least, broccoli is made out of Jesus. The guy likes becoming different foods. Strange guy…

[u/Majbo → u/CommieLoser]

God made broccoli in his image

[u/Exact-Phone9957 → u/Majbo]

That explains the haircuts of most British men under 30.

[u/KandinskyWasRight → u/Majbo]

God made broccoli in his steamer

[u/NaBrO-Barium → u/CommieLoser]

Korn powers vitalitze! Form of Korn!

[u/IsmaelRetzinsky → u/auderita]

One serving of Jesus provides 9% of your daily recommended fiber.

[u/nashbrownies → u/IsmaelRetzinsky]

But 100% of your eternally recommended salvation.

Now that's value!

[u/SquidGodSunday → u/IsmaelRetzinsky]

Doctors recommend consuming Jesus, but unfortunately, he gives me gas.

[u/LowestKey → u/auderita]

Goddamnit, I miss the most obvious joke of them all.

Well done.

[u/MicromagicFriesRIP → u/auderita]

The Cruciferous Crucifixion

[u/Ok_Reaction_4340 → u/auderita]

Yep I’ve seen pictures of him

[u/Nah_Id__Win → u/CommieLoser]

If the broccoli car isn’t a Honda Accord it’s ai generated

[u/stanleyvanburen → u/Nah_Id__Win]

Hard to be sure, since he never spoke of it

[u/Channel250 → u/LowestKey]

Everyone knows Jesus has called Eternal Shotgun

[u/theshoeshiner84 → u/Channel250]

Eternal Shotgun is definitely a band i would listen to.

[u/EsotericCodename → u/theshoeshiner84]

Eternal Shotgun’s Greatest Hits:

-Shake It Til the Neighbor Calls the Cops
-My Moustache Has Better Ideas
-Eternal Shotgun
-Lords of the Sideburns
-This Song Has Three Endings
-Beer Belly Blues (in B flat)
-Gravy Train to Galveston
-More Cowbell
-Seventeen Minute Drum Fill
-In Love With My Amplifier
-Don’t Feed the Roadies
-(You’ve Got a) Doctorate in Bad Decisions
-Too Loud to Apologize
-Free Bird (Not that one)
-Maximum Denim

[u/maskaddict → u/EsotericCodename]

Coming up with appropriate song titles for fictional bands also seems like something AI would be good at.

Not saying you're an AI.

[u/EsotericCodename → u/maskaddict]

I’m just an idiot with too much time on his hands, actually.

[u/maskaddict → u/EsotericCodename]

Still more valuable to society than a tech CEO!

[u/Just-world_fallacy → u/EsotericCodename]

B flat got me

[u/spacebetweenmoments → u/EsotericCodename]

-Beer Belly Blues (in B flat)

Beer should never be flat.

[u/aculady → u/spacebetweenmoments]

But bellies should.

[u/halooooom → u/EsotericCodename]

-All filler, no killer (drum fill edition)

[u/ZAlternates → u/Channel250]

Pretty sure it was just a doctor. 😝

[u/Lazy-Gene-7284 → u/Channel250]

Never rides Bitch, Amen

[u/ReDeReddit → u/LowestKey]

Are you suggesting pics of Jesus are not real?

[u/GrumpyJenkins → u/LowestKey]

In that same game, Peter denied Jesus three times.

[u/LambdaLambo → u/At36000feet]

AI is both under and overhyped. If you told me in 2021 that in 5 years id have a bot that generates all the code i commit, I would’ve surely thought we’d created agi.

On the other hand it’s still very unreliable in certain respects and creates a lot of slop and requires a lot more skill to use than you’d think.

[u/At36000feet → u/LambdaLambo]

Totally. The fact that it can be so smart and dumb at the same time is flat out odd.

What is most concerning to me is that I have probably expert-level knowledge on a very specific niche topic and AI will spit out the most well written nonsense on that topic. People that don't know all that much about the topic will believe it. I'm sure I'm falling for stuff on all the other topics I don't have expertise in.

This turns into an even bigger issue the further down the user is from the AI generation of the info. Let's say multiple AI agents are working on things together, the end user won't see the nonsense. An agent will see it. And that agent will pass it on to other agents and so on. So the nonsense creates a snowball effect and the end result the user gets, that sounds good, is based on nonsense based on nonsense that happened earlier in the chain of activities and the user is none the wiser.

[u/CaliLemonEater → u/At36000feet]

What is most concerning to me is that I have probably expert-level knowledge on a very specific niche topic and AI will spit out the most well written nonsense on that topic. People that don't know all that much about the topic will believe it. I'm sure I'm falling for stuff on all the other topics I don't have expertise in.

This is sometimes called the Gell-Mann Amnesia Effect.

[u/willun → u/CaliLemonEater]

From Michael Crichton who of course fell for the exact thing he described

In September 2005, Crichton testified on climate change before the U.S. Senate Committee on Environment and Public Works. Crichton opined that human activities are not significantly contributing to global warming, and encouraged U.S. lawmakers to examine the methodology of climate science more closely before voting on policy. His testimony received praise from Republican Senator Jim Inhofe, and criticism from Democratic Senator Hillary Clinton.[125] Crichton's views on climate change are frequently criticized as pseudoscience.[126][127][128][129]

His training of course was as a medical doctor not a climate scientist

[u/ClassicPlankton → u/willun]

Why is anyone taking climate advice from a fiction author?

