A million dollar math problem may just be the beginning for OpenAI
Drama in the world of pure mathematics
Two mathematicians, 10,000 AI agents and a million-dollar prize are all part of yet more AI drama this week, with heated back-and-forth over allegations of stolen work and academic malpractice.
uncertain
mathematicians → steal → work
But despite the controversy, some experts say it's indicative of the unmistakable force of AI in helping break through sticky problems.
asserted
it → say → problems
To others, it misses the point of academic research and careful human collaboration.
asserted
it → miss → research
So what happened in the world of pure mathematics this week and why is it controversial?
asserted
it → happen → mathematics
The claim
On Tuesday, OpenAI said it had solved a legendary problem in mathematics involving the Navier-Stokes equations.
uncertain
it → say → equations
Easier said than explained, the equations describe how fluids — including gases and liquids — move and change over time.
asserted
fluids → say → time
As equations do, they give us a way to try to predict what will happen if you plug in the variables.
asserted
you → do → variables
The issue — and why this is one of the famed Millennium Prize Problems that come with a million-dollar award if a solution is verified — is not knowing exactly whether the math can blow up and produce physically impossible results.
asserted
math → come → results
"It's a very deep mystery," said Ravi Vakil, mathematics professor at Stanford University.
asserted
Vakil → say → University
"It seems this huge thing that's out of reach, like this mountain you see in the distance, and the question is: can we get there?"
asserted
we → seem → distance
Vakil says it's a way to understand the universe and whether it works the way we think it does.
asserted
it → say → universe
The problem with Navier-Stokes is kind of like saying you can know everything about your foot, your shoe and a ball — but there's no ruling out you can kick that ball into space.
asserted
you → say → space
So "resolving" the problem is about figuring out whether this breakdown can happen.
asserted
breakdown → resolve → problem
OpenAI says yes: in a certain circumstance, you can get a bonkers, physics-violating result — at least, on paper.
asserted
you → say → paper
Moreover, the task "involved on the order of 10,000 concurrent agents" — AI that can perform tasks independently and doesn't need to be prompted constantly —
asserted
that → involve → tasks
that "had access to tools such as the ability to read from a cached version of the internet and the ability to run code.
asserted
that → have → code
Within 88 hours, the company said, its agents had found the solution to this problem, which has roots going back more than 200 years.
asserted
which → say → roots
It's worth mentioning that while this problem is a curiosity, the equations are used for practical applications including the design of airplanes, artificial heart valves and climate modelling.
asserted
equations → mention → airplanes
Vakil isn't surprised the company was able to achieve it, but is still impressed, though he and other experts point out that the claim now needs to be rigorously verified.
uncertain
claim → achieve → it
"No one is yet ready to fully vouch for all the details because that requires human time," Vakil, who is originally from Toronto, told CBC News from Stanford, California.
asserted
who → vouch → Stanford
It passes machine checks, but we know better than to believe those."
The counterclaim
The controversy began before OpenAI announced its findings and involved two other mathematicians, Tristan Buckmaster of New York University and Levent Alpöge, who works for OpenAI competitor Anthropic.
Among other things, Buckmaster — who used AI tools such as Anthropic's Claude and OpenAI's Codex — suggested OpenAI learned the pair were close to a solution and pursued it themselves.
uncertain
pair → pass → it
He alleged OpenAI tried to offer him credit so long as Alpöge's name wasn't on it because he works for a competing AI company.
asserted
he → allege → company
At the time, he said he didn't get a response when he asked if OpenAI's agents had been able to see his own use of its Codex tool before coming up with their solution.
asserted
agents → say → solution
OpenAI acknowledges pursuing the solution after hearing rumours of a potential solution.
asserted
OpenAI → acknowledge → solution
But it denies its internal system of agents learned from their work, saying after an investigation, it "confirmed that Buckmaster's Codex prompts … could not have influenced the system in any way, including through training."
uncertain
prompts → deny → training
To Davide Gaiotto, who specializes in theoretical and mathematical physics at the Perimeter Institute in Waterloo, Ont., it's the modern version of an age-old problem.
asserted
it → specialize → problem
He uses an example of a professional seminar where you hear about upcoming research.
asserted
you → use → research
"Normally, this would require you to be so fast and capable that you can see what they told you at the seminar and use it to do the final step," Gaiotto said.
asserted
Gaiotto → require → step
But now, it may soon be possible to use AI tools to leap faster and farther off those giants' shoulders, so to speak.
uncertain
it → use → shoulders
"Because if you have enough money, you can compress months of work into a few hours," Gaiotto told CBC News.
asserted
Gaiotto → have → News
It's worth noting that this Navier-Stokes work does not exist in a vacuum, and that Buckmaster credits Spanish researchers Diego Córdoba from the Institute for Mathematical Sciences and CUNEF University's Luis Martínez-Zoroa for work on this approach.
asserted
Buckmaster → note → approach
The drama, Vakil says, is unfortunate and overshadows the real human accomplishment.
asserted
Vakil → say → accomplishment
"These are things that people have been chasing for a hundred years that we didn't think would be within reach," Vakil said, "And it's this sequence of people assisted by technology that made something new happen."
asserted
something → chase → technology
Buckmaster, in his Sept. 7 statement, said his original intent was to show "the significance that a mathematician and an LLM model can now do all this work in a month."
asserted
mathematician → say → month
Vakil agrees that these tools are changing the game.
"
asserted
tools → agree → game
I do believe that it's clear we're going through a massive transition in how we do science.
asserted
we → believe → science
At least 25 winners of the Fields Medal, one of mathematics' most prestigious awards, signed an open letter saying that AI is "misaligned" with the goals of the mathematical community and a "general threat to intellectual work.
asserted
AI → sign → work
But the furor over the tools to help answer deep questions perhaps misses a point made by Fields Medal-winning UCLA mathematician Terence Tao: Pure math is driven by curiosity.
asserted
math → help → curiosity
In recent social posts, Tao talked about the greater value of not just solving the problem, but seeking what could be learned by studying it.
uncertain
what → talk → it
He likens it to kids trying to one-up each other by playing 'who can name the largest number?'
asserted
who → liken → number
…and 1 more, not listed.
The Aporia
