Tao: Open math problems being non-renewably mined by AI
33 points by _alternator_ 3 hours ago | 14 comments

dvt 3 minutes ago
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.

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colinhb 9 minutes ago
Seems like in current cultural and economic context, short term extraction is what we’re going to do

> 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.

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olalonde 10 minutes ago
Can't mathematicians still gain novel insights by reverse-engineering AI-generated proofs? Just like chess players learn new concepts by studying what engines play.
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_alternator_ 45 seconds ago
Yes, and they will. But what's happening here is that the system that cultivates mathematics (and mathematicians) is recieving likely the biggest shock of its history. How do you reward merit and identify talen when people can't absorb the number of proofs being generated, much less understand them? Perleman's proof of the Poincare conjecture took several years for the mathematical community to digest; the proof of Navier-Stokes will probably take a similarly long time. In the mean time, it looks like all open problems will be solved (or proved that they can't be solved).

It's not that the horizon is expanding because of this. It's more like a forest getting clear-cut.

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lalalanananana 3 minutes ago
It's possible but the approaches these tools take are usually verbose and strange. Think about it like anything else llms do. Even when the picture is right and there are only 5 digits on each hand all the textures are off and so is the lighting and postures. Or in code, the code is always way larger then it needs to be and tightened up strangely with weird loose ends. Or in writing weird idioms, words, structure, and a weaselly way to turn 3 sentences into 8 paragraphs.

People usually use these tools in math and science to find an answer. Then often they will work it back using more sane or human pathways. So it's shareable or even beautiful.

Knowing the answer has value. But, often in math the best thing was how someone got there.

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_alternator_ 33 minutes ago
This series of posts by Terry Tao is a direct response to the Navier-Stokes results (multiple results!) from the last 24 hours. The question is what is left after the levelling of mathematics, in all its senses, occurs? How can you protect a field that's under this much pressure in the next 6 months?

> [I]t is now the identification of a promising problem which is the scarce and precious resource. We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential.

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calvinmorrison 27 minutes ago
> How can you protect a field that's under this much pressure in the next 6 months?

Sounds like they're going the way of the DoDo. better take that PhD, migrate to the new world and become a tuktuk driver.

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ModernMech 26 minutes ago
If math is solved then move to an area that’s not. Why do fields need “protecting” from ai?
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dgellow 22 minutes ago
Have you read his tweets?
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ModernMech 14 minutes ago
yes but the tweets don't really address why the field needs to be protected instead of adapting and evolving.

And to reply to the sibling since I hit my comment limit and I'm going to probably forget about this conversation until tomorrow:

But our situation before 2023 was one in which we had an endless abundance of solutions and ideas. I understand that AI can generate bad ideas faster than we can discern them, but we already have tried and true mechanisms to filter good ideas from bad (e.g. the scientific process), why can't they be adapted?

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vouaobrasil 15 minutes ago
The reason is because the entirety of society, historically, has been based upon humans using their differential skills to further it, which in turn promotes societal cohesion. If most human endeavours are solved, then we will enter a period of abundance that paradoxically will erode the glue holding society together. In short, endless abundance of solutions and ideas cannot coexist with a healthy society. Only those who are priveleged and have a naive belief in a Star Trek utopia think otherwise.
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SadErn 18 minutes ago
[dead]
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program_whiz 23 minutes ago
Timing is everything https://nonlineartransform.substack.com/p/ai-swarms-timing-i...

Article arguing math is the next "human calculator".

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turtleyacht 3 hours ago
If proofs are tropes, explanations are stories. There won't be an end to stories.
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vouaobrasil 14 minutes ago
Actually there will because if you've actually ever spent time doing math, you only really get to that level of truly understanding and appreciating the stories if you've actually done the hard work yourself, which in turn will be economically infeasible due to AI. The analogy is interesting but incomplete and misleading.
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