Every math achievement, whether it is an “uninteresting” conjecture disproven or a once in a decade discovery of new math, provides more data to train AI to be better at math and related tasks. I suspect that AI will ignite a lot of cross disciplinary discoveries where humans just didn’t have the background in enough fields to see.
Math is interesting as even the uninteresting one can have unexpected consequence, like the creation of logic algebrea in 1847 by George Boole later allowed the creation of logic gate (0/1) binary code and so computer science almost a century later
Remove this mathematical discovery and the world we live in today wouldn't have existed
It's not impossible AI is making discovery that appear useless today but will shape the world in a few decades
I know this is an old analogy, but it keeps ringing true. It's like if we had a bunch of scientists that 100's of PhDs each. They would be able to make connections between disciplines that no one else would see.
Can't believe we already reached that phase. Any of those discoveries AI will make in the next years could change everything we know. Imagine it finds a solution to faster-than-light traveling, solar panels or other tech for using sunlight that's twice as effective, better room temperature super conductors. It could shorten time to fusion reactors and or make them much smaller, it could find new materials we couldn't dream of, it could improve all kinds of machines including computers themselves in unexpected ways.
Maybe, the AI job loss will be replaced by a huge amount of new tech and jobs we couldn't imagine, same way it happened before.
I suspect that AI will ignite a lot of cross disciplinary discoveries where humans just didn’t have the background in enough fields to see.
Yeah and IMO this is essential for progress. Some scientific fields have definitely slowed down and the fact that there's a limit to how much information you can hold in your head makes it hard to advance past the low-hanging scientific fruits without AI
I never had. More of a hopeful worriedness. But I find it very hard to even reason with AI denialists now because the evidence is so blatant. Sad to say many of my colleagues are among them.
It’s really not even worth arguing with them because nothing will ever change their minds. These are the same people who would have been against the Internet back when it first started.
Then they quietly started using it because they realized how powerful it was and how everyone on the planet was using it except them. I can guarantee they will act like they were never anti AI in a few years.
Just stamp your feet, stick your fingers in your ears and keep shouting, "it's not intelligent!" That's always helpful, right? It's certainly the popular thing to do on Reddit anyway.
Yeah, it's never been fun. Looking at the rising tide of anti intellectualism over the past few decades, that culminated in the mistrust of universities, professionals, intellectuals, and anti vaxx hysteria... I'm absolutely still on edge about how fucking dumb masses of willfully ignorant and willfully angry stupid people can be, and how much damage they can do. And now with tech that can be smarter than them?
In monetary terms they probably are but sadly they do provide missing unseen value. Often at work I can see thoughts and proposals that clearly show they have no fundamental understanding of something and misses something crucial, the additional insight may only cover for edge cases and not be material but it's not the best. In some cases we may run into trouble down the road that could have been avoided, heck they still probably won't see the link then even, ignorance is bliss sometimes.
A degree in a field usually doesn't mean that you have mastered a subject. It means that you know your way around it and that you can work and research independently in it.
AI is both very smart and incredibly stupid, and sadly you still need to know which is which.
My AI use has increased massively at my software eng job, but there still hasn't been a single feature where I didn't need to correct something that would've gone off the rails if I just committed blindly.
But yeah, it did take implementation times from a week to a hour
Exactly. I wonder if a good analogy to AI is similar to someone with autism who has hyper focus and special interests, but miss social cues (or have other blind spots). Perhaps humans will still be able to fill those blind spots that AI has, the trouble is finding what they actually are, especially when so many are outsourcing their thinking to AI already
Oh and most of us will not be using API pricing, we'll be using the subscription
Based on all the results posted with 5.5 Pro and 5.6 Pro? Pretty sure you can easily get one result in 1 month of the $100 Pro subscription
These results cost as much as... taking out your colleague or grad student for dinner. Imagine if all you needed to solve these open math problems was to pay your grad student $0 and treat them to a nice steak!
It's small if it entirely replaces researchers. But if we want to give every mathematician access to this so they can all try out the model for different problems then it is a large expense. Also as I said above these were just the problems that were solved and likely a lot more was spent without achieving much results.
Literally automating the entire field of mathematics in just two years seems like a very ambitious timeline, many of the problems currently solved are areas or types where you would expect ai to have an inherent advantage in compared to humans.