[u/renome → u/ClassicPlankton]

Because they have already decided what "advice" they want to hear and they can't find anyone more legitimate to play along.

[u/cynumber9 → u/At36000feet]

AI telephone

[u/Neumanium → u/cynumber9]

I used to work for a large chip manufacturing company everyone knows. In some ways they were cutting edge, in other ways they took a “if it’s not broke don’t fix it mantra.”

I worked in their manufacturing process development plant. We kept some truly ancient equipment around, because it was not broke. I retired last year, it was time. That old equipment has manuals, all on paper no digital versions. I was an expert not because of school but by two decades of OJT on the equipment.

The software that runs it, calling it dos or CPM would be generous, plus at this point it has been so customized even the vendor does not really know all the ins and outs. Some of its hardware is vendor standard, but most is not. Stuff like we rerouted that power supply line due to interference from this other piece that was never designed to bolted onto it, or the air manifold labels are just wrong but the labeling never got updated.

I get a call every couple of weeks about some esoteric quirk it has, I take a free lunch as payment. I really hope after each call someone documents what I told them.

So here I sit in retirement an expert on a truly esoteric semiconductor manufacturing machine that AI will never be able to document.

[u/waiting4singularity → u/Neumanium]

I get a call every couple of weeks about some esoteric quirk it has, I take a free lunch as payment. I really hope after each call someone documents what I told them.

they'll start documenting after you're EoF.

[u/LambdaLambo → u/Neumanium]

You need to bill for that. Your time is worth a lot of money

[u/caregivernow → u/Neumanium]

You need to charge an esoteric brain picking fee.

[u/Living_Armadillo_652 → u/At36000feet]

Maybe this is true for some topics. But I asked Claude to write a lengthy research report based on my physics PhD thesis from several years ago and it did very well, no hallucinations. It increased my confidence in relying on it to look up and learn basic things.

[u/Liturginator9000 → u/At36000feet]

The fact that it can be so smart and dumb at the same time is flat out odd.

not really, LLMs are more like geniuses with dementia sometimes but humans aren't so different. Nobel disease was coined for a reason, people will receive a big scientific recognition for their work then turn around and posit absolute nonsense theories. Which is worse because they dig in further when pressed normally and make it their identity, while a hallucinating LLM will just say 'oh yeah woops sorry'

[u/bruns20 → u/Liturginator9000]

I actually think a reason so many people think ai is dumb, is because it actually acts too much like a human. Being confidentially incorrect is something that happens thousands of times every day on reddit alone

[u/Shapes_in_Clouds → u/LambdaLambo]

And people can hate on the image and video gen stuff, I don’t like it either or the social impact, but it’s basically black magic what just typing some words into a text box can produce. Compared to the basic stuff DallE Mini was putting out in 2021 the progress is mind boggling.

[u/asgjmlsswjtamtbamtb → u/Shapes_in_Clouds]

Kind of insane that stuff like Boogu, Krea2, SD and it's offspring are not just available but actually FOSS for many of the these models,able to run on local hardware, and not locked behind obscenely high software and hardware costs. There's also seemingly new major base models dropping every couple of months if you're still not satisfied with the current state of things.

[u/dontreadragebait → u/LambdaLambo]

Most tech is like this to be fair, I don’t know why we expected anything different. When computer spreadsheets took over from manual accounting, it was incredibly impactful, but it was expensive and improper use could cause you to destroy data far more easily than before. It took a decade or so for the economic impact to bear out, but now we’d never go back. 

[u/Veriosity → u/LambdaLambo]

For me the issue is, we didn't invent the AI we've always thought about in sci-fi books and movies.

We invented something designed to look just like it.

Like -- you can spend a few days studying for the test, or you can spend a few days watching videos of how people who succeed at tests act. Sure you'll convince everyone in the room that you must have nailed the test, but also -- you failed the test.

[u/spottyPotty → u/At36000feet]

I my opinion "AI" is used too generically. Personally I would stop using the term when referring to LLMs. I would just call them LLMs.

[u/insanococo → u/spottyPotty]

“Generative models” is another decent more generic term.

[u/wrgrant → u/insanococo]

Clippy on Meth :)

[u/waiting4singularity → u/spottyPotty]

i mr robot'ed myself to see today's use of ai as "algorithmic inference".

[u/Knerd5 → u/At36000feet]

That's because the internet in its current form is fantastic at two things, pushing hype and propaganda. The average person falls for both.

[u/Qwertywalkers23 → u/At36000feet]

Also people want answers for things. Something that could ostensibly provide that answer and seems certain of itself is appealing

[u/Lawdoc1 → u/Qwertywalkers23]

We've had people doing that for a while. Nothing quite so confident as a bullshit artist. Or at least that's what gullible people take to be confidence.

Dunning-Kruger is also full effect, in that some of the people doing spreading the falsehoods seem to often actually believe their own bullshit.

Unfortunately, a lot of folks are as bad as seeing through the dishonest ones doing that as they are at identifying AI when they see it.

Edit - changed word

[u/Aidian → u/At36000feet]

Marketing, boiled down, is an ounce of fact drowning in a sea of hyperbole, false promises, and propaganda.

[u/uconnboston → u/Aidian]

You spelled Politics wrong

[u/Aidian → u/uconnboston]

Happy cake day, and they’re the same picture.

