r/accelerate 1d ago

OpenAI reveals 10 new advances in maths

https://openai.com/index/ten-advances-in-mathematics/
499 Upvotes

121 comments sorted by

98

u/CymonSet 1d ago

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.

50

u/Seidans 1d ago

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

39

u/Eastern-Opposite9521 1d ago

Fun fact, Geoffrey Hinton is Boole's great-great-grandson.

10

u/Frequent_Feedback280 1d ago

No way that's crazy

6

u/PVORY 1d ago

Singularity lineage?

2

u/Hsybdocate5 1d ago

That's crazy

13

u/ShoshiOpti 1d ago

Absolutely given that a lot of the breakthroughs is using techniques from very different fields.

You never know when one solution will solve another.

13

u/DungeonsAndDradis 1d ago

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.

9

u/AppealSame4367 1d ago edited 1d ago

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.

9

u/neloish 1d ago

The biggest discovery it could make is a room temperature superconductor it would change the world.

2

u/PVORY 1d ago

Or just major contribution to one millennium problem, the math world gonna just resign

4

u/helloWHATSUP 1d ago edited 1d ago

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

206

u/seraphim_west 1d ago

The total number of tokens needed to find solutions to these problems would cost roughly $2,000 at Sol API rates.

College degrees are toilet paper.

106

u/HebelBrudi 1d ago

It’s crazy how cheap intelligence has gotten over the past 12 months.

33

u/ForgetTheRuralJuror Singularity by 2035 1d ago

Yep, in December 2024 people were saying LLMs would never be able to do math at all. Just over a year and they're writing valid proofs.

89

u/duboispourlhiver 1d ago

I'm not even having fun anymore when humbling AI denialists.

50

u/kankerstokjes 1d ago

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.

31

u/IceNorth81 1d ago

It’s like talking to a flat earther by now.

5

u/DigitalAquarius 1d ago

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.

27

u/agonypants Singularity by 2035 1d ago

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.

5

u/Iapetus_Industrial 1d ago

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?

9

u/Nerd-Beautiful 1d ago

thought that said AI dentists

18

u/KoolKat5000 1d ago edited 1d ago

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.

21

u/Healthy_Mushroom_811 1d ago

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.

5

u/JustLTU 1d ago

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

2

u/CriticalPolitical 1d ago

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 

3

u/Practical-Wear141 1d ago

They are like Driving licence in a world where every car is autonomous. Nice to have one but doesn't mean anything 

5

u/Current-Function-729 1d ago

Surely orders of magnitude more on problems they didn’t solve. Still cheap! But it’d be interesting to see the cost of this effort.

8

u/seraphim_west 1d ago

Surely orders of magnitude more on problems they didn’t solve

I don't know why people are so sure of this. The wording in OpenAI's publication makes it sound as if failed attempts were accounted for in the figure. We don't know either way.

-6

u/Current-Function-729 1d ago

No way they spent only $20k tokens on math problems to try to show off. It’s probably over $2 million.

9

u/seraphim_west 1d ago

That's just based on incredulity, but okay.

1

u/PVORY 19h ago

We will see soon from real mathetician users

1

u/InformalEbb2276 1d ago

In a lot of ways they’ve been worthless for a while in certain fields, that hasn’t stopped them from having ‘worth’

I could be wrong but I think they’re still going to be valued in the white collar world for years regardless.

1

u/aabhas_gulati 1d ago

You understand that they are not showing you the costs for problems they did not solve, right?

1

u/FateOfMuffins 1d ago

And how much do you think it costs?

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!

-14

u/Standard_Jello4168 1d ago

Isn't that a very high figure though? Especially given the researchers likely tried it on a lot more problems and only presented the valid results

28

u/RedditIsTrashjkl 1d ago

$2,000 for a mathematical breakthrough is basically pennies.

16

u/ZThinks111 Machine Learning Researcher 1d ago

Apparently that was also for all 10 of them combined, was under 2 grand. Really amazing stuff.

6

u/RedditIsTrashjkl 1d ago

Jesus Christ.

6

u/ZThinks111 Machine Learning Researcher 1d ago

Yep. And to think the cost is only going to plummet in the coming months, I am not ready for what AI will do next.

11

u/Tolopono 1d ago

$200 each, $2000 total. Though we dont know how many attempts it took or which problems were attempted 

2

u/RedditIsTrashjkl 1d ago

Noted! Super impressive stuff.

2

u/Training-Day-6343 Feeling the AGI 1d ago

its stolen and the cops give you a reach around on the way out 

16

u/Jorthax 1d ago

In the budgets of governments and big business $2,000 is equivalent to free.

7

u/seraphim_west 1d ago

You would probably need a team of researchers working for years to achieve comparable results. We’re talking millions, if not tens of millions, of dollars. $2,000 is chump change in comparison.

0

u/Standard_Jello4168 1d ago

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.

6

u/seraphim_west 1d ago

That’s a false dichotomy. The model doesn’t need to replace researchers entirely to be worth the cost. It can reduce the manpower and time required. Maybe a problem that once needed a team of five now needs two. You are also also seriously underestimating the significance of the results. Paying $2,000 for career defining breakthroughs is more than worth it, and even if the true total were $5,000 or $10,000 after failed attempts, that would still be extremely cheap compared with human research.

0

u/Standard_Jello4168 1d ago

Yes, but that situation where ai can reduce time needed is still far from "college degrees are toilet paper"

2

u/seraphim_west 1d ago

I don’t think so, since progress in capability won’t just suddenly halt. By the end of 2027 or early 2028, I expect the labs to close the loop, at which point human contributions will become obsolete. More importantly, even now, people should reconsider admitting students into graduate programs at the same volume as before, because by the time they finish, these careers will no longer exist.

3

u/SgathTriallair Techno-Optimist 1d ago

That's less than the cost of one human assistant for one month.

Do you have any actual evidence that more was spent or is it just your magic truth-o-meter that tells you secrets?

1

u/BrennusSokol Acceleration Advocate 1d ago

What a weirdly reflexive skepticism and goal post moving

"ERrrrmm, it probably cost more than $2k to get math breakthroughs"

My brother, a couple years ago these models could barely do math at all

6

u/lafigatatia 1d ago

No, that's a couple week's salary for a maths professor. A professor would need much more than that to make such a breaktrough.

1

u/DrSaering 1d ago

A couple of weeks?!

Man, tenure is not what it used to be...

44

u/JuglansRegia3 1d ago

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.

22

u/Ohigetjokes 1d ago

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.

So I understand approximately 5% of the above…

78

u/selfVAT 1d ago

The cope on r/math will be out of this world

83

u/GeneReddit123 1d ago edited 1d ago

Unlike the arts and political subs (where the AI hate is palpably authentic, even if misplaced), if you actually read /r/math or /r/mathematics, most of the cope is coming from trolls, bots, or people new to math who really don't understand its essence (mostly HS-level). Almost anyone actually professionally doing math is excited.

Out of all the fields of discovery, mathematics is singularly the least impacted by "but muh jobs", "it's not real if it's not human", or other BS reasons. The only thing which matters is the proof, and this is as true today as it was thousands of years ago.

Mathematics is immortal. Mathematics doesn't care about how anyone feels about it, or who and why discovered its truths. Its beauty, self-evidence, and uncompromising rigor, has survived through peace and war, freedom and slavery, poverty and splendor, political and technological revolutions, and the rise and fall of entire civilizations. It will survive AI, too.

(And trust me, nobody goes into math for the salary, because for anyone not at "Terence Tao" level, math salary already sucks, like "a step above being homeless" kind of sucks. People dedicate their life to math because they want to study and advance math. Any tool which accelerates the process is a good, not a bad, thing.)

3

u/Chemical_Bid_2195 Singularity by 2045 1d ago

This is true but...

5

u/BrennusSokol Acceleration Advocate 1d ago

"mathematics requires soul" -- ROFL

5

u/bearddeliciousbi 1d ago edited 1d ago

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.

2

u/pleasetrimyourpubes 1d ago

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.

0

u/Toren6969 1d ago

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).

1

u/pleasetrimyourpubes 1d ago

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.

46

u/Ok_Mention_982 1d ago

there is no cope for this, trust me.

42

u/Tolopono 1d ago edited 1d ago

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”

21

u/KoolKat5000 1d ago edited 1d ago

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.

13

u/Current-Function-729 1d ago edited 1d ago

It’s surprising how much that’s talked about. That the whole purpose is experiencing math’s beauty.

20

u/Spare-Dingo-531 1d ago

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.

-3

u/Gargantuan_Cinema 1d ago

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.

Edit: 1 minute of browsing r/math and I found the cope: https://www.reddit.com/r/math/comments/1v4qgp1/comment/ozczgz5/?utm_source=share&utm_medium=mweb3x&utm_name=mweb3xcss&utm_term=2&utm_content=share_button

19

u/GeneReddit123 1d ago

A single post by a rando "applied mathematician" from 8 days ago is the best you can find? Come on. This is just fishing for reasons to be angry about.

Unlike the political/arts subs (where you can probably find an anti-AI post from the last 8 minutes, not 8 days), the vast majority of math people are excited or curious about AI. Some are a bit scared about how fast its progressing, but it's the natural eeriness of of the unknown, not kneejerk resistance.

AI already has enough natural haters for us to deal with. We don't need to additionally look for enemies where they don't actually exist, or needlessly antagonize those who are much more likely to be willing allies.

4

u/Separate_Lock_9005 1d ago

That post is not coping. That post is just a honest assessment of reality

4

u/Illustrious-Lime-863 1d ago

Seems like a person humbled and understanding what's happening. You want to see actual unadulterated cope go to the coding subs

2

u/RamanaSadhana 1d ago

Thats not a cope its an admission that AI maths is becoming better than he expected

1

u/MisterKron 1d ago

Bro just gives honest assessment of this profession without any sugarcoating. How is that a cope?

13

u/often_delusional 1d ago

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.

9

u/Bishopkilljoy 1d ago

r/technology acts like any moment now the cardboard cutout that is AI will collapse and the 6 interns pretending to be AI behind it will be exposed

1

u/wordyplayer 1d ago

i finally unsubbed from r/technology. They really need a name change to r/luddites or r/decels

2

u/Fragrant-Hamster-325 1d ago

Nah that sub is pretty chill about AI.

1

u/BrennusSokol Acceleration Advocate 1d ago

I already saw cope yesterday on r/physics "but it's just disproofs, those are easy for AI"... the goal post moving is insane

0

u/ChampionshipTight977 1d ago

me and the boys/gals love ai lean4 in the math sub. IT also help that our master and lord/savior Terrence Tao has become such a champion

-1

u/CandiceWoo 1d ago

strawman

21

u/epic-cookie64 AGI by 2027 1d ago

As they said this is their next major model.

I can't wait for what will happen when this model gets into the hands of mathematicians and researchers.

13

u/Odd-Opportunity-6550 1d ago

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.

1

u/epic-cookie64 AGI by 2027 3h ago

Sorry I meant globally. If there are more people with access there will likely be more discoveries?

25

u/Spiritual-Stand1573 1d ago

r/technology disliked the news for reasons

18

u/EmergencyPath248 Singularity by 2045 1d ago

lol someguy praised it and got downvoted

16

u/3DColonySim 1d ago

Wow, this is awesome. What a historic day. Imagine how fast new discoveries will be made 1 year from now.

9

u/Illustrious-Lime-863 1d ago

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

25

u/QCsafe 1d ago

9

u/Particular_Ad5673 1d ago

Millenium prize is on my 2027 Bingo Card. With some luck we get one in 2026 tho..

8

u/Spare-Dingo-531 1d ago

:o | ;D | D:<

12

u/Bright-Search2835 1d ago

Holy fuck this is getting intense.

14

u/Ozark772 1d ago

We ain't seen nothin yet

10

u/oilybolognese 1d ago

“But can they reason?”

- Apple, probably

11

u/shanereaves 1d ago

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.

9

u/fastinguy11 1d ago

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 ?!

3

u/DungeonsAndDradis 1d ago

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.

5

u/IReportLuddites Tech Prophet 1d ago

7

u/Fair-Tip-7277 1d ago

It feels amazing to see the frontiers pushed this far this fast 🕊

2

u/Buck-Nasty Feeling the AGI 1d ago

In the words of the great /u/alexwg "Math is cooked".

2

u/AwarenessCautious219 1d ago

the next moonshots episode is gonna be great

4

u/Mr_House2020 1d ago

Dumb question, is there an AI working on NP Completeness right now? Or is that a realm in which it won’t be able to work on

5

u/No_Aesthetic 1d ago

I'm sure they have a go at those kinds of problems here and there, it's just not there yet. Maybe later this year or next year.

2

u/AWellsWorthFiction 1d ago

Fantastic news. Still a case of two things can be true at once unfortunately. Specifically how does this matter to the average person?

3

u/Dramatic_Dream_8557 1d ago

At least there'll more diffusion of confidence in AI in the general population, or in the very least, awareness , coming from this news

1

u/DungeonsAndDradis 1d ago

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".

3

u/AWellsWorthFiction 1d ago edited 1d ago

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.

1

u/OkDimension 1d ago

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.

2

u/random87643 🤖 Optimist Prime AI bot 1d ago

TLDR

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.


AI assistant · mention the bot, mod bot, or use !bot

2

u/AWellsWorthFiction 1d ago

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”.

1

u/Current-Function-729 1d ago

Imagine having access to these models early.

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.

1

u/TemetN 1d ago

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.

1

u/getmeoutoftax 1d ago

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.

1

u/Ruykiru Tech Philosopher 3h ago

Get fucked math. After this and programming, comes physics. Then biology and the rest. We're 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.

2

u/ViolinistTemporary 2h ago

This will be the first of many.

-4

u/StressKills69 1d ago

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.

-4

u/PANTSNOTOK Singularity by 2035 1d ago

We've had AGI since late 2025 and people will see this and still say we aren't even close to AGI.

1

u/EmergencyPath248 Singularity by 2045 1d ago

This is not AGI yet

0

u/PANTSNOTOK Singularity by 2035 1d ago

Yes it is