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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

#361

Post by nullbio »

timr wrote: post #353
nullbio wrote: post #350

Earlier quoted context omitted.

> problems that require knowledge that simply doesn't exist yet. Obtaining the knowledge is a process of trial and error, bruteforce, observation, search, etc. Humans follow that same process. Machines can do that too. If they discover or are taught the same heuristics humans use, and a computational capacity greater than that of all humans combined, they will outpace us in this endeavour. > Until "AI" turns into gen…

> Obtaining the knowledge is a process of trial and error, bruteforce, observation, search, etc. Humans follow that same process. Machines can do that too. If they discover or are taught the same heuristics humans use, and a computational capacity greater than that of all humans combined, they will outpace us in this endeavour. Sure, you can reduce the 99.9% of research labor that matters to "a process of trial and e…

> Biology and chemistry are the sciences I know best, so I will use those examples -- every major breakthrough of the last 50 years has involved invention of some fundamental new mode of observation, such as crystallography, NMR, mass spec, electron microscopy, various kinds of light microscopy, DNA sequencing, PCR, etc. Someone invents some innovative technique, and a wave of progress happens. Expert practitioners in in the lab are probably the second rate-limiting step, but the part that LLMs can do -- taking data and turning it into hypotheses -- is the part that carries the least value. Any postdoc has enough ideas to keep a lab going forever.

Technology is not made in a vacuum though, it is a process of incremental advancements, often in parallel, over multiple industries. If LLMs are watching the worlds scientific and hardware progress on all fronts and compute is dedicated to exploring combinations of new ideas and ranking them on estimated practicality toward outstanding problems or current goals that humans have, I see no reason why they won't be able to come up with creative new technology. The issue with cutting edge technology is that it's expensive and time consuming to validate. If AI can develop sufficient simulations, it could be validated digitally.

Surely you don't believe that this isn't around the corner, given the scale we are now seeing? For example dedicating 80,000 agents over 88 hours to write a proof for Navier-Stokes.

Maybe this isn't a wildly creative exercise or you consider math "small" in comparison, but I think it's quite clear to see that this isn't a question of whether it's possible but rather a question of how long it will take to get there.

There's no shortage of talent being dedicated to this pursuit, either. For example: https://finance.yahoo.com/technology/ai/articles/deepmind-ch... - The company aims to accelerate scientific and engineering breakthroughs by building autonomous systems that handle entire research cycles.

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

#362

Post by wrsh07 »

adastra22 wrote: post #244
wrsh07 wrote: post #168

Earlier quoted context omitted.

Yes, many mathematicians have. As Tao points out, merely suggesting new open questions isn't really sufficient. Part of what gives these problems their fame is their notoriety, their difficulty, the fact that many prodigious mathematicians have spent an evening or week or month or several years studying it. It wouldn't be as interesting if it had just been solved by the fifth random mathematician who considered it No…

Mathematics isn't art. It doesn't gain its value in human affairs from being interesting to study. I fail to see why we should cater to that.

Importantly, which mathematicians will understand deep useful math? Who will actually care about the knowledge we can generate at will?

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

#363

Post by irishcoffee »

oefrha wrote: post #332
Alien1Being wrote: post #327

Earlier quoted context omitted.

Here most local STEM PhDs try to get into finance. This is largely due to lack of funding for science and poor opportunities for PhDs. Why be a poorly paid postdoc when Jane Street is offering a million USD signup bonus ? PhDs from poorer overseas do try to get related jobs here, mainly to be able to get a permanent resident visa.

> Why be a poorly paid postdoc when Jane Street is offering a million USD signup bonus? One reason is despising that line of work. Quant firms were pummeling my @prestigious.edu inbox throughout my PhD and I fucking hated those parasites. Well, jokes on me if AI shatters my current career. Btw a former classmate Caroline Ellison who went to Jane Street eventually landed in prison, lol.

Why put @prestigious.edu and name a famous person? Why not just say you went to Stanford? Lots and lots of people have gone to Stanford.

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

#364

Post by oefrha »

irishcoffee wrote: post #363
oefrha wrote: post #332

Earlier quoted context omitted.

