AIās dramatic acceleration of mathematics research continues apace, with the infamous Navier-Stokes puzzle being the latest and greatest solution yet produced by artificial minds. But not everyone is happy about the discovery.
What has OpenAI discovered?
In short, a solution to the long-standing Navier-Stokes puzzle ā one of the toughest and most enduring problems in mathematics. Whoever solved it stood to win $1 million from the Clay Mathematics Institute, because it was one of its six Millennium Prize Problems.
Advertisement
The slightly longer version is that Navier-Stokes equations are used to model fluid flows, such as air over aircraft wings and blood in veins. There has been an outstanding problem in that we donāt knowĀ if these equations always work, or if there are situations where they stop making sense and start spouting nonsense, what mathematicians call āblow-upsā.
OpenAI has discovered they do, indeed, blow up.
Why is that controversial?
The work itself isnāt controversial. It hasnāt been peer-reviewed, but it has been formalised. This is the process of theories and proofs being turned into computer code that allows machines to grapple with them, methodically working through the logic and exposing any flaws. That means we can be fairly sure the results are correct.
The controversy arose because, shortly before OpenAI released its news, a pair of researchers,Ā Ā at New York UniversityĀ and Ā at AI company Anthropic, rushed out their solution to a close cousin of Navier-Stokes, the Euler equations, which experts suggested could open the door to a full solution.
Those researchers heard rumours that OpenAI was due to make its announcement, and contacted the company for clarification ā knowing its own solution was on the way. BuckmasterĀ claims he was met with opaque responses, and that stopped short of making any accusations but pointed out that his own work was being stored on OpenAIās servers ā as a customer, not a research partner.
OpenAI has explicitly denied any wrongdoing, pointing out that no person or AI from the company had seen Buckmaster and Alpƶgeās work, and that its solution was, in any case, different.
Do we know exactly what happened?
In a word, no. Although more will become clear when full papers of all the work emerge. All we know for sure is that AI is causing upheaval in the world of mathematics. In recent months, it has made rapid progress on mathematics problems, peaking with this weekās news.
Mathematicians are mixed on the impact of AI. Some are excited about the prospects; others are fearful of their own careers. All say that on some level, AI will change the field and there will be a period of adjustment. There will also be questions to answer on how results are credited when AI was used.
Are mathematicians happy that AI is accelerating mathematical research?
at the University of California, Los Angeles ā arguably the worldās greatest living mathematician ā certainly isnāt. There has always been competition among mathematicians to be first, he says, which was fine, because mathematics is so difficult that it created a natural brake to stop things getting out of hand. AI is changing all that. āNow thereās no speed limit, and suddenly things are breaking down,ā he says.
Tao fears that with this pace, new findings will keep landing. There will be no time to absorb the results and assimilate them into the wider field ā to fully understand them, put them into textbooks and teach them to students, he says. That means progress could begin to hurt the field.
āThese companies are dumping carcasses of raw meat onto our communal village table and saying, āhere you go, I solved your food problemā, and then they just leave,ā says Tao. āTheyāre expecting us to prepare the food and cook it and eat it. All that work is left to us, to clean up, and itās demoralising.ā
Who will win the $1 million prize?
Itās not clear yet if anyone will. āThe process of evaluation is deliberately unhurried, and we shall ensure that it is absolutely rigorous,ā , president of the Clay Mathematics Institute, wrote toĀ Ā鶹“«Ć½Ā in an email.
If someone does win, the question will be whether it should go to Buckmaster and Alpƶge, as some have suggested, or to OpenAI.
An interesting aside is that if it does go to OpenAI, the cost of solving the problem (if charged as a customer) would run to $15 million ā many times the prize money. But such a headline may also mean the companyās upcoming IPO is a much more attractive proposition for investors, potentially recouping many times the outlay.
