351–360 of 642 posts
But is science/mathematics ultimately a pursuit of knowledge, or a pursuit of recognition?
Recognition helps keep people motivated, but that shouldn't be the pursuit of science or mathematics.
Earlier quoted context omitted.
Are you aware that Tao is among the largest proponents of using AI in mathematics? The usage itself is not the point here.
Tao doesn't go as far as Baudelaire, but there are some similarities. In particular, Tao has criticized that AI is not being used to create new interesting conjectures, and that the rush to prove old conjectures is not giving human mathematicians enough time to carefully analyze and understand the proofs and the methods used in those proofs. My answer to both is the same: nothing stops mathematicians from doing both…
Mathematics is about discovering and understanding the logical implications of assumed axioms under various inference rules. Alternatively, some claim that mathematics is about understanding these implications. Under the first definition, AI is already, and forevermore will be faster and better at proving theorems. Just like it is better at checkers, chess, and now go. The author asserts that AI proofs are incomprehe…
That's like saying that programming is about producing valid programs in various programming languages.
Seeing how /r/singularity and /r/accelerate are leaking into maths forums, I foresee a wave of comments that fail to understand Tao's message, whether on purpose or not, so let's try to be clear here: Tao is not someone who is anti-AI for the sake of being anti-AI. He has been advocating for the usefulness of AI in maths for a long time, to the point that people have started calling him a shill for the commercial com…
I think this is an aspect of academic math that a lot of people whish to see crash and burn - the attention and accreditation economy.
> it's probably easy to miss if you have never engaged with research in maths
I don't think anybody are missing anything, in particular not here.
The argument is not far from the senio developer who knows the ins and outs of a code base. Now AI comes along and they complain that they will loose grip of the code base.
At first that is correct. Secondly you accept that the grip might not be that important after all. At least not for a commercial project where you are a cog in a machine.
The question is whether it is different for mathematics.
That's the open question.
Earlier quoted context omitted.
> Nothing is stopping these folks from continuing to study the problems My understanding is they are? And literally everything in this world is based around incentives. If you say “well you can continue to work on understanding, but your kids are going to starve” that’s not nothing.
It boggles my mind. Why cure cancer? The cancer researchers will be out of a job and their kids are going to starve!
I have a the cure for cancer. Simply kill the host. Does it work? Yes. Have you learned anything from it? No.
Earlier quoted context omitted.
The statement is not about AI but about the behaviour of AI companies. OpenAI have put vast resource into solving open maths problems: many millions of dollars of compute just on the Navier-Stokes result, plus whatever they spent on the broader Millenium Prize problems initiative and the other results they have published. Anthropic are doing the same. The statement is asking them to stop doing this. AI companies are…
Humanity is better off for knowing these proofs. This strikes me as academic NIMBYism.
The point is that these proofs are largely useless without the insights. The value of a proof is largely in the travel, not so much in the destination.
1 + 1/2 + 1/4 + 1/8 ... = 2
The big objection to finiteism is that it's a lot more work. Infinity swallows many special cases. Proofs get longer without infinity, and most of the special cases are uninteresting. That's not a problem for AIs.
Someone may start up an AI and make it grind through Hilbert's program for putting mathematics on a fully consistent foundation, starting from a finiteism base. This is a huge, unrewarding job. Great for machine work.
In the Economist article Tao links, Hugo Duminil-Copin, draws a comparison: airdropping someone on the summit of Mount Everest is very different from climbing it. The fundamental issue with AI solving any perceived difficult problem is that we have lost the journey. The sight atop Mount Everest looks much different when you have climbed compared to being dropped from above.
As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skeptici…
Mochizuki was still one human and it required legions of other humans to unpack and untangle to confirm that it didn't lead to anywhere in particular.
AI is now capable of constructions so complex that no human or human team can unpack. And its ability to increase that complexity is growing while our human ability is stagnant.
meta-AI analysis cannot help. We (software professionals who use AI regularly) already know that if you run into a situation where a Fable/Astra-generated analysis reaches the limits of our comprehension/complexity due to their subjectivity, throwing more AI at the problem doesn't always converge.
There are many reasons to feel optimistic about AI, and ultimately its general ability to help science and mathematics.
I see no reason to feel optimistic about the future of mathematics and AI based on the current path of frontier labs, unless the misalignment Tao is writing about can be reconciled.