> Why be a poorly paid postdoc when Jane Street is offering a million USD signup bonus? One reason is despising that line of work. Quant firms were pummeling my @prestigious.edu inbox throughout my PhD and I fucking hated those parasites. Well, jokes on me if AI shatters my current career. Btw a former classmate Caroline Ellison who went to Jane Street eventually landed in prison, lol.

Why put @prestigious.edu and name a famous person? Why not just say you went to Stanford? Lots and lots of people have gone to Stanford.

prestigious.edu isn’t Stanford; went to a different school for PhD. And the prison bit is just something funny about Jane Street (that sort of vindicates my view of these people) that I edited in later, didn’t think much about it.

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

#367

Post by program_whiz »

znnajdla wrote: post #330
hn_throwaway_99 wrote: post #271

Earlier quoted context omitted.

Doesn't this seem to be where all domains are headed? I get kinda freaked out when I feel like all the AI "utopianists" haven't taken the next logical step of thinking about what society looks like when humans are subpar in every domain (and you may argue this won't happen, though I'm becoming more and more a believer that it will, but my point is the utopianists believe that this absolutely will happen, and that it'…

I don't think humans necessarily become subpar when AI can do most of the work. Taking my own personal example, I have far more intellectual curiosity and improved my skills in programming far more with Claude Code than for 15 years of programming without AI simply because I was bogged down by boilerplate and grunt work. Now that AI handles most of the boilerplate and grunt work and can handle harder and harder probl…

So when AI is also better at coming up with the tasks and already solving the frontier problems? 1M AI agents running full time thinking at 10M times faster than humans, with 100 times the intelligence in each agent? Any human ideas regarding "frontier problems" or "what the AI should focus on" are irrelevant. We have automated our own thinking and human cognition will be about as important as being "the best at abacus". Its an interesting party trick, but in no way useful.

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

#368

Post by an0malous »

Squarex wrote: post #326
haunter wrote: post #301

Earlier quoted context omitted.

Download a book and you are a thief Download 1 million books and you are OpenAI

What? HN has always praised Library Genesis for example.

Libgen isn’t trying to sell you back the content for $100/month. No one would be complaining if OpenAI open sourced their models.

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

#369

Post by jasonhong »

Alien1Being wrote: post #252

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.

There was a recent link on HN about Tao explaining Six Essential Mathematical Concepts https://news.ycombinator.com/item?id=49503521

Here's an excerpt of the video where he explains his idea: https://www.youtube.com/watch?v=svl_1upFpQo

My summary: Science is like a hike. You have a general sense of what direction you want to go. You explore things along the way. You might make wrong turns but might also discover something new and interesting. While on your journey, you might spot new mountains or waterfalls or other vistas that look like they might be good to explore.

In contrast, AI is like taking a helicopter to your destination. Yes you got there quickly, but you missed a lot on the way.

Related, Tao later talks about the pipeline. It used to be that seminal proofs were rare, so there was lots of time for the community to review them, process them, share them, and summarize them in textbooks. Nowadays, AI helps a lot with generating more proofs, but not so much with the other parts of the pipeline.

Tao also explains the math pipeline issue in his talk at the International Congress of Mathematicians, also shared on HN last month: https://news.ycombinator.com/item?id=49056620

My overall take: Tao is very thoughtful and insightful about progress in AI and math, and about what the tradeoffs are. We're seeing similar problems in computer science (my field), where conferences are now getting over 10x the number of submitted papers over just a few years ago (not an exaggeration). It's straining the research community in ability to review, understand, and present the papers.

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

#370

Post by aprilthird2021 »

znnajdla wrote: post #330
hn_throwaway_99 wrote: post #271

Earlier quoted context omitted.

Doesn't this seem to be where all domains are headed? I get kinda freaked out when I feel like all the AI "utopianists" haven't taken the next logical step of thinking about what society looks like when humans are subpar in every domain (and you may argue this won't happen, though I'm becoming more and more a believer that it will, but my point is the utopianists believe that this absolutely will happen, and that it'…

I don't think humans necessarily become subpar when AI can do most of the work. Taking my own personal example, I have far more intellectual curiosity and improved my skills in programming far more with Claude Code than for 15 years of programming without AI simply because I was bogged down by boilerplate and grunt work. Now that AI handles most of the boilerplate and grunt work and can handle harder and harder probl…

> I have the time and space to work on unexplored frontier problems.

Like what?

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