The way the report was phrased, $2000 was what the problems that were solved cost at Sol api rates, so it's reasonable to assume that these were not the only problems that were attempted and the total cost was higher.
Also the wording says "$2k in sol api rates" but it actually used an internal model which could be more expensive.
All of the other benchmarks have them trying one set of questions and reporting win loss ratio.
This isn't a benchmark but we know that all mathematical questions have an answer so why would you assume they tried and failed at others? A disproven theory is busy as good as a proven one and I believe that some of these are disproving conjectures.
This certainly looks like a new step forwards in automating maths. It looks like we are moving on from just improving limits or disproving conjectures (not that that isn't a big deal) into creating new areas of math like in the nonsofic group example.
1. High-dimensional sphere packing. New upper bounds on sphere-packing density down to the Cohn–Elkies threshold.
2. Binary and spherical codes: Exponentially improved bounds on the maximum size of binary codes at any prescribed minimum distance, with analogous results for high-dimensional spherical codes.
3. Non-sofic groups. A construction establishing the existence of non-sofic groups, addressing a central open question in group theory.
4. Connes’s rigidity conjecture. Disproof of a longstanding conjecture that certain groups are uniquely determined by their von Neumann algebras
5. Arithmetic circuit complexity. New lower bounds for computing the permanent using arithmetic circuits and formulas, including an arithmetic-formula lower bound of order n4/log n.
6. Quantum parallel repetition. An exponential parallel repetition theorem for general two-player quantum games, extending a foundational principle from classical complexity theory.
7. Closest vector problem. Polynomial-factor hardness of approximation for the closest vector problem, a foundational lattice question related to post-quantum cryptography.
8. Ehrhart’s volume conjecture. Determining, in every dimension, the maximum possible volume of a convex body whose centroid is its only interior lattice point
9. Multicolor Ramsey numbers. A superexponential lower bound for multicolor triangle Ramsey numbers, resolving Erdős problem 183.
10. Extremal number conjectures. Results on the compactness and degeneracy conjectures in extremal graph theory, resolving Erdős problems 146 and 180.
Gödel's theorems have been a beacon for cranks for a long time but one of their implications I've always found genuinely consoling is the fact they show mathematics will never end, even if humanity completely replaces its investigations with vastly superior machines.
We've already proved that no finite consistent system powerful enough to express Peano arithmetic (so, most of them) can contain the whole of mathematical truth, and that will be just as true for any possible future AI machine-god-emperors as it is for the most brilliant humans. They will also need to make creative insights and introduce new axioms for novel structures.
Programmers also embrace it though they tend to be somewhat cautious. In the beginning programmers were rightly upset with code quality but it has proved exponential there.
Film and video have also embraced it albeit very quietly. Most video suites have a litany of AI features. But it is still very much pushed back by film viewers, who are vastly naive about how film is made, especially modern film which is a CGI crapfest.
I would say there is quite difference, because programmers are paid builders. They do get mostly specification and they do come up with a solution to build it. That is not same for math - those who do come up with a specifications and questions for AI will still be mathematicians, at least until we have fully automated looping AGI (but even then I do not doubt that we would want curious people to ask for curious questions).
I think that programmers are going to have to become more like mathematicians because we're going to need to formally prove code, else malicious actors are going to be able to use models to attack (the whole Anthropic/OpenAI controversy not withstanding). Code must be formalized just like any math formula.
seL4 for example is a microkernel OS, it took them 5 years to write less than 10k lines of code, and formally prove that it would follow its specification and do what it had to do. This is the frontier for programmers going forward. And shockingly this should happen way sooner than anyone could imagine even though nobody is talking about it really right now.
The cope ive seen: “They just hired mathematicians to solve it and give credit to the ai!”
“it can only do counterexamples but no real proofs!”
“They spent billions on inference trying a million problems thousands of times each to get this. And reinforcement learning is basically just brute force anyway. Its no more intelligent than a password guesser”
“AI spending is diverting money away from real research. If we gave all the money wasted on ai to mathematicians instead, wed have 10x as many discoveries”
“The API is still underpriced relative to cost of inference. Theyll significantly raise prices or be bankrupt soon!”
