- My first impressions and thoughts on the presentation speak to the need for human mathematicians to accept, absorb, and understand new AI-generated proofs—and to the fact that it takes time to do so, as well as the increasing burden of sorting through essentially unsolicited material, which robs that same group of the time to work. Software developers are seeing this same issue with AI-generated contributions of software changes in the open-source arena. What they are seeing is a very high number of trivial submissions, which Dr. Tao points out is a propensity of AI generation. The second problem is that submissions are often not good, forcing reviewers to read hundreds if not thousands of lines of intricate yet incorrect code—and they waste their productive time doing so, making them less amenable to future consideration of such contributions. This is a real problem. As to the issue of human mathematicians needing to accept work as useful before it can enter wider consideration—now that is an interesting problem if humans are indeed unable to understand work AI creates that is useful and correct, but not understood to be so (perhaps due to the above issues), and yet we have to consider a point in time when models become more capable. Let me put it another way: how long would you spend trying to get your dog to understand calculus? AI has inexhaustible patience (unlike humans), and it will keep trying to explain its ideas and theorems to us (or our dogs) far past the point humans would be willing to listen—though our dogs, at least, are amenable to treats and used to us talking a lot while handing them cookies.
- I think it is important to divine what currently AI is good for and what it is not even in such verifiable environments like math. Current hyped announcements about breaking conjectures are notable and are a marker of how much improvement was made. But as I read them, and maybe I am wrong, I see it as a large model+ harness executing a broad brute force search and trying solutions until something sticks. There are lots of problems like that and they should be solved, as often they are perhaps less important or overlooked, or just a slog, any field of research has these, math even more so.
However, this is very different from inventing new mathematical machinery that allows to break old problems, I think it will be a while until AI will be able to do it if at all. For now I think we will be moving to a symbiosis where an AI cracking a problem and giving a solution, inspires a human to invent new techniques.
- I loved the appearance of Bill Thurston. He proved enough of what he saw to be considered one of our greatest mathematicians, but his brilliance was what he saw.
The obvious question Terry Tao seems not to address: AI mops up our unsolved problems? Whose unsolved problems? The architecture of mathematics will remain a human endeavor long after we replace human construction workers with machines.
- Recording of a talk with the same title. I’m not certain it’s the same content as the linked PDF though
https://youtu.be/mS9Lr43cIB4
by light_triad
2 subcomments
- This is the taste question applied to Mathematics in a similar way it's been applied to code. In an era of AI abundance, the question becomes what the goals are and what gets verified and digested (adopted by users). Goodhart’s law: the goal of producing code is not just about maximizing the number of tokens used, but the productivity gains and economic surplus.
This could serve as the template for any field in the age of AI:
"We are not trying to meet some abstract production quota. The measure of our success is whether what we do enables people to
understand and think more clearly and effectively about math (or products, or science, or hardware...)"
by megaloblasto
3 subcomments
- This is the thought process that I fail to see many people take (both here and other places). AI is changing many fields, ok what does that look like and how do we adapt? What can we do now that we couldn't before? What skills should I learn to adapt to this changing world? I think this is how we move forward. If you can get past the scary aspects of AI (not talking about datacenters or billionaires, that is a different subject) then you might be able to see how exciting this can be.
by bobmarleybiceps
1 subcomments
- I feel like at a certain point, there's is not necessarily a reason to go through the peer review publication process for some AI proofs.
Not because "ai bad," but because at some point AI outputs should probably just be treated like public knowledge. Specifically stuff that's provable by "AI please output lean showing X is true," where anyone could kind of reach the same conclusion by asking ai.
by andyjohnson0
3 subcomments
- A few predictions:
1. I fear that AI is about to change from being a human art to becoming something like a bulk-extruded, industrial product.
2. I also suspect that mathematics is about to become substantially less open. As the number of entities on the planet that are capable of top-level maths explodes, and because most of those entiries will have no interest in the validation that publishing papers brings, we will see balkanisation and hoarding of "secret maths".
3. Areas of science that are downstream of maths -- basically everything -- will, in time, be degrated by lack of openness, before suffering the same fate.
by jimmy76615
0 subcomment
- It was an excellent talk. If nothing else, it really helps to establish some much needed vocabulary for us to constructively talk about the future of math
by Schlagbohrer
0 subcomment
- A pleasure to read such a presentation which carefully lays out its argument brick by brick.
- However, the writing often dwells at length on trivialities, while passing very
briefly through (or even obscuring) the most interesting and novel portions of
the argument.
This is consistently my experience chatting with LLMs. It's an very interesting anti-feature, what does it mean about them fundamentally, could more sophisticated machines one day surpass this, etc.
Chomsky for example took the position that LLMs will never be able to explain things and he thought this anti-property was fundamental to their model of computation. But that was years ago.
by 0x1ceb00da
1 subcomments
- Is there a video for this?
- [flagged]
by kiaansaraiya
0 subcomment
- [flagged]
by richard_chase
2 subcomments
- [flagged]
by 4848488448
1 subcomments
- It really is sad that supposed leaders of technical fields have been reduced to TED tier clowns for profit
- The man just cannot stop. First, a lengthy introduction with caveats which can be used to hedge later.
Then he goes all in on AI again. He is sponsored by the AI for Math Fund (Renaissance Technologies) and I'd really like a yes/no disclosure about OpenAI stock options.
People give him the benefit of the doubt because he always has been unable to stay off the Internet for more than a day. But this is really unprecedented.
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