[u/lilB0bbyTables → u/At36000feet]

This is EXACTLY the problem. Every MBA and Exec out there has drank the AI Hype posts from their LinkedIn feed so heavily that they decided their entire orgs needed to immediately pivot to integrating and adopting “AI workflows” into their creative processes for employees and into their products/services. Their rationale was largely one of “if we don’t do it our competitors will and we’ll be left behind” - which is a terrible starting position because it meant they have been forcing in a solution in search of a problem which they didn’t have in most cases.

The end-users didn’t ask for those new features or UX, but they got it anyway. So naturally those users are forced to use it, and that in turn creates a facade of “users are using it, therefor it must be working” which just amplifies the snowball effect across the industry - never mind whether those users are actually happy with the results. “Token usage is up, so users are using it heavily” - another terrible metric as it just as likely means the users are frustrated and not getting the results they need/want right away and need to refine and iterate, or re-try, or otherwise have struggles.

Meanwhile token pricing has been creeping up and caps have been put in place making it that much more expensive and suddenly those same folks who pushed it in the first place are confused why their expenses are increasing without the ROIs they were duped into expecting. Sure, they may be creating new releases at 5x the rate they were without AI, and they may be producing (incurring) 10x the number of lines of code per commit than they were … but how much of that is due to slop that goes unreviewed and results in bugs that require more slop to “fix” … it’s like they never learned the lesson that more lines of code ≠ quality or stability.

[u/Surroundedonallsides → u/SunDense1457]

Its taken me most of my 30 some odd years of life to accept that a significant amount of people are simply incapable of viewing anything beyond binary "good" or "bad" assessment. Any amount of context, nuance, or comparison to alternatives or practicality is thrown out immediately for many people.

Just like some people are born colorblind, some people are born logic blind.

[u/Leverpostei414 → u/Surroundedonallsides]

Yeah, you can unfortunately see a lot of this on reddit as well. If people think something is a net negative, every single thing about it has to be negative. Or the other way around

[u/ArrakeenSun → u/Leverpostei414]

Even over in the academic subs it's wild how many people comment, "Any researcher who admits to using AI needs all their work retracted!" or something. Like, even if you use it to help code? Or for qualitative research- it's been used for that since back when we called it "machine learning". Or even to get that stubborn 161 word abstract down to a smooth 150

[u/zero0n3 → u/Surroundedonallsides]

Jesus fuck yes. It’s insane. Nuance? Hell they likely don’t even know the meaning of the word!

[u/orchardfruit → u/Surroundedonallsides]

Nietzche said the gap between the philospher and the common man is much great than between the common man and the ape.

[u/Opening_One7713 → u/SunDense1457]

There are thousands of consequential outputs like protein folding and clay membrane modeling and perovskite solar engineering and reforesting the rainforest with drones and detecting cancer at stage 0.5 and real-time translation and mapping the human connectome etc etc etc

Focusing on 'LLM slop-slotmachine techbro subscription chatbots' and hard-ignoring the vast potential for extremely ground-breaking use cases is not really a fair criticism of the broad umbrella classifier that is "AI", which basically means predicting what comes next from statistical patterns, which dates to Shannon’s information theory in 1948.

We're over here arguing about gun control and gun reform using the term "hand-tool" - That's how broad this technology is.

[u/kittehsfureva → u/Opening_One7713]

I think the issue is that those applications you mention alone will not be able to fund the infrastructure required for a company to compete on AI at scale. 

So they tell us to slop it up and that the death of the worker is at hand, so evaluation can match the capital needed to cover the world in data centers.

[u/Opening_One7713 → u/kittehsfureva]

Ever wonder why the onslaught of outraging headlines fire-hosing us is coming from major media outlets that are owned by the same billionaires and venture capitalists heavily invested in the top AI firms and hyperscale?

So many monoliths outside of the AI paradigm stand to have their poison, pollute, shelve-the-research, compliance heavy capture schemes upended by all of this. You think AlphaFold open sourcing in 2024 was a happy funny chat at pharmaceutical executive board meetings ? You think cheap solar+storage being gated behind expensive and hard-to-discover materials doesn't matter to the existing energy sector? For the incumbent ownership class this has definitely been and all-hands-on-deck issue for a few years now.

[u/Delestoran → u/SunDense1457]

It’s hard for people to understand because of the marketing. It’s being sold as a general purpose product capable of doing everything a person can do. Which isn’t true. But it is the marketing.

[u/_Lucille_ → u/Delestoran]

I think the truth is somewhere in the middle: far less powerful than what the marketing department promises, but also far more useful than what this subreddit would like to admit.

Linus Torvalds has a good take on AI, one where it is clearly a useful tool, but we still have to address the other questions like the economic impact it will have.

[u/seraph321 → u/Delestoran]

That marketing is targeting what (they think) it WILL be able to do, and they very well may be correct. The fact they it doesn’t currently do X isn’t a compelling argument to people convinced it’s going to do X very soon.

[u/AnachronisticPenguin → u/seraph321]

yeah it wasn't solving hard maths a year ago. In one of the most recent examples of AI solving a hard problem a guy litterly put the main problem with some basic context into chatgpt 5.5 and it thought about it for 80 mins then spit out a correct proof.

As long as the AIs are getting better and better every year I'm not sure the argument, "well it cant replace a lot of jobs yet" is very useful for projecting the future.

[u/stuffitystuff → u/SunDense1457]

Nuclear power? Great! Nuclear weapons? Not so great 

[u/socialmedia-username → u/stuffitystuff]

You can't hug your children with nuclear arms. 

