Posted by Anon84 9 hours ago
I would have assumed that, by producing new proofs, the AI has either validated existing principles, or discovered new ones? Isn't that worth studying?
Are mathematicians complaining that reviewing AI's proofs is not as fun as writing your own? Try being a programmer... welcome to our world!
If AI lacks imagination and is not discovering new principles, then it's doing us a favour: it's crossing out the problems that don't need new principles. So the problems/conjectures that are still left are the more interesting ones.
Source? I assume that many of the approaches embedded in this proof dump will eventually be distilled and generalized into new techniques. That's how proof techniques tend to come about anyway (before AI): human mathematicians do something novel and unexpected to solve a particular problem, then efforts are made to understand how the "trick" works.
Sure, but that's a real technical limitation with current AIs, not something that AI firms should be blamed for. And if anything, this creates a viable career path for the mathematicians who were "scooped" wrt. the original solution: they can at least puzzle out what exactly the AI managed to do. Many practitioners are actually quite excited by this possibility; Tao's stance is by no means universally shared.
I'm just not happy with the presentation of OpenAIs result. Maybe they could have gotten into contact with the people of the research areas of the problems that they solved and worked with them to create a better exposition. Sure, it's a slow process and requires lots of staff. But I believe that they can afford it.
The way I see it, it's no different from a lot of grad student work where you have to figure out what a human-written proof is doing.
> Maybe they could have gotten into contact with the people of the research areas of the problems that they solved and worked with them to create a better exposition.
That's what Anthropic is doing, and the issue is that people will complain that they weren't the chosen "person to work with". OpenAI's approach is more like a race where everyone's at the same starting point: they get the AI's raw proof to work on and have to figure out how it works.
"Reaching these lighthouses [resolutions of open problems] prematurely by automated tools can disrupt the exploration of the paths not taken, and sterilize the surrounding field."
This crucial issue is centered in mathematician psychology and the incentive structure of academic/institutional mathematics worldwide. For mathematics to flourish going forward, we will need to realign our brains to think differently about the nature of mathematical progress. And we need to reorient our institutional incentive structures towards the promotion of meaningful mathematical progress itself rather than targeting proxies that are no longer faithful.
Regardless of the precise nature or the causes of the "sterilization" Tao refers to, we (the mathematics community) can only rely on ourselves to repair it. Though, since it will involve fundamental change at the level of ossified academic institutions with many stakeholders and divergent vested interests, any such repair will be slow, frustrating, controversial, and lacking any guarantee of success.
I'm a big fan of Tao. He must be so shaken by the AI storm that he's now writing arguments that even teenagers could quickly dismiss. A sad day.
"Oh no! Not like that!"
- everyone with Very Strong opinions on mathematics academia when he talks about the thing they are (or consider themselves to be) experts in
I'm excited!