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How An AI math breakthrough ignited a controversy

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Re: How An AI math breakthrough ignited a controversy

#141

Post by pickleRick243 »

sherburt3 wrote: post #97
pickleRick243 wrote: post #49

Earlier quoted context omitted.

I'm not sure if you meant it this way, but this is more an insult directed at mathematics, not openAI.

That would be an incorrect interpretation

I thought as much- my point is that as AI capabilities continue to expand, AI skeptics inadvertently and ironically end up belittling the humans they presumably hold in high esteem vs. the "cold machines" that aren't capable of true thought or creativity. When one says that solving a Millennium prize problem is not impressive, one is essentially demeaning practically all mathematicians and the field of mathematics itself.

Re: How An AI math breakthrough ignited a controversy

#142

Post by dgellow »

shmoil wrote: post #98
bsenftner wrote: post #54

Earlier quoted context omitted.

Only the idle and curious rich

Ramanujan was dirt poor.

How many Ramanujan didn’t get the same opportunity to show their work to what was considered the intelligentsia of that time?

Re: How An AI math breakthrough ignited a controversy

#143

Post by dgellow »

JohnKemeny wrote: post #45
sherburt3 wrote: post #40

Earlier quoted context omitted.

Its called an analogy

It's one of the seven most important problems in mathematics. Pick a better analogy.

If you want to be pedantic it’s one of the 7 problems a specific institute considers to be the most important in mathematics: https://en.wikipedia.org/wiki/Millennium_Prize_Problems

(Not that I think the comparison to pi digits make sense)

Re: How An AI math breakthrough ignited a controversy

#144

Post by lolakutty »

ndriscoll wrote: post #128
elgertam wrote: post #93

> “I certainly don't expect the industry to continue to spend millions of dollars to solve problems in mathematics, because there is no profit in it,” Columbia University mathematician Michael Harris wrote in an email to Science. But he worries the highly publicized achievement will be “extremely damaging to mathematics; it convinces decision makers that human mathematicians are obsolete, and it convinces young peopl…

I only have an undergrad in math, so very little understanding, but I'd be pretty surprised if it couldn't do forall just as well. Like, say it found this counterexample which relies on axial stretching or whatever approach. Then it already knows how that made the proof work, and can use it to try to prove NS has smooth solutions modulo this particular kind of defect (so it could make some statement about cohomology,…

>Then it already knows how that made the proof work..

I think you cannot assume so, because pattern matching is not reasoning.

Re: How An AI math breakthrough ignited a controversy

#145

Post by fpvandoorn »

JohnKemeny wrote: post #50
sebzim4500 wrote: post #36

Earlier quoted context omitted.

Are you asking if it uses additional axioms of `sorry` in the proof? It's easy to check that it doesn't by compiling it and telling lean to list the axioms.

It's highly non-trivial to confirm that the theorems written in Lean are actually the same as the Navier–Stokes (non-)theorem.

They actually used Lean statements that were carefully human-written and human-reviewed, from here https://github.com/google-deepmind/formal-conjectures/blob/m...

This doesn't guarantee that the statement is correct (Lean cannot do that), but makes it highly likely.

Re: How An AI math breakthrough ignited a controversy

#146

Post by cmiles8 »

rakejake wrote: post #44
rsfern wrote: post #18

Regardless of what you think of the priority dispute issue discussed on sibling threads, I’m highly skeptical of the closing quote that this Navier Stokes result means that the same approach of casually spending a few million on agentic computation is going to solve end to end materials design or drug development. Those problems can’t be formally verified with an automated theorem prover. We have a lot of physics bas…

Yeah, I think you can't just throw money randomly at problems and expect results unless you know a line of attack that can get you all the way. OpenAI chose the line of attack only after it became known to them via rumors. They "front-ran" the researchers.

Yes. What the headlines hailed as an AGI discovery the facts show more to be someone spending years mining for gold, rumor gets to OpenAI that there might be gold in this specific place, they mine there and instantly discover gold, then tell the world they’ve developed the worlds best gold finding/mining machine.

Separate from all the allegations of more nefarious actions and ethical issues, that’s the most charitable version of what happened here.

Re: How An AI math breakthrough ignited a controversy

#147

Post by epolanski »

dgellow wrote: post #142
shmoil wrote: post #98

Earlier quoted context omitted.

Ramanujan was dirt poor.

How many Ramanujan didn’t get the same opportunity to show their work to what was considered the intelligentsia of that time?

Irrelevant in 2026, you can share your results with a click.

Re: How An AI math breakthrough ignited a controversy

#148

Post by greenowl »

kurtis_reed wrote: post #111
elgertam wrote: post #93

> “I certainly don't expect the industry to continue to spend millions of dollars to solve problems in mathematics, because there is no profit in it,” Columbia University mathematician Michael Harris wrote in an email to Science. But he worries the highly publicized achievement will be “extremely damaging to mathematics; it convinces decision makers that human mathematicians are obsolete, and it convinces young peopl…

> it convinces decision makers that human mathematicians are obsolete, and it convinces young people that their passion for mathematics has no future Maybe those things are true, so maybe they should be convinced?

In that original statement you can easily substitute "mathematicians" for "programmers", "researchers", "writers", "designers", "teachers", etc, etc.

I don't see why mathematicians think they should be an exception here.

Re: How An AI math breakthrough ignited a controversy

#149

Post by rsfern »

jgalt212 wrote: post #127
rsfern wrote: post #18

Regardless of what you think of the priority dispute issue discussed on sibling threads, I’m highly skeptical of the closing quote that this Navier Stokes result means that the same approach of casually spending a few million on agentic computation is going to solve end to end materials design or drug development. Those problems can’t be formally verified with an automated theorem prover. We have a lot of physics bas…

> Those problems can’t be formally verified with an automated theorem prover. It certainly seems like any problem that is amenable to reinforcement learning will be solved.

It does, yes. So designing objections functions and making sure you can afford the training rollouts becomes really important in defining which problems are tractable. It will be really interesting to see how that shapes the kinds of problems people choose to work on

Re: How An AI math breakthrough ignited a controversy

#150

Post by simianwords »

plaidfuji wrote: post #125

The whole thing reeks of the desperation of an unprofitable venture-backed startup looking for its next PR win to keep the wind in the sails. But I think what’s being overlooked in the race to claim absolute credit is that both sides ultimately relied on a LLM (and one of OpenAI’s at that). Either a human researcher made a breakthrough discovery with the help of Codex, or the latest GPT model made a breakthrough with…

A company that can solve Millenium problems is somehow still can’t ever make profits. How did you come to that conclusion
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