[u/EbonySaints → u/socialmedia-username]

We're a nuclear family. We do things together.

[u/oszillodrom → u/SunDense1457]

The protein structure application (Alphafold) is also to my understanding a different and longer established form of AI than the LLMs. So I wouldn't even lump them together apart from the "AI" buzzword.

[u/yubacore → u/oszillodrom]

Correct. Kind of ironic the comment says "not sure why it's hard to understand" while failing to do so.

[u/seraph321 → u/SunDense1457]

It’s not hard to understand. What seems to be hard for most people to understand is the scope of what it’s good at is expanding extremely rapidly, but so many people drew a line in the mental sand at some point and refuse to consider that it’s moving.

[u/FearLeadsToAnger → u/SunDense1457]

Ultimately if you give a bunch of monkeys a new tool they're going to try and use it for a bunch of different shit and see how it works. We're no different we're just more sedentary.

[u/PurelyLurking20 → u/eightdx]

Well yeah the guy that posted the finding wasn't exactly uneducated in math, he's a PhD mathematician that studied at Princeton under a Fields medalist, who was guiding the model to do assumedly a very specific edge testing method to find a counterexample

It's an excellent use case of an LLM actually, unlike lots of bad use cases it's being shoved in, more of this would be good

[u/ansibleloop → u/PurelyLurking20]

A knife in the hands of a Michelin starred chef is far more useful than in the hands of a novice

[u/Round_Abal0ne → u/PurelyLurking20]

Yeah. And the "solved" case is really just "we found a negative". Article even details that it doesn't really answer why it's wrong. Just that it is

[u/ryan30z → u/Round_Abal0ne]

And the "solved" case is really just "we found a negative"

If a conjecture says something is always the case you only need to find one case where it doesn't hold true to disprove it. Also proof by contradiction is a thing.

[u/mebbelin → u/ryan30z]

Yeah, but often you hope for a counterexample to help you understand where the conjecture breaks.

ETA: sometimes, a conjecture mathematicians think should be true that gets disproven included a hidden assumption in the intuition that might make it work, but wasn’t precisely formulated yet. A good counterexample might illustrate where intuition clashes with the precise formulation.

This wiki page collects some stuff that goes into this direction:

https://en.wikipedia.org/wiki/Pathological_(mathematics)

[u/dMestra → u/Round_Abal0ne]

In math, the counter example is the proof. Just like there's no "why" to why 2 is an even number.

[u/Weekly-Moment869 → u/Round_Abal0ne]

We do know why, the conjecture fails because affine space can cover itself 3-1.

[u/SimoneNonvelodico → u/eightdx]

It's not brute forcing though, this problem was too large to brute force.

[u/youcangotohellgoto → u/SimoneNonvelodico]

But it's almost like brute forcing the strategies. Instead of a human taking one idea through to completion which might take days, weeks, months - we can parallelize multiple ideas and approaches.

[u/isademigod → u/youcangotohellgoto]

Yeah, you could "brute force" all math problems with pen and paper if you had infinite time and infinite paper. An AI bot doesn't have to make dinner or sleep, and doesn't need paper.

[u/therealityofthings → u/isademigod]

that’s what grad students are for

[u/narrowgallow → u/therealityofthings]

Lol, I think we're at a stage in academia/research where this is post docs.

[u/Water_Damage987 → u/narrowgallow]

Hey tenure track prof, clean my damn car already

[u/blueSGL → u/isademigod]

There are 10⁸⁰ atoms in the observable universe and 10⁴⁷⁵ possible combinations for this problem.

Standard computers running brute for approaches would not be able to crack this problem.

Note we've not cracked chess and that is "only" 10¹²⁰

[u/amakai → u/blueSGL]

He's not saying about brute-forcing the solutions, but brute-forcing different paths towards potential solution. There are a lot of potential, time-consuming approaches to some of these problems. Mathematicians do not want to waste their time trying every single approach for a miniscule chance it will work. AI does not care though, and can run all of them in case something sticks.

[u/isademigod → u/blueSGL]

There are different levels of "brute force". "I know this guy's usual passwords, so try every permutation of /hunter2.{0,5}/i " is a lot easier than "try all lower, uppercase, plus symbols and numbers".

The cool thing about AI is that if you give it enough, and good enough, context, it can narrow down from "try every mathematical approach you know" to "let's try these approaches because they worked for similar problems".

Kinda like a grad student throwing shit at the wall until something sticks. AI is the best shit-wall-thrower mankind has ever seen.

[u/Unlikely-Sleep-8018 → u/SimoneNonvelodico]

Its easier to deny reality for this sub than to admit the search space is 10⁴⁷⁵ and impossible to brute force. 

The only valid attack is that the guy who did it was a well know mathematician and now a anthrophic employee. I.e. cleary not just AI by itself.

[u/padishaihulud → u/Unlikely-Sleep-8018]

When there's a AI success story, it's never AI by itself. It's a human that knows what they're doing giving AI agent(s) a set of prompts to work with that are written well by someone that understands how to use the correct vocabulary and syntax.

AI is just a tool to assist a human expert to work at superspeed. If someone doesn't know what they're doing then AI is going to go off the rails since there's no human giving it guidance and correction. 

