A NYT article, ‘Breathtaking,’ ‘Devastating’: Mathematics Reels After New OpenAI Release, adds to the rapidly mounting evidence that AI could be on the verge of a sharp increase in its ability to catch up with the intelligence or most advanced thinking of the most intelligent humans on Earth. That is not to say that AI has achieved general intelligence on all areas of knowledge. But where it is being focused, math in this instance, indicates that a long, slow march of little advances is ending and a period of rapid major advances is now underway.
A couple of days ago, the AI giant OpenAI released a torrent of advances in mathematics it had accumulated recently. Mathematician Alex Kontorovich, chair of the department of mathematics at Rutgers, commented: “If a human did this, it would be an instant Fields Medal, no questions asked.” The Fields Medal is the equivalent of a Nobel Prize (which has no medal for math).
That was about was just one of the more than 300 math advances that OpenAI released all at once last Tuesday. The released advances include movement on crucial open questions in nearly every subfield of math, including algebra, number theory, theoretical computer science, mathematical logic and topology.
Martin Bridson, a mathematician at Oxford and the president of the Clay Mathematics Institute commented: “Until very recently, it would have been impossible to imagine that the frontiers of mathematics could move so far in one day. ….. breathtaking ….. The list of problems includes several that were guiding challenges in my own research. I have thought hard about all of these problems.”
Ken Ono, a professor at the University of Virginia and founding mathematician at Axiom Math, a math-focused artificial intelligence firm, commented: “I imagine many mathematicians, like me, felt like they got punched in the stomach yesterday. But that feeling is quickly giving way to excitement and determination. For those working to push mathematics forward, this is a challenge and an invitation to aim higher. ….. We should embrace the power that the machines offer, but we should not be indentured to follow their lead.”
Bryna Kra, a mathematician at Northwestern University, articulated how big and unsettling this advance is to mathematics: “Peer review is gone in this process. So, the question is, what kind of impact will these A.I.-generated results have? This is going to take a long time for the math community to digest. ….. Perhaps the most relevant issue is that by releasing this trove of material in this manner, the companies are in the process of destroying the ecosystem that made it possible for this work. While this batch of papers has improved in the citations to the past literature, there are numerous indications that they have benefited from access to many arguments, only some of which are published. The mathematician who wants to make use of these amazing tools to advance their research instead risks giving their ideas away.”
Ah yes, the human element is there is spades. Retired French mathematician, Jean-Pierre Serre (emeritus professor, Collège de France in Paris), put his finger directly on the human element: “Mathematicians take pleasure in doing maths in two different ways: learning and finding new things. Hence a conflict: A.I. increases the first pleasure and lowers the second one. The problem is it may lower the pleasure too much; that is especially serious for young mathematicians”. Simply put, AI making new findings might impair the motivation and pleasure in doing the very hard, very slow work of people doing math the old-fashioned, pre-AI way. It’s a human thing, not an AI thing.
Kai Shaikh, a PhD math student at the University of Toronto, Simons Laufer Mathematical Sciences Institute, comments: “Just like a photograph of a mile marker can’t provide much of the value of actually going on a hike, it would seem to me that proofs without stories, or even stories without struggle or mystery, and first glimpses of strange beasts, are not very meaningful or valuable to us humans.”
For mathematicians, things will never be the same – has the AI genie left the lamp, or is the Kraken unleashed?
There’s the human condition again. It cannot be denied or escaped.
Clearly, AI is now at the outer limit of human knowledge in mathematics and maybe also human mathematical intelligence. This is exciting and scary at the same time. We’re playing with something we do not fully understand. It can help us, hurt us or both.
Q: Given the human condition, or at least American politics since ~2000, does it seem increasingly apparent or important that we need intelligent, competent, pro-public interest guidance and regulation of AI, or should that just be left to the markets running free, wild and butt-naked without any regulations?
The quasi-Reimann hypothesis advance is what the expert called instant Field Medal work for a human
This stuff just goes on and on and on
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