Live data from Hacker News

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

mathstodon.xyz

341–350 of 354 posts

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

#341

Earlier quoted context omitted.

I mean mathematics has enough history that something can both have been false for centuries of mathematics research and true for centuries. Sometimes in different places simultaneously. Terrence Tao can do his job perfectly well without being aware of any mathematical history, though I consider it unlikely that he is. I'm not seeing the direct link you're talking about, in fact history is frequently left out of mathe…

> in fact history is frequently left out of mathematical teaching even when the history would in fact help in the understanding of some concepts. That is well-known I assumed and continue to assume. > I'm not seeing the direct link you're talking about You are stating that link yourself; indirectly: "though I consider it unlikely that he is [being unaware of any mathematical history]". Why is it unlikely, precisely?…

Any one of the arguments you make here is already stronger than the original one. The problems with appeals to authority isn't that they are always false, it's that they are not a good argument.

And you say his "expertise is directly linked to his ability to not misstate the history of mathematics". And frankly, I disagree. If he happened to be misguided or even outright wrong about some parts of mathematical history I wouldn't think any less of him, nor do I think it matters much for the work he's actually paid to do. At worst it would result in an online discussion, which is arguably a good outcome not a bad outcome.

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

#342
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…

The story of the cubic equations is another great example: https://en.wikipedia.org/wiki/Cubic_equation Dudes straight up used to hoard solutions to equations and use them in math battles.

[deleted]

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

#343

Earlier quoted context omitted.

Funny, the stuff that was stolen is still there. A strange kind of theft. Copyright maximalism is a bad look on a site called "Hacker News." Perhaps other sites beckon.

> Copyright maximalism is a bad look on a site called "Hacker News." Perhaps other sites beckon. Frankly it's more of an insult to the "hacker" name to be apologising for big companies profiting off of frontrunning existing work for PR purposes, if the claims about piggybacking on human-directed efforts/prompting are true. Being pro-copyright in order to protect the work of an individual from being reconstituted into…

In my mind being a hacker is something very anarchist/left libertarian coded. Hackers don't try and get laws passed to achieve their goals, they do it themselves no matter if it's legal or not. Activists fight for right to repair, hackers jailbreak their device and publish the keys. We need both to fight big tech effectively.

Copyright is not a hacker thing because it restricts peoples freedom to share and hack on anything they see. Now abusing a bad system to do something good, as you said, would be hackery. But that's not the same thing as supporting copyright as it is right now or wanting to expand it. It needs to be in the spirit of "we turn their own tools against them". The ultimate goal is still eliminating IP laws as far as they limit individuals free speech.

It would be different if it was an asymmetric system. Protect creators from companies trying to make money off their work, but not the companies from users taking their profits. That would mean switching to a form of copyright that only applies to commercial use and abolishing work for hire / any form of rights assignment as opposed to a license. That's one idea I can get behind.

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

#344
post #51
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…

The mathematical community was very competitive in its early years, but in the last 70 to 100 years, it has been generally less competitive and very collegial. The community was in a good place, and progress has been very good. In a few cases when competitiveness was ramped up, it lead to bad behaviour and destructive fights. Few would like to return to those competitive years.

The overarching geopolitics have always taken precedent over the preferences of the mathematical community as far as I can tell

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

#345
post #51

Earlier quoted context omitted.

The mathematical community was very competitive in its early years, but in the last 70 to 100 years, it has been generally less competitive and very collegial. The community was in a good place, and progress has been very good. In a few cases when competitiveness was ramped up, it lead to bad behaviour and destructive fights. Few would like to return to those competitive years.

The overarching geopolitics have always taken precedent over the preferences of the mathematical community as far as I can tell

Same is true for any area/topic though. Countries at war stop playing friendly football games against each other, as a very basic example.

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

#346
post #311

Earlier quoted context omitted.

Of course you can. Stockfish plays very different compared to a human, and it never ever blunders or makes mistakes.

I’ve never played against a grandmaster, but I have a feeling that he/she would play very different compared to me and would never make mistakes I could notice. Though admittedly I’m not very good at chess.

Grandmasters absolutely make mistakes, and you could learn to notice them with a few months of guided practice.

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

#347
post #334

Earlier quoted context omitted.

What do u think lean is? That's like saying a program that works, is inscrutable because it appeals to the oracle of "code test cases" to prove itself correct. You're either being intentionally obtuse, or unintentionally ignorant.