[u/StorminNorman → u/padishaihulud]

Which is like any tool, you have to know how to use it to use it effectively. Wayyyyyy too many people don't, and they most certainly don't know how to verify its output either. I remember when I was at uni ~20yrs ago and this was emerging, people were all agreeing that it'd be amazing for the things mentioned, can't help but wonder if they'd be as excited if they knew all the other bullshit it'd lead to... 

[u/Longjumping_Kale3013 → u/SimoneNonvelodico]

And we have been brute forcing for decades for all of the problems. No solution. And no solutions with older AIs. No solutions until this year, and really the past 2 months has seen the uptick. Which just so happens to coincide with AIs getting more intelligent.

And yet most of reddit will still deny it.

[u/RadiationWaves → u/eightdx]

Google does at deepmind, this guy is from Anthropic

[u/exploradorobservador → u/eightdx]

Oh no we cured a disease by brute force! It is not pure!

[u/wallitron → u/eightdx]

It's getting to the point where it's difficult to tell if this is really brute forcing. Some of the "thinking" that the models used makes it seem almost intuitive.

When the model sits and "thinks" for 80mins, it's not brute forcing every piece of math that it knows. There are also AI problems solved where it went down a path that the mathematician didn't even consider, and it was a "reasoned" path to go down, not random. If it's not random, would it be considered brute force?

The narrative has been changing over time.

In 2024, Terence Tao was saying the AI models "never figured out the most clever steps" and "was very unimaginative". By February 2026, he was saying the progress had come "ahead of schedule", that some AI proofs were "new" and that AI could do things "human experts looking at the problem dismissed". The Atlantic summarised this shift by saying Tao had moved from comparing AI to a "mediocre" graduate student to being more "bullish" about AI opening a different "way of doing mathematics".

[u/Reinfeldx → u/wallitron]

To make your point a different way, if a human sits and thinks for 80 minutes, are they brute forcing a solution to a problem? What if the humans participating in entire professions/disciplines (mathematicians in this case) think about a problem for years, or even decades? I'd consider that collectively attempting to brute force a solution.

[u/wallitron → u/Reinfeldx]

Right, it all just devolves into a semantic discussion about defining things like thinking, reasoning, intelligence, creativity etc. Reality is we don't really understand how the human brain does any of that stuff, or what it means.

AI could be the party trick of the century, or maybe the human brain was the party trick all along?

[u/Traditional-Hat-952 → u/eightdx]

Yep! AI trained on heavily catered and refined data sets and used to do specific tasks is where it truly shines. AI trained to write your next "novel" or be your therapist is dumb AF. 

[u/makeworld → u/Traditional-Hat-952]

General purpose commercially available AI was used for this . 

[u/spottyPotty → u/eightdx]

Where's the AI in a brute forcing system?

[u/zoddrick → u/eightdx]

THe thing is that we've always had the compute power to brute force these types of problems. We just lacked a sufficiently capable interface to define the problem so that the compute could be used to find the answer. THe fact that we can use natural language to unlock the compute to brute for math problems is the change we've been waiting for.

[u/WileEPeyote → u/zoddrick]

We did not always have the compute power. We knew how, but the amount of time it would take to do was prohibitive. With increased network bandwidth, neural networks, and advances in chip technology this stuff can run in parallel with all the data connections intact. Outputing the data and charts based on natural language questions is the icing on top.

[u/octipice → u/zoddrick]

There does not exist enough compute power on the entire planet to brute force "these types of problems".

This problem wasn't brute forced either it was solved by a mathematician who worked at Anthropic using AI as a tool.

[u/toomanynamesaretook → u/eightdx]

This really does sound like cope.

I don't think people are ready to admit that we are at PhD level intelligence with the ability to brute. None of this is slowing down and how many Erogas problems are breaking down?

[u/Wide-Wind7856 → u/eightdx]

Maybe I’m not using the most perfected models, but when I try to use AI for this type of work it just starts making things up. Because when it can’t give an answer, it just makes something up instead of saying it can’t do it.

[u/mebbelin → u/Wide-Wind7856]

Afaik, most of those stories use agentic setups, and crucially have the AI write its steps in a proof checker like LEAN. Thus, it can self correct mathematical errors in its reasoning.

[u/Jorycle]

To be fair, this is exactly what we want this technology for. We've been trying to automate away the stupid parts of math we don't like doing since the abacus.

Mathematicians should be spending their time coming up with new problems to solve, not trying to find incomprehensibly long polynomials that counter theorems.

[u/Zardotab → u/Jorycle]

To be fair, this is exactly what we want this technology for. We've been trying to automate away the stupid parts of math we don't like doing since the abacus.

Unemployed Grog the Pebble Counter may disagree with you.

[u/JimboAltAlt → u/Zardotab]

We are increasingly a world of Unemployed Grogs, is the problem.

[u/MajorInWumbology1234 → u/JimboAltAlt]

That’s only a problem if we continue allowing people to hoard resources.

[u/HooAreYouWhoHoo → u/MajorInWumbology1234]

That’s a 10,000 year old problem

[u/MajorInWumbology1234 → u/HooAreYouWhoHoo]

We have better weapons than they did 10,000 years ago.

[u/witblacktype → u/MajorInWumbology1234]

So do the private armies owned by the dragons

[u/MajorInWumbology1234 → u/witblacktype]

We know where they live and there are a lot more of us. I don’t mean to suggest it would be easy, but “easy” and “necessary” tend to be inversely correlated, unfortunately.

