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Tao: Open math problems being non-renewably mined by AI

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Re: Tao: Open math problems being non-renewably mined by AI

#221

Post by meken »

mrbungie wrote: post #219
meken wrote: post #213

I don’t see why it makes a meaningful difference if a human solves a math problem versus AI - it seems like the same amount of understanding will come out in the end. Either the understanding will come from humans arriving at the proof in the former case, or the understanding will come from humans understanding the proof that the AI came up with in the latter.

Probably an AI-written Lean proof is very different to how a human would write it, and some may say it's more like mathy neuralese. For sure it works but it is not human-friendly and needs to be transformed into something more readable and digestible to be able to extract insights from it. Not that different from when trying to read an out-of-control vibe coded codebases, or an sloppy AI long email that someone may s…

Tao has a spiel in his recent interview with Dwarkesh where he says that AIs are very good at explaining things - so just have the AI explain the proof in a human-friendly way.

Re: Tao: Open math problems being non-renewably mined by AI

#222

Post by magicalist »

Wissenschafter wrote: post #172
magicalist wrote: post #130

Earlier quoted context omitted.

Surprised to see someone on HN arguing against open science. Seems like the opposite of the lessons we should learn from Newton and Gauss, actually, hoarding results for decades at the expense of progress. (the Pythagorean thing isn't really competition either, is ahistorical, and from what we actually do know it's again people hoarding results instead of sharing them). FWIW, your post comes off as a middlebrow dismi…

They aren't arguing against open science, they are trying to educate you on the history of science. It's always been this way. Also, your third paragraph is highly ironic.

> They aren't arguing against open science, they are trying to educate you on the history of science. It's always been this way.

Always been what way? And how does that contrast to what Tao said (since it was apparently "a misstatement of mathematical history")?

> Also, your third paragraph is highly ironic.

You'll have to be more specific, since I engaged with my parent's argument, while they waved away Tao's quote by suggesting he was wrong because of exactly the kind of events that helped lead to the norms and mores working mathematicians have today.

Re: Tao: Open math problems being non-renewably mined by AI

#223

Post by nine_k »

senshan wrote: post #165

From "Jokester" by Isaac Asimov 1956: "Early in the history of Multivac, it had become apparent that there was one big bottleneck: the questioning procedure. Multivac could answer the problems of humanity, all the problems, if -- if it were asked meaningful questions. But as knowledge accumulated at an ever-faster rate, it became ever more difficult to locate those meaningful questions." [0] https://web.archive.org/w…

I'd say that a more appropriate reference from that time would be "The Nine Billion Names of God" by Arthur C. Clarke [1], which actually deals with the finiteness of the list of problems that a machine successfully exhausts.

[1]: https://hex.ooo/library/nine_billion_names_of_god.html

Re: Tao: Open math problems being non-renewably mined by AI

#224

Post by XenophileJKO »

dayjah wrote: post #193
sashank_1509 wrote: post #180

Earlier quoted context omitted.

It demotivates mathematicians. That’s a pretty large negative!

* current mathematicians Were early in this cycle, we will learn to do more, and exercise our new capabilities more fluently, which in turn will create more skilled practitioners Consider the abacus, calculator, computer, etc, each of these enhanced mathematicians’ capabilities and thus outputs.

This feels a lot like drafters complaining that nothing will get designed when CAD starts being used.

Re: Tao: Open math problems being non-renewably mined by AI

#225

Post by pixl97 »

pictureofabear wrote: post #127
thymine_dimer wrote: post #80

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…

I think the problem with AI asking questions is that it will ask questions that are interesting to it but not necessarily us. AI, as a model, will never be a perfect copy of a human. It will always be a simulation, and thus to some extent, will ask questions that humans find irrelevant and solve problems that humans find irrelevant. For anyone facing an existential crisis on AI, your ace in the hole is your humanity.…

>your ace in the hole is your humanity

Average HN Poster: [nervous sweating]

Re: Tao: Open math problems being non-renewably mined by AI

#226

Post by mrbungie »

meken wrote: post #221
mrbungie wrote: post #219

Earlier quoted context omitted.