Have you tried to read the Lean proofs produced for any of the recent high-profile results? They're extremely long, terribly structured, and don't indicate which parts are restating known results from literature and which are unique to the proof at hand. That's what makes them inscrutable. It's similar to Mochizuki claiming to have proved the ABC conjecture, with a proof depending on ideas developed over a large numb…

>It's similar to Mochizuki claiming to have proved the ABC conjecture

Now I wonder if someone could port his proof to Lean

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

#348
post #315
post #269

Earlier quoted context omitted.

How is this any different from people in any field that are impacted by AI and lose the utility of their skills and endeavors over the past decades? Are we saying that we're running out of problems to solve because of AI and hence it should be stopped? I am not underestimating the importance of the collective knowledge of the mathematics community and the role of mathematics as the enablers of other sciences, but opp…

His point is twofold: that the process of solving the problems leads to more than just solving the problem in front of you but other interesting things (he has an example of going on a hike to a waterfall and all the other things you might spot over in the distance or nearby on the way, which you’d miss if you were able to jump straight there), and also lots of the simpler open problems are ones early researchers lea…

Ability to jump straight to waterfall doesn't prevent you from taking another hike looking specifically for those other things.

If solving any problem is possible with ai, the job of mathematician is finding new problems, not trying to do what a machine can do better.

As for training, most of it is already done by solving known problems, and no one was suggesting to forget analytical geometry so that solving school geometry problems becomes cutting edge research.

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

#349
post #269

Earlier quoted context omitted.

How is this any different from people in any field that are impacted by AI and lose the utility of their skills and endeavors over the past decades? Are we saying that we're running out of problems to solve because of AI and hence it should be stopped? I am not underestimating the importance of the collective knowledge of the mathematics community and the role of mathematics as the enablers of other sciences, but opp…

Do you see an end state in this? When AI is better than humans at everything (and I used to be very sceptical of that claim but I'm getting less and less by the day), I don't see the Wall-E version of humanity as some sort of utopia, and that's the good outcome.

To paraphrase the not-so-great philosopher Ted Kaczynski: Either we will maintain control of the machines or we won't. And if we do, it won't be you or I who control them, but a small group of elites.

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

#350
post #313

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 paradig…

> 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. Sure there is: problems that require knowledge that simply doesn't exist yet. Until "AI" turns into general purpose robots that can develop new tools to explore the world, it is, in fact, pretty damned limited in what it can do without human help. The world is vast…

> 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 general purpose robots that can develop new tools to explore the world, it is, in fact, pretty damned limited in what it can do without human help.

For sure, but this isn't a question of if, but when. LLMs are already rapidly accelerating the pace of every scientific field, so advancements in technology will start to compound.

> Biology is replete with examples. Computers "solve" protein folding [1], and midwits immediately leap to conclusions that drug development will also quickly fall. But we literally have no idea how most of biology works, and simply getting to the starting line for drug development problems is often 95% of the battle. Come talk to me when you've done a million experiments to find the fundamental knowledge that unlocks the pathway(s) we didn't know about that makes a drug discovery program possible in the first place [2].

I don't disagree with you. The amount of complexity in biology is incredible and due to its unpredictable squishy and noisy nature and the advanced machinery needed to analyze it with precision at the microscopic scale, vast amounts of data accumulation are still required to discover the useful patterns here, and the search space will be enormous. Still, it will be done. Here is some recent movement in that direction: https://www.anthropic.com/news/model-hardware-standard-resea...

> I am not pessimistic about humans running out of challenges. We'll just declare one class of problems "done" [3], and move on to the next frontier, as we always have.

This is fair, you're probably right about that. I think they'll be challenges for the AI to solve though, not humans as a collective. Hopefully we have something to contribute to that process, other than just expressing our desires.

> The problem with AI doomers is that they lack imagination that extends beyond computers, or perhaps more accurately, are so sophomoric in their thinking that they skip over the hard parts of any problem they don't fully understand. This stuff reminds me of the endless smartypants whinging about the end of human intelligence when chess machines started beating grandmasters. Chess was never really that great a measurement of human intellectual capacity, and we found new things to do with our big monkey brains.

I'm not an AI doomer, I despise the AI doomer movement and the incessant fearmongering, it's incredibly unhealthy and its only purpose is to perpetuate panic in the aim of maintaining and establishing power, and preventing others from obtaining power that threatens the status quo. What cultