Terence Tao: AI is mining math's best open problems — and they're running out

That’s not untrue. But it’s also a misstatement of mathematical history. Many leading mathematicians historically have been highly competitive — Gauss comes to mind. Woe betide the lesser intellect that sent Gauss some ideas. The Newton Leibniz controversy was very serious business at the time in the UK and the continent. It was considered at the least a sin to reveal that sqrt(2) was irrational to those outside Pythagoras circle.

Mathematics has always been highly competitive.

Tao's central point seems to be:

"In short, the indiscriminate use of powerful solution-extraction tools can achieve the immediate short-term goal of solving problems at hand, but at the cost of sustaining the ecosystem for the next wave of progress, or in understanding the progress already obtained. "

I am no mathematician, may have misunderstood his point and would be delighted to receive any corrections.

I'm with @nilesh on this one, and not exactly sure how merely the existence of a solution precludes the advancement of human knowledge. If a problem is "solved" (say, symbolically verified) without any insights gained, it doesn't seem very interesting to the profession.

Navier-Stokes is a bit different (because there's a prize attached, so "scooping" matters), but almost all interesting problems don't have any prizes attached.

There's nothing that AI won't be able to mine and accomplish (aside from being literally human), it's only a matter of hardware and scale at this point. Generalized problem solving is a factor of search efficiency over the problem space. The actual software part is all figured out, the only open questions are how to do things efficiently and what the trade-offs are from a hardware perspective, but if hardware paradigms are unlocked then efficiency becomes a secondary factor for the problems we care about. Why bother making an LLM twice as fast if you can make a chip that can process 100mil TPS, for example. You're already in a ballpark where it can do anything you want, with plenty left to spare.

The awkward part about all of this is that we're about to enter an age of extreme enslavement at the hands of the major tech companies if we do not focus on distribution of hardware and research, so that everyone can participate in the abundance and automate their daily lives. If we're beholden to frontier labs because they have hoarded all of the cutting edge hardware and we're left with overpriced scraps, we're collectively screwed. They will ensure a false economy is maintained so they can clutch onto a permanent class hierarchy of haves and have-nots and remain the key global decision makers. Automating hardware manufacturing is irrelevant if the hardware is not being distributed fairly, and is weighted to real scarcity instead of artifical scarcity.

Take Louis Vuitton for exampl […]

In short, after after training AI on an extraordinarily amount of human cognitive output, we are now facing the possibility that our ability to train by working on hard problems will be slowly stripped away at least in some domains.

It’s like someone offers to build mag lev gym weights. It’s very cool that I can now lift the 500 pound weight with a finger. But what will I do when there’s no power and 500 pounds to lift?

Of course, cognition isn’t a single outcome problem like weight lifting. But we build cognition not wholly unlike how we build muscle: one needs resistance. Otherwise I’m not at all confident we “learn” in any depth.

We're having to rediscover in real time the extremely hard way, why enabling mass theft is so incredibly damaging to society. This is literally why we need a functional copyright system

If theft becomes more profitable than genuine creation, then nobody will create anything. Then there's nothing to steal, at which point all progress collapses

Doesn't this just suggest that the next frontier for powerful AI models is to ask challenging questions, not simply solve them?

Terry even says this: "In fact, it is now the identification of a promising problem which is the scarce and precious resource."

The creativity and insight needed to ask a question that Terry gets excited about is the next step. Perhaps OpenAI should create a set of challenging questions and offer a prize to solve them.

It is now clear to me why the AI labs are sponsoring these mathathons: https://mathathonchallenge.com/. They are basically crowdsourcing human researcher data to get access to promising directions possibly later to scoop others.

I didn't realize that open math problems were a finite resource.

I recall a story about some famous mathematician (Gauss?) dismissing interest in Fermat's Last Theorem claiming that he could crank out problems of equivalent interest.

Clearly Tao knows a hell of a lot more than I do about this, but I'm surprised that math that close to completion.