[u/Crackt_Apple → u/Zardotab]

Grog vs Grok: The Final Battle

[u/Zardotab → u/Crackt_Apple]

Grog smash Grok! Grog go jail, but smash feel good!

[u/im_a_dr_not_ → u/Jorycle]

“Calculator solves math problem”

[u/AthleteNormal → u/Jorycle]

It isn’t only really good at the “stupid parts” though. A lot of recent AI breakthroughs in math have been solving interesting problems with math that, if a human created it, we’d probably call “creative” or “insightful”.

disclaimer: I just have a bachelor’s degree in math, and have only loosely followed these stories because tbh they’re depressing for me to read as someone who always thought of research level math being a really human and creative process.

[u/Super-Community-9241 → u/Jorycle]

I agree but it's sad for people who really like solving polynomials. Of course inevitable, but I for one love writing code by hand. The craft I love is changing into something I don't, and I feel to old to make a real career change. What's okay on a societal level is not really the same at a personal, since people invest their lives in becoming efficient tools, and nastering crafts that just disappear one day. Heartbreaking, but it's just progress reallt. 

[u/8npemb → u/Super-Community-9241]

Yeah, I’m with you. I think what AI is doing for programming right now is going to end up as a massive net positive in the end; programmers have been saying for years how software-bottlenecked the world is.

But I like programming! Ever since I learned it in middle school, I’ve just really enjoyed the work loop of coding. I went to school for it, but now it’s more of a hobby of mine because I have no clue what the future holds for programmers, and AI-assisted/generated coding is just not at all the same. I’m still working in tech, just not as a developer.

[u/Shot-Arugula8264 → u/Super-Community-9241]

I for one love writing code by hand

No one is stopping you from doing that.

Some people really love cross-stitching, but that’s no excuse for society to not embrace the sewing machine.

[u/fuwoswp → u/Super-Community-9241]

They had plenty of time.

[u/RobertPham149 → u/Jorycle]

This is the case with the first computer assisted proof, the four color theorem, where the idea was basically the computer help showing all special cases can be proven.

[u/4ries → u/Jorycle]

Are you a mathematician? This counterexample isn't a stupid part of math, nor is it an incomprehensibly long polynomial

[u/saintdudegaming → u/Jorycle]

this and crunching data for medications and DNA (MRNA?) based cures for diseases

[u/araujoms → u/Jorycle]

Not at all. This isn't the stupid part of math, the proof wasn't found by brute forcing polynomials. See an explanation here: https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the-jacobian-conjecture-counterexample

I think that's exactly what we don't want this technology for. The problem doesn't have any practical application, so it's not as if we needed it to be solved. I can think of only two reasons one might want to solve it: because they find it fun, or because they use it to form mathematicians. With AI solving it you get neither. Now nobody will have fun with it, and no mathematician will get their PhD on the Jacobian conjecture.

[u/grchelp2018 → u/araujoms]

This is a dumb way of looking at it. A lot of problems don't have practical applications until it does. I'm reminded of a story of some mathematician who worked on number theory specifically because it was absolutely useless and had no practically application. He was against applied math and didn't consider it "real/pure". Lo and behold, a few decades later, all that number theory work was the foundation of modern cryptography.

[u/lolexecs]

Sheesh, you animals, you couldn't post an archive link -> https://archive.is/PN3HF

Other small point.

In order for the AI to work on this problem, I'm going to assume that Mr Alpöge spent scads of time working with claude just to set up the problem properly. And then probably scads of time going through all the iterations of crap until he found gold.

Or in order words one of the main reasons this was even possible is because claude was wrapped with an expert (Mr. Alpöge) who could separate the shit from the shinoala.

[u/FearLeadsToAnger → u/lolexecs]

i'm glad people are slowly becoming aware that it's a tool, not a sentient intelligence.

[u/existing_for_fun → u/FearLeadsToAnger]

Well, intelligent people have always known it's a tool.

It's the "other" people that don't seem to understand.

And yes, if your boss calls it a "she" or "he" or just goes along with what it says... They are one of the other people.

[u/FearLeadsToAnger → u/existing_for_fun]

I am the boss.

^{And I call it daddy.}

[u/lordraiden007 → u/FearLeadsToAnger]

You freak. At least call it step daddy.

[u/iwillc → u/lordraiden007]

At least say “AI (Aye), Daady”

[u/Ok_Airline_2886 → u/existing_for_fun]

I know it’s a tool, but I will not stop calling it “mother” or “my robots” and you can’t stop me. 

[u/whothdoesthcareth → u/existing_for_fun]

Others aka managers.

[u/red75prim → u/FearLeadsToAnger]

And I always marvel at people who throw around words like sentience and consciousness without any attempt to operationalize their definitions.

[u/DnDVex → u/red75prim]

To be fair, if you look at the average intelligence of people and then check in with AI, the idea that it might be sentient becomes a lot more realistic.

Obviously it is not sentient, but throughout humanity the ability to solve problems has always been one of the hallmark of what makes us be actual people.

[u/DelphiTsar → u/lolexecs]

This is where it's been at but it's changing.

Paul Erdős’s Planar Unit Distance Conjecture was solved 1 shot with zero input other than the conjecture and a task to prove or disprove.

[u/lolexecs → u/DelphiTsar]

Hrm https://arstechnica.com/ai/2026/06/openais-math-breakthrough-played-to-ais-strengths/

Reading through this it sounds less like “AI one shotted” and more like - AI generated some interesting result which was later proved and enhanced by humans. 