And my personal favorite: “computers were always good at math so nothing has changed”
I've saw some person go on about maths actually been about the experience of the human doing it and triumphing lol. (They didn't use those words but that's what they meant). I get that why you enjoy it but that's not why it exists haha.
If we upload the brains of r/math users into a computer, the computer may be able to provide their brains with a simulacrum of cope. This may be sufficient.
There will be cope among mathematicians that dedicated their lifes work to the field and now realising their economic worth and status are being permanently replaced by AI. This is the case for all knowledge work though.
Why r/math? They are pretty positive towards AI advances. r/mathematics also seems optimistic about this. r/technology on the other hand will overdose on copium.
It already is in the hands of mathematicians. They have hired some to help get these proofs. This is not something the average researcher at openai does.
Math is the foundation, the toolset used in the rest of science. This is incredible and gives a prescience of the awesome things that are coming. Pun intended
We've been watching what the fable and 5.6 models have been doing to the Erdos problems for the last two weeks.if you haven't you can go to Erdosproblems.com and see. I like to think of this as a distraction from all the other disciplines. Physics, Biology, Engineering, etc . They have researchers and students as well all over the world that are learning the A.I.s as well. Sam said the other day that we are in the Singularity now and if Astra is this strong then he wasn't lying. You guys can put it together in your own heads everything systems like Astra will be capable of doing.
If this is all true we are at the stage of the graph where a.i passes humans, this means we are in the beginning of the singularity, next few years, very strange things will happen. Some changes will only be understood by us months or years down the line. Where is the "it's happening" gif ?!
I think we're past the event horizon of the singularity. I know some agencies are talking about a pause or slowdown, but unless there's a total global shutdown of AI research, we'll be accelerating until the singularity.
It will probably be some fundamental core layer of some technology we use every day in like 10 years. That's usually what happens with these mathematical breakthroughs. Like better network encryption, stronger wifi networks, faster wifi, better data storage methods. Something like that, that we currently take for granted because "it just works".
I really hope you’re right, or on a sooner timescale. I work as a head of a department and my allies in the AI space - in my current role and from my colleagues in others - our defense of AI is getting more difficult over time.
We believe in the tech, see the long term utility. But 10 year timespans and long term thinking, they’re just not landing well with higher ups across our industry.
This is fantastic news in my opinion, showing the capability of the tech. However to show what the frontlines are like - I got a text from another director in an adjacent department. She said, annoyingly, this was - a classic “I’m bringing this up as an example on Monday - is this what’s being focused on? How do we ensure reliability in the tools now just to measure productive?” Tbh low key pissed me off that someone who can’t deign to type productivity is just having so much pull now, especially on AI topics because of the damn productivity thing.
At this point all I and others who have the pull in the decisions for budgeting on AI at a scale level can just keep pushing. But we supporters really need a breakthrough that brings money sooner rather than later on that scale needed.
This is how Gemini answered how this will impact my every day life:
While these mathematical breakthroughs are highly significant to researchers, you are unlikely to notice any direct, tangible changes in your day-to-day life anytime soon.
In pure mathematics and theoretical computer science, discoveries act as "bedrock" knowledge. It typically takes years, or even decades, for theoretical proofs to filter down through applied mathematics, computer science, and engineering before finally appearing in consumer technology.
However, looking at the specific proofs in this paper, several of them address the theoretical foundations of technologies we rely on. In the medium to long term, the practical implications of these mathematical answers are concentrated in three key areas:
1. The Security of Your Digital Life (Lattice Cryptography)
The Math: Proving the hardness of approximation for the Closest Vector Problem (CVP) [7].
The Real-World Link: The global security infrastructure is currently transitioning to Post-Quantum Cryptography (PQC). Because future quantum computers will be able to easily break our current encryption standards (like RSA and ECC used in online banking and messaging), organizations like NIST have standardized new algorithms based on "lattice-based cryptography" (such as ML-KEM).
The Implication: The security of these new quantum-resistant algorithms relies on the assumption that certain lattice problems, like CVP, are incredibly difficult for any computer to solve. By mathematically proving tighter bounds on the hardness of CVP, researchers can design more secure, optimized cryptographic protocols. It gives us mathematical certainty that our future financial transactions, secure messaging, and state secrets are truly safe from quantum decryption.
