Maybe the next frontier for AI is to make it more pedagogical.
If the aim of mathematics is to promote greater human understanding, then surely elevating everyone’s grasp and appreciation of math is of greater import than chasing another theorem feather for our hats - especially if AI can automate the plucking.
Arguably it is succeeding on this front - LLMs have been much more helpful for learning about mathematics topics than Wikipedia for a while now. Admittedly a somewhat low bar, but they are genuinely helpful. In many other fields the models can still only pull up equal (in my opinion).
>Finally, the next few years will be extremely interesting. We are at a new frontier, where our communal norms, values, and expectations are beginning to break down, and it’s up to all of us to figure out what should replace them
I'm tired of this cautious optimist talk. It is inevitable that without regulation, AI will eclipse humans in every possible domain, leaving everyone without direct control over the most powerful models completely powerless, economically redundant, and at the mercy of the new AI hegemony. Anything which doesn't confront this possibility honestly is just lying to people.
A lot of people are tired of a lot of talk. It's not going to get anywhere if they all just consider the other views as only possibly held by liars instead of something to discuss and reason about.
>Can every interesting mathematical question be answered that way? Probably not, and even questions that can may have more interesting and satisfying solutions that invoke novel ideas and insights. Perhaps, in the near future, AI systems will be able to come up with such insights, but, at the very least, let’s recognize that we are not there yet.
This keeps being repeated by AI skeptics, yet AI keeps solving more and more complex tasks. We've reached the point that it's even started solving Millennium problems.
>Telling us that some AI agent is spinning out theorems that are highly interesting to it and other AI agents does nothing for us.
This is the future of pushing the frontier though. AIs need to be pushed to get better and better. AI understanding of math is millions times more important than human's.
Math as a field is unbounded. There's always more to discover, new systems to invent, new problems to find. It's not just some predefined set of unsolved problems.
Math is also a matter of what is both interesting and useful to humans.
For some reason there is this virulent strain of anti-human AI rhetoric that machines will replace us. But what is the purpose of math as a field of study if we're not in the loop?
It’s like people think problems are given to us by God.
We make our problems up!
> For some reason there is this virulent strain of anti-human AI rhetoric
It’s just… nasty, isn’t it? Facts aside, one does have to wonder what motivates not the beliefs themselves, but the, well, frankly aggressive, way in which they’re expressed. Bitterness and envy felt towards those who have actually done the hard work and achieved things?
Tasks are not simply integer “difficulties” where, if your “intelligence” exceeds the “difficulty” then you will solve it.
The question is to what extent AI will affect creation of new branches and elegant ideas in mathematics. This question applies to every area. Has it created an interesting new way of thought in any area other than those where massive tree search can be mistaken for such?
I don’t think it’s impossible but the evidence doesn’t point clearly to it.
What do you expect from Avigad, who works on Lean? Tao is herding the sheep into the AI enclosure with a stream of AI-positive guest posts.
There are no concerns about being funded by a small number of rich AI-boosting foundations, no concerns that intuition and radical new thoughts might be impeded by staring into a glowing rectangle all day and only some concerns about job losses.
It is all very well for the directors and the tenured, who apparently hope they can solve a major problem with AI while avoiding hard work.
> [mathematics] being funded by a small number of rich [people]
Historically this has always been the case. Rich people or people supported by rich people did math, while peasants worked the fields and workers worked in factories/mines/etc. This is just regression toward the mean.
If the aim of mathematics is to promote greater human understanding, then surely elevating everyone’s grasp and appreciation of math is of greater import than chasing another theorem feather for our hats - especially if AI can automate the plucking.
Is this the aim of mathematics?
I'm tired of this cautious optimist talk. It is inevitable that without regulation, AI will eclipse humans in every possible domain, leaving everyone without direct control over the most powerful models completely powerless, economically redundant, and at the mercy of the new AI hegemony. Anything which doesn't confront this possibility honestly is just lying to people.
This keeps being repeated by AI skeptics, yet AI keeps solving more and more complex tasks. We've reached the point that it's even started solving Millennium problems.
>Telling us that some AI agent is spinning out theorems that are highly interesting to it and other AI agents does nothing for us.
This is the future of pushing the frontier though. AIs need to be pushed to get better and better. AI understanding of math is millions times more important than human's.
And now you're hearing it from a guy who's one of the foremost, early proponents of AI in math.
> AI understanding of math is millions times more important than human's.
Important to whom?
Since you’re so certain, how long do you think it’ll be before all of the millennium problems are solved by AI (by leveraging the current literature)?
Math is also a matter of what is both interesting and useful to humans.
For some reason there is this virulent strain of anti-human AI rhetoric that machines will replace us. But what is the purpose of math as a field of study if we're not in the loop?
We make our problems up!
> For some reason there is this virulent strain of anti-human AI rhetoric
It’s just… nasty, isn’t it? Facts aside, one does have to wonder what motivates not the beliefs themselves, but the, well, frankly aggressive, way in which they’re expressed. Bitterness and envy felt towards those who have actually done the hard work and achieved things?
The question is to what extent AI will affect creation of new branches and elegant ideas in mathematics. This question applies to every area. Has it created an interesting new way of thought in any area other than those where massive tree search can be mistaken for such?
I don’t think it’s impossible but the evidence doesn’t point clearly to it.
There are no concerns about being funded by a small number of rich AI-boosting foundations, no concerns that intuition and radical new thoughts might be impeded by staring into a glowing rectangle all day and only some concerns about job losses.
It is all very well for the directors and the tenured, who apparently hope they can solve a major problem with AI while avoiding hard work.
Historically this has always been the case. Rich people or people supported by rich people did math, while peasants worked the fields and workers worked in factories/mines/etc. This is just regression toward the mean.