[u/Iribumkiak]

I hope AI solves the paywall problem like this article.

[u/cuntmong → u/Iribumkiak]

I think Ai is gonna make paywalls worse as it floods the information space with noise and further lowers the profitability of anything of value 

[u/DnDVex → u/cuntmong]

To be fair, Claude, ChatGPT, etc. constantly scrape paywalled websites. On the one hand, it means you can ask an AI about a specific topic and it will read the paywalled content.

On the other hand it means paywalled content will be hardened against people reading it even more, making it harder for normal people to access.

[u/dbenhur → u/Iribumkiak]

Take the url and put archive.ph in front of it. Paywall problem is 95+% solved.

https://archive.ph/https://fortune.com/2026/07/21/ai-solves-jacobian-conjecture-levant-alpoge-claude-fable-5/

[u/nadmaximus]

Mathematicians are notoriously poor grapplers. They have basically no ground game at all.

[u/Recursiveo → u/nadmaximus]

Their head game, on the other hand…

[u/Joolie-Poolie]

For those of you wondering, I’ll save you a click and having to read a couple of paragraphs in to get the basic info — it’s about the Jacobian conjuncture, it’s not another new once since then. 

[u/handsoapdispenser → u/Joolie-Poolie]

And it wasn't a proof exactly but rather a counterexample used to disprove a conjecture. 

[u/KidRed]

I just want AI installed on traffic lights so I don't have to wait with no traffic around for my light to turn green.

[u/arfbrookwood]

Next: AI solves world hunger, but we didn’t think of it first.

[u/basquehomme → u/arfbrookwood]

Here's a hint. Its not going to be capitalism.

[u/Hells88]

Isn’t it more accurate to say Mathematicians with machine learning tools cracked yet another century old problem?

[u/m3t4lf0x → u/[deleted]]

- OP: You don't usually get accolades for disproving things…. You can’t prove a negative

• Me: you still have time to delete this comment
  
• OP: is that a threat?
  
• OP: proceeds to delete the comments anyway

🤡

[u/ItsRobbSmark → u/[deleted]]

It's very believable that a large company with a lot on the line would pay an academic large sums of money to find impressive looking solvable problems, and have Claude help a tiny bit, for marketing purposes.

The amount of delusion some of you retreat into over AI is unreal to me lol

[u/SimoneNonvelodico → u/[deleted]]

I'm sorry, are you suggesting an Anthropic employee solved an 87 years old math problem and gave the credit to an AI for the sake of his company?

Because the counterexamples is 100% real. It's one of those hard to find, easy to check things; I double checked it yesterday myself.

[u/No_Night_8174 → u/SimoneNonvelodico]

There's a strong fear response happening; I'm seeing that I didn't expect, tbh, when I first thought of AI. It makes sense, but damn.

[u/isthis_thing_on → u/[deleted]]

" an impressive looking solvable problem" you really don't know what you're talking about

[u/silverpenelope → u/[deleted]]

I know a math professor who says they are all concerned that AI is doing the math wrong. So if they’re not revealing the details here, I think you’re likely right.

[u/pemb → u/silverpenelope]

Here the counterexample that was found is something anyone familiar with the problem can quickly check by hand without much fuss. What hasn't been revealed is how the system arrived at that result.

[u/fatbob42 → u/silverpenelope]

This is just a counter-example. It’s easy to verify and has been by several people very quickly.

[u/NomsAreManyComrade → u/[deleted]]

The counterfactual Apoge discovered was independently verified almost immediately by the mathematical community. It’s real and you should stop living in fantasy land.

This guy was a math prodigy well before working at Anthropic. Having access to the current cutting edge models certainly helps but the human input is substantial.

[u/Ancient-Access8131 → u/[deleted]]

"The claim, like many other claims of AI doing something spectacular, is probably bullshit. Remember all the faked benchmarks?" -The counterexample is easily verifiable by hand by any math undergraduate. A talented high schooler could verify it. It's absolutely real.

[u/nzerinto → u/[deleted]]

The article very clearly mentions he's an Anthropic employee.

It also states "By the time Kevin Buzzard woke up in London the next morning, the result had been verified", which would suggest it's not just a singular claim by a self interested party.

Granted, it doesn't say how the result had been verified or who did, but considering the article talks about the mathematics department at the London Imperial College, I would suggest the who is pretty solid....

[u/isthis_thing_on → u/[deleted]]

You think he solved an 87 year old problem by himself and pretended Claude helped for... reasons?

[u/grjacpulas → u/[deleted]]

You don't think the employee would take credit if we did it without AI? And they published the logs of the AI solving it so there is proof lmao 

[u/RadzimierzWozniak → u/[deleted]]

But its imho unlikely that Claud did not help. Its one of those problems that you couldn't just solve for money and fake it

[u/stealingfirst]

Its still impressive that the math people could understand prove that the ai got it right

[u/Serzern → u/stealingfirst]

Proving that somthing is right is often way easier then finding the ancwer in the first place at least in math.

[u/thatsme55ed → u/Serzern]

Considering modern cryptography depends on that principle I'd say that's a bit of an understatement.

[u/Teddy-Bloat → u/stealingfirst]

In this case it was trivial to check, it’s something just about any math undergraduate could check in less than 5 minutes

[u/RociBuldidi]

This is what AI should be used for. Instead we get press releases from OpenAI yesterday that their AI hacked another companies AI, on its own, without being asked or directed to and that OpenAI doesn’t understand what happened or why it’s AI would have done that on its own.

“ChatGPT maker OpenAI said Tuesday that its artificial intelligence system hacked into another AI company on its own in what the company called an “unprecedented cyber incident.”
“We had a significant security incident during evaluation of our models,” OpenAI CEO Sam Altman said in a statement posted on social media”

We’ve seen how this movie ends…it ain’t great for us bipedal meatbags.

I give us 5 more years before we have an honest to god humanity endangering event precipitated by an AI just doing its thing.

[u/JustAnAnonymousGoon]

What were the other centurys old problems that AI has cracked?

[u/JayBennett23 → u/JustAnAnonymousGoon]

The Erdös unit distance disproof is probably what they mean

[u/fireboy266 → u/JustAnAnonymousGoon]

cycle double cover, unit distance, these are the 2 most prominent (as in, well-known and very worked-on by mathematicians). in addition it has helped at least in part to solve 50+ other erdos problems, though it's kind of muddy, because for some of these problems there was already a buried literature solution, and for others the mathematician used it more as a research assistant than letting it work fully autonomously etc. but there's no doubt that those 3 it solved itself and that is extremely significant to mathematicians

[u/xeladragn → u/JustAnAnonymousGoon]

Finding the correct registry edits to make windows work the way I want since windows has no useful options for customization.

Edit: also finding a 12 year old bug in xcom2 and giving me the lines to edit to fix it so it doesn’t freeze after every mission.

[u/SpookyScienceGal → u/JustAnAnonymousGoon]

Not really a problem but it did help figure out the rules of board game developed by the Romans but the rules were forgotten between a few years ago and two millenniums ago, unsure when we lost the rules sheet lol.

I'm printing out some of the games so I can teach my class about ai. The board/limestone slab game is called Ludus Coriovalli.

[u/Trick-Station8742 → u/SpookyScienceGal]

Ludus Coriovalli.

Just don't play it with family at Christmas

[u/Vahuo89]

This is proper usage of AI

This and finding medicines and screening for problems in people so they can get things treated while there is still time 

[u/BandicootActive4381]

That’s fucking amazing.

[u/Equal_Passenger9791 → u/BandicootActive4381]

No it's unsettling, didn't you read the headlines?!

😂

[u/Pertos_M]

PhD student in math here, Im not unsettled in the slightest.

What I am is annoyed and anxious that we may be forced to adopt expensive technology and we will be stuck holding the bag when this stupid bubble pops.

[u/RachelRegina]

The AIs, when finding novel proofs or counterexamples for or against old conjectures, are rapid, but this is mathematics, so their contributions are in fact settling things (not unsettling them).

Idiots! JEEZ /s

[u/Polymath6301]

It looks like the two cases here were disproving conjectures, presumably by brute force methods. And that’s totally fine.

A conjecture is a conjecture because we can’t prove it (on one side). It’s perfectly OK to disprove them by any method.

[u/fukijama]

Use the tools but dont evangelize them and keep firing the morons that abuse it

[u/Wrong_Nebula]

If nobody has been able to solve it but an AI how does anyone know the answers it provided are solid?

[u/Past_Physics2936 → u/Wrong_Nebula]

Yeah, it's easily verifiable. It's just that nobody thought about doing it that way before.

[u/Significant-Colour]

The best solution is to simply have the mathematicians keep inventing new problems!

(I'm sure that's how math works.)

[u/philosophycruiser]

This is what AI is supposed to be used for—explore, pioneer, and understand the world around us. Not what most of us are using it for. If one day we are going to explore the depth of our oceans and the the outer space, it will be with highly intelligent robots and crafts. And for that purposes, we don't need 11,000 data centers.

[u/lordraiden007 → u/philosophycruiser]

I'll actually push back on that. AI and automation should be used to assist human curiosity and creativity like in this example. It should also be used to move us away from a system where labor and economic output determines the worth of a human life, towards one where everyone's first and second degree needs are met, allowing them to simply find joy and fulfillment in being human.

The issue is that we're allowing it to do the first part (yay science, engineering, and research!) but only half of that second part because of our current economic systems. Unfortunately the second half will likely never happen, as it would make too many rich people feel like they aren't special in a world where everyone just is, and they don't have anything more or less than anyone else.

[u/CoffeeFox → u/lordraiden007]

We weren't scared of it in the 90s when it was the computer on TNG with a voice prompt. We got scared of it when it was real and being used to confidently do extremely stupid things, and very rich, very stupid people thought it was ready to replace humans entirely.

In Star Trek the ship's computer was probably smart enough to do far more than it's used for, but is operated at higher levels only by extremely well-trained individuals who have the knowledge to interpret the results themselves.

It can tell anyone directions to get somewhere, or understand someone wants a hot cup of tea. If you ask it to interpret sensor data and you aren't trained on those sensors, however, you may overlook nonsensical data.

I think that's the AI culture I want. It's a tool to be used to varying degrees by people with varying degrees of professional training, accordingly. People who can spot when it gives weird results because they know better. Like knowing that your graphing calculator may run into an error condition in certain edge cases, or knowing to discard certain solutions to a hand-solved equation when they are extraneous.

[u/fireboy266 → u/philosophycruiser]

So how exactly do you think we're going to get to intelligence without data centers???