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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

#321

Post by logicchains »

20k wrote: post #303
conz wrote: post #293

Earlier quoted context omitted.

Only in the sense that you reading a book from the library also constitutes theft of knowledge. Does it?

If I stole someone's private research notes and republished them loosely in my own words, they'd correctly be pissed This was unpublished research that was stolen, and constitutes plagiarism and academic fraud by even the strictest definition

>This was unpublished research that was stolen, and constitutes plagiarism and academic fraud by even the strictest definition

It was not stolen, it was willingly given.

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

#322

Post by neuroticnews25 »

magicalist wrote: post #214
modemNoises wrote: post #150

Earlier quoted context omitted.

Nothing in their comment reads to me as "arguing against" Reads like nothing but historical context

> Nothing in their comment reads to me as "arguing against" If competition is somehow the opposite of "centuries of traditions of open science", and "mathematics has always been highly competitive", then open science is neither sufficient or necessary for the future of mathematics. Their clear implication is that we don't need to worry about it, though, because it's always been that way. > Reads like nothing but hist…

>If competition is somehow the opposite of "centuries of traditions of open science", and "mathematics has always been highly competitive", then open science is neither sufficient or necessary for the future of mathematics

For the future of past mathematics, it says nothing about the current future. Also, open science can be nonsufficient and unnecessary but still extremely beneficial and desirable.

>Their clear implication is that we don't need to worry about it, though, because it's always been that way.

Lets just ask him if that's what he meant, I bet no.

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

#323

Post by oefrha »

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.

One related problem I see is the pipeline for producing working mathematicians seems to have been completely and irreversibly decimated. What’s the point of doing a long and arduous PhD when all PhD level research problems that used to take months to years can be solved by far less talented people with $100/$1000/$10,000 to spare? How do you even select people into your program (this part is likely hypothetical, classical talent selection probably still works at the moment, but what about in a couple years)?

Disclosure: I did a theoretical physics PhD, but got admitted to quite a few top math programs back when I was applying to math and physics programs simultaneously. If you asked me whether I’d do a PhD today I’d say why bother.

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

#324

Post by rzerowan »

tmp10423288442 wrote: post #229
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-…

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.

Ah but heres the thing , society/gov expects mathematicians to be productive and tries to measure that by awards/publications/citations gained. Within a guild ope or secret they could possibly use a local LLM (even if slow) to accelerate their collective output.While ensuring their credit/publication/citations remain intact rather than with the AI labs taking a lions share of that.

Think along the lines of the Nicolas Bourbaki persona/collective : " was a collective pseudonym chosen in 1934 by a group of young French mathematicians. None of them carried the name alone; all of them carried it together. And under that name, they launched the most ambitious mathematical publishing project of the twentieth century: a series of texts rebuilding modern mathematics from scratch, on entirely axiomatic foundations."[1]

[1] https://abakcus.com/articles/nicolas-bourbaki

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

#326

Post by Squarex »

haunter wrote: post #301
orangecat wrote: post #182

Earlier quoted context omitted.

Which is not "theft" according to current legal precedent, and also common sense.

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.

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

#327

Post by Alien1Being »

oefrha wrote: post #323
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.

One related problem I see is the pipeline for producing working mathematicians seems to have been completely and irreversibly decimated. What’s the point of doing a long and arduous PhD when all PhD level research problems that used to take months to years can be solved by far less talented people with $100/$1000/$10,000 to spare? How do you even select people into your program (this part is likely hypothetical, clas…

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.

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

#328

Post by 20k »

logicchains wrote: post #321
20k wrote: post #303

Earlier quoted context omitted.

If I stole someone's private research notes and republished them loosely in my own words, they'd correctly be pissed This was unpublished research that was stolen, and constitutes plagiarism and academic fraud by even the strictest definition

>This was unpublished research that was stolen, and constitutes plagiarism and academic fraud by even the strictest definition It was not stolen, it was willingly given.

The terms of service does not dictate what constitutes plagiarism

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

#329

Post by 2b3a51 »

vessenes wrote: post #3

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 Pyth…

Andrew Wiles was also careful about communicating progress on his Fermat's Theorem proof during the years in his attic. So yes I take the point.

I read the Mastodon thread as more about the 'flattening' and 'rawness' of the proofs these systems and their operators are producing. I mean what is the cultural significance of a lean proof that is half a million lines long or something? And what tools can be extracted for further work from such a construction?

The late William Thurston wrote about the culture of mathematics in that sense.

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

#330

Post by znnajdla »

hn_throwaway_99 wrote: post #271
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.

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

So, no, my skills have not become subpar, but have only become stronger because of the presence of AI.

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