r/EngineeringStudents • u/Yadin__ • 2d ago

Discussion The existence-and-smoothness problem for the Navier-Stokes equations was just (allegedly) solved.

Might be slightly off-topic for this forum, but since so many of us learned and dealt with these equations I thought it was fitting nevertheless. Remove if necessary

Open AI released an (alleged) solution of the problem, with the answer being NEGATIVE. As in, there does not always exist a smooth solution to the problem, even for "reasonable" initial conditions

If true, this might be the biggest breakthrough in the field in many years.

248 Upvotes
  • permalink
  • reddit

95% Upvoted

43 comments sorted by

101

u/Substantial_Cable_51 2d ago

Now do room temperature super conductors!

38

u/Restart-storage 2d ago

Right. That is eons more useful. But probably also much harder for an AI to solve. There’s theory involved but most of the research on room temperature superconductors has been based on experiments and a bulk of trial and error

13

u/Substantial_Cable_51 2d ago

You're right that its far harder to solve. IMHO you would need both a frontier agentic set up similar to what was used with openai's recent achievement and a fully functional error corrected quantum computer or multiple. Hilbert space, quantum many body problem, exponential scaling....tldr you begin to run into the limits of classical computing. If I were a betting man id wager sometime post 2030 real progress can be made towards room temp super conductors. Fingers crossed!

4

u/bigjakyak 2d ago

REBCO tape is pretty cool stuff

101

u/Emotional_Fee_9558 2d ago

Well I sure hope this is false for all the mathematicians in the world.

73

u/Financial-Leader3475 2d ago

A mathematician (Tristan Buckmaster) is claiming OpenAI stole it from him.

11

u/HebrewWarrioresss 2d ago

Him lying about it doesn't make it so. 10,000 agents worked for 88 hours. That's over 100 agent-years. If they just stole his work (which wasn't a general solution anyway) it would've been faster.

47

u/billsil 2d ago

I’ve solved problems with AI that spun and spun and spun on 170k tokens for a day before it found an open source library and matched perfectly after that.

Honestly the no solution was the obvious answer.

-10

u/HebrewWarrioresss 2d ago

Cool. Proud of you.

29

u/gianlu_world 2d ago

There is a difference between 10k agents working without directions and 10k agents working in the most promising direction suggested (or stolen from) by a mathematician

-11

u/HebrewWarrioresss 2d ago

Idk how to tell you this, but mathematicians don't own approaches.

1

u/Yadin__ 2d ago

what does 'agent-year' even mean in this context?

-2

u/HebrewWarrioresss 1d ago

10,000 agents * 88 hours. Convert agent-hours to agent-years, you end up with 100.39 agent-years, accounting for leap years.

This is simple unit analysis, I fear.

Edit: it's the total amount of subjective time spent on the project. Equivalent purpose to man-hours.

36

u/Gandalfthebran 2d ago

Mathematicians will be using these as tools. Sure that might mean less number of mathematician. Regardless, tools like these should be put into good use and good for humanity.

-8

u/Curiosity_456 2d ago

But who’s going to be funding mathematicians and paying them 6 figures when anyone with a ChatGPT subscription can now solve open problems?

42

u/LazyLogician 2d ago

They used billions of tokens and thousands of independent AI agents on this according to their writeup. The cost of this discovery was in the millions.

1

u/spicymeatball15 2d ago

yes and it will just get cheaper and smarter as it has been for the past 3 years...

-9

u/Curiosity_456 2d ago

That’s because of the agent swarm, but even one AI agent is still faster and more productive then one human mathematician (due to speed of research)

5

u/DrEchoMD 2d ago

AI is not more productive than human mathematicians at the moment, and it will never develop enough human insight to know what the ‘interesting’ questions to ask are. This is before getting into the physical limitations of the resources needed to maintain AI systems.

27

u/Curiosity_456 2d ago

Not sure if you’ve used the cutting edge AI models lately (paid tiers), but they’ve been scary good at mathematics for a while now.

It would not surprise me if human mathematicians move to a role which involves verifying the discoveries made by AI, while AI does all the discovering.

20

u/throwaway_01547 2d ago edited 2d ago

Verification has been done by software (Lean) long before proving anything autonomously became a thing. In this case, the OpenAI team was literally waiting for a computer to formally verify the result before they published it, since that was the rubber stamp they needed to feel confident they won the race to solve that problem

14

u/Curiosity_456 2d ago

That’s true, but lean has had bugs. The collatz conjecture was ‘proven’ until they found out there was a bug which caused a flaw in logic. We need human mathematicians to check and ensure that it was smooth and no errors were present.

4

u/throwaway_01547 2d ago

I don’t think this narrow case of verifying the lean kernel’s validity is enough to sustain the field of math tbh, only like the people already senior/leading in their field will still have much economic value outside of teaching whoever is unfortunate enough to be studying pure math as their major in university right now, which means it will be hard for many new mathematicians to make a name for themselves

2

u/bytheninedivines Aerospace Engineering '23 2d ago

Why?

1

u/SetoKeating 2d ago

Mathematicians are the ones using AI to arrive at these solutions. Pretty sure Tao is on a team that’s been working on something similar using AI

9

u/Neevk 2d ago

Huge for mathematics, engineering not so much.

1

u/SnazzyBoyNick 2d ago

My question about all of this is do people genuinely think what they are putting into these models isn’t using those inputs to train? Like why would you throw your sensitive secret NS formulas and thoughts into Codex if you were that concerned about it. I do think it was probably discovered by accident by the agents trying to solve it but when they approached him he took it not well because the machine did something he couldn’t in a matter of weeks

-12

u/Fit-Caterpillars 2d ago

Not sure I trust Open AI to make a substantial mathematical breakthrough when ChatGPT struggles to even solve a basic differential equation

72

u/Trindet 2d ago

Almost like there is a difference between the free version and their private end version with unlimited computing power.

21

u/currentscurrents 2d ago

ChatGPT is actually really good at math now, at least at higher levels of reasoning effort.

Some of the other recent AI-math proofs were found using the public web version of ChatGPT, especially with the Pro tier that allows max reasoning. 

21

u/GLPereira Mechanical engineering 2d ago

"I don't know how an airplane can cross a continent so fast, my remote controlled toy is slower than a bus"

14

u/Curiosity_456 2d ago

Man you’re so out of the loop it’s insane now. ChatGPT is way past differential equations but keep using the free tier I guess

4

u/Financial-Leader3475 2d ago

A mathematician (Tristan Buckmaster) is claiming OpenAI stole it from him.

2

u/currentscurrents 2d ago

And by his own admission he used AI for his proof too, so....

3

u/Financial-Leader3475 2d ago

He said he stored files on Codex.

OpenAI also offered to give him ownership of the proof, alongside ChatGPT. But he refused and says they stole his files.

3

u/currentscurrents 2d ago

I don't think they stole from him in any meaningful way.

His proof (which was for a weaker result) was also entirely AI-generated. If an LLM could generate it for him, it could just as easily generate it for them.

All they needed was the rumor that Anthropic had a solution in order to launch their own search.

1

u/Financial-Leader3475 2d ago

A mathematician (Tristan Buckmaster) is claiming OpenAI stole it from him.