One of my theories for why colleges are facing price resistance (example) is that colleges and universities are now, by definition, collections of second-rate humans. The first-rate humans have all been hired by Nvidia or the AI companies. That’s obviously true in engineering and computer nerdism, but the AI companies also want to do great things in medicine, law, literature, art, etc. It is difficult to think of a truly effective human in any academic field who couldn’t be useful at OpenAI or Anthropic and, therefore, since these companies have infinite money and infinite impact, they should be able to hire away anyone that they think they need. Maybe it makes sense to pay between $0 and $6,440/year in tuition for University of Florida (Go Gators!), but how can it make sense to spend $70,000+/year on tuition at a lower-ranked private university, e.g., University of Rochester?
Where are America’s first-rate mathematicians now working? “OpenAI Says It Has Cracked One of Math’s ‘Millennium Problems’” (New York Times) gives us a hint:
OpenAI said on Tuesday that its newest artificial intelligence technology had solved one of the “Millennium Problems,” a collection of important unanswered math questions meant to push the world’s leading mathematicians to new heights.
The company announced that one of its latest models, which has not yet been released to the public, needed just 88 hours to solve what mathematicians call “the Navier–Stokes existence and smoothness problem.” This problem involves a series of equations that are often used to predict the weather.
The equations describe the movement of water and other fluids. The Navier-Stokes problem, which has no clear practical value, asks whether these equations completely break down in certain situations. OpenAI’s proof claims to have defined just such a situation.
This would imply, at least theoretically, that the laws of physics themselves would break down under certain conditions: that, for example, water could be made to spontaneously explode. But mathematicians and physicists do not believe that this mathematical breakdown could really lead to such an outcome in the physical world.
What does OpenAI get besides bragging rights?
The Navier-Stokes problem was one of seven “Millennium Problems” selected by the Clay Mathematics Institute in the year 2000 as a way of tracking the progress of mathematics in the new millennium. The institute, founded by an American businessman named Landon T. Clay, offered a million dollars for the first correct solution to each problem. Before OpenAI’s announcement, only one of the problems had been solved.
Dr. Evil would be happy (below), but isn’t $1 million what a receptionist hired in 2023 at OpenAI earns every month now as his/her/zir/their stock vests?
Aside from no taxpayers having been injured in order to fund this, the beauty of the biggest news in mathematics in 23 years (since Grigori Perelman’s proof of the Poincaré conjecture in 2002–03?) is that it has absolutely no practical implication. Solving the Navier-Stokes equations hasn’t gotten faster or easier because of these AI/math nerds. The bizarre situation where the equations can’t be used (what ChatGPT proved existed) doesn’t exist in our universe.
Perhaps someone in what’s left of Hollywood could make money off this, nonetheless… how about a movie called “Navier-Stokes” in which a diverse crew of NASA astronauts go through a wormhole into a parallel universe where Navier–Stokes singularities arise naturally in ordinary fluids and don’t have to be forced with 88 hours of GPU crunching? Aliens are discovered who get around by exploiting vortices produced by these singularities. Air turns into plasma without any warning. An enormous sea monster threatens our heroes, but then a massive whirlpool suddenly forms for no reason in the alien sea and the monster is dragged into the abyss. The astronauts themselves are safe within their ship, though, because it turns out that the life-size hollow titanium bust of George Floyd that President AOC mandated be included just outside the ship’s Islamic prayer room resonates to break up singularities that are forming within the cabin air. The crew also discovers that they can be safe on the alien planet surface if they travel together like a Christian saint procession, with the Bust of Floyd held in front of them.
Johnny Depp as the token white male on the crew and Amber Heard (#BelieveWomen) voices the sea monster?
See https://philip.greenspun.com/blog/2022/06/12/who-paid-for-the-consequences-of-the-aclu-authored-amber-heard-signed-op-ed-you-did/
Might be tough to be grad student in math right now :-(.
The great danger (or opportunity?) here is that soon AI will be spitting out correct proofs that humans don’t understand, so they don’t get accepted by the math community and don’t find their way eventually into textbooks, creating a divergence between “human math” and “AI math”. Probably true in other disciplines as well.
The current approach is increasingly to provide a ‘LEAN certificate’, a machine checkable proof for the proof assistant Lean.
However, the proofs, while valid, are apparently poorly structured for human understanding.
I have seen things, but am not old enough to remember times when grad mathematics was a good career choice. I solved a couple of previously unsolved problems from theory books’ footnotes but never thought about being full-time mathematician for living, although I considered getting math ph d in order to get adjunct gigs after retirement, but I guess I will go with playing stock market instead. Will check this LEAN certificate thing. Tom. if you have more info you can link here.
Phil, surely my Academic Specialty of Black Studies Plagiarism will still have an Important spot in Academia, and at Harvard in particular, going forward in a world of AI?
How can we be sure that the proof is correct unless mathematicians verified and confirmed it? Just had a very dangerous suggestion from Chat GPT that would blow the entire security model under the guise of improving security. Said mathematicians do not have to work at universities of course, they can work anywhere. In case of Perelman in his mother’s flat.
I think that there are 2 categories of math problems, one consists of problems that can be solved based on combining existing knowledge and deriving new solutions from it and another category consisting of problems that require breakthrough and leap of imagination. First category can be handled effectively by LLMs with human validation, second category problems may make use of LLMs and specialized computational and Ml. technics which are not new in math, but require human direction.
Also, based on quantum mechanics, anything could happen, it just that the probability of events that go against entropy laws is very small
There is now a system for machines to verify a math proof. No humans required.
@Roger S, no system is perfect. Maybe more perfect than individual humans or human groups with incencitives, fears or agendas, but still, what is the purpose of mathematics if not human understanding?
It is amazing how far imperfect humans’ understanding took us so far, LLMs are one example.
NOT ANY MORE MUAHAHAHAHA
Perplexed and his ancestors were never considered grade 1 humans, but when sh1t hits the fan we are usually drafted/paid a little above miserly level to fix what geniuses broke.
Doctor Evil is so 90th.
Nowadays perpetually fighting civil wars (at least until Trump and 2026) Democratic Republic of Congo and Bulgaria, the poorest European Country with population of half NYC both have GDP above $100 billion.