Probably an AI-written Lean proof is very different to how a human would write it, and some may say it's more like mathy neuralese. For sure it works but it is not human-friendly and needs to be transformed into something more readable and digestible to be able to extract insights from it. Not that different from when trying to read an out-of-control vibe coded codebases, or an sloppy AI long email that someone may s…

Tao has a spiel in his recent interview with Dwarkesh where he says that AIs are very good at explaining things - so just have the AI explain the proof in a human-friendly way.

For sure, but this was supposedly ~18 million dollars of compute, afaik 100 pages paper / lean proof and only god knows how many bytes of chat interactions + thought traces. Scale matters.

Re: Tao: Open math problems being non-renewably mined by AI

#227

Post by monkpit »

bityard wrote: post #211
rzerowan wrote: post #201

Earlier quoted context omitted.

More of a 'its the journey' rather than the destination type of thing.Since the insights , quirks, tricks and procedures gained along the way allows insights intoother at that moment unknown problem/domains in the future. As far as researchers sharing their data/notes with the AI hyperscalars looks like that would be coming to an end wihth a mor guild-like structure going forward to prevent their progress being fron-…

I wonder if it would be possible for researchers and scientists to submit their papers to an organization which would then collect them, submit them for peer review by other experts in the field, and then release them in periodical form ONLY to individuals and organizations who pay a subscription fee in order to read them while suing those who try to redistribute them without permission?

To what end?

Re: Tao: Open math problems being non-renewably mined by AI

#228

Post by nine_k »

evenhash wrote: post #197
dbmikus wrote: post #158

Earlier quoted context omitted.

An AI-generated solution always provides two pieces of info: 1. proof that there is a solution 2. a solution that you can work backwards from to build understanding Maybe the solution is pretty inscrutable, but it's almost always better than nothing. So, both of these pieces of info would be at least marginally useful for advancing human knowledge.

> An AI-generated solution always provides ... proof that there is a solution This is only true in the most trivial sense. A solution is a solution, sure... but how do you know it's a solution, and not an incoherent jumble of words? A human has to review and vouch for it. Just because the AI gives you an arxiv-worthy PDF, or a Lean proof which compiles, doesn't mean it proves what the AI says it does. The AI could gi…

That's why the solution should be presented in a verifiable formal language, such as Lean. Which is the case with the Navier-Stokes problem.

Re: Tao: Open math problems being non-renewably mined by AI

#229

Post by tmp10423288442 »

rzerowan wrote: post #201
dvt wrote: post #52

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…

More of a 'its the journey' rather than the destination type of thing.Since the insights , quirks, tricks and procedures gained along the way allows insights intoother at that moment unknown problem/domains in the future. As far as researchers sharing their data/notes with the AI hyperscalars looks like that would be coming to an end wihth a mor guild-like structure going forward to prevent their progress being fron-…

Why would society fund mathematicians if they decided to become a guild that hides secrets? They could pursue that as a hobby, but they’d end up like the coders who refuse to use LLMs - rapidly becoming irrelevant and a bit sad from an outsider’s perspective.

Re: Tao: Open math problems being non-renewably mined by AI

#230

Post by pixl97 »

johnsmith1840 wrote: post #156
qlte wrote: post #151

Earlier quoted context omitted.

Pure mathematics (defined by anything without a known application) exists not to "solve problems" in the real world, but by whatever mathematicians find interesting or lacking in current knowledge. Based on the agreed set of rules formed over time that ensure rigor. It just so happens that even bizarrely esoteric math can later turn out to have some extremely useful and economically valuable applications. And even mo…

In that case isn't it actually more valuable to have an AI do this? It works faster and solves more math. The random engineer looking at a funny problem 10 years later now has the literal author of the math to talk to about it and implement it. I have never even spoken to a world class mathematician and now I can have them design with me? How is this not better in almost everyway?

Guess it depends...

If said human is kicked to the street with thousands of other homeless people that can't get jobs because AI then robots replaced them, then those fast math problems sound like a pretty bad trade off.

Now, if there's some future where AI leads to abundance and we can all live off UBI, well, probably a worthwhile trade.

The biggest issue I see is the more controversial people leading the AI race at the moment are not the kind of people I'd hand kids safety scissors much less the future of the human race.

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