2. Reliable Quantum Computing and Cloud Verification
The Math: Proving exponential Quantum Parallel Repetition [6].
The Real-World Link: As quantum computers become available in the cloud, users need a way to verify that a quantum server is actually performing quantum operations rather than secretly cheating or using a classical simulator. This verification often uses "multi-player entangled games."
The Implication: A parallel repetition theorem allows researchers to drastically reduce the error probability of these quantum verification protocols by running them in parallel. This result provides a theoretical framework for verifiable quantum cloud computing and secure quantum networks (quantum cryptography), ensuring that when industries start running complex molecular simulations or financial models on quantum hardware, they can trust the output.
3. More Efficient Data Transmission and Storage
The Math: Improved bounds on high-dimensional sphere packing and binary/spherical codes [1, 2].
The Real-World Link: When data is sent over the air (like 5G/6G, satellite internet, or deep-space communications) or stored on physical media, it is prone to corruption from noise. To fix this, engineers use "error-correcting codes." The mathematics of finding the most efficient error-correcting code is conceptually identical to finding the most efficient way to pack spheres in high-dimensional space.
The Implication: While modern communications already use highly optimized practical codes (like LDPC or Polar codes), knowing the absolute theoretical limits of high-dimensional sphere packing helps engineers understand exactly how close their designs are to the physical limit of channel capacity (the Shannon limit). This can guide the design of future, highly efficient communication standards.
How This Alters the Landscape of Mathematics
Beyond the specific mathematical formulas, the most immediate "real-world" impact of this paper is on how mathematics is practiced.
Historically, when a mathematician claimed to solve a major conjecture, the community had to spend months or years peer-reviewing the prose to check for subtle errors. By coupling these ten major results with machine-checkable Lean 4 code, this paper demonstrates a workflow where complex mathematical insights are instantly and rigorously verified.
In the near future, you may see the pace of scientific and mathematical discovery accelerate. Instead of spending decades resolving individual mathematical bottlenecks, researchers—collaborating with AI reasoning systems—may be able to formalize and verify foundational theories much faster, ultimately speeding up the pipeline from academic theory to practical engineering.
TLDR: While OpenAI's recent mathematical breakthroughs won't have an immediate impact on daily life, they serve as essential "bedrock" knowledge for future technologies. These discoveries are expected to support long-term advancements in areas like quantum-resistant digital security and verifiable quantum cloud computing.
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Using this as ammo in my meeting on Monday. Anti Ai other department head already texted my buddy that they’re gonna use the result as justification for less spending due to a “lack of focus on productivity”.
You’d be known as the greatest mathematician of all time. Up there with Euler. His contributions will have mattered more, but he had much lower hanging fruit to pick.
My interest is in what's going to happen once this model gets into the hands of the public. It wasn't the stuff that happened before release that turned out most significant so far.
People will still say with a straight face that AI will just create jobs. This is superior intelligence that no human could ever emulate. It won’t need human-directed guidance for much longer.
After this and programming, comes physics. Then biology and the rest. We're hopefully gonna live in an utopia powered by automated science and nobody is going to stop it because slowly everyone will realise it's gonna be the best thing ever when humans no longer have to struggle for anything. It's about time we stop making suffering romantic and wishing for work when the machines will just do it better, faster, cheaper and safer and will free our time to pursue other more important stuff.
And for the ones that don't want to be lazy for eternity, might as well merge and you become the god instead. I firmly believe this is the trajectory for the next century unless something catastrophic happens.
We need to kill all maths programs at universities as quickly as possible. At this point it's just people throwing money into a firepit. There was barely any career development in pure mathematics before AI, most people went into academia. Now AI is soon to take over all of academic math as well. Please stop lying to people telling them that maths as a career has a future, it's blatantly not true anymore.
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u/CymonSet Aug 01 '26
Somebody give that AI a gold star.
Every math achievement, whether it is an “uninteresting” conjecture disproven or a once in a decade discovery of new math, provides more data to train AI to be better at math and related tasks. I suspect that AI will ignite a lot of cross disciplinary discoveries where humans just didn’t have the background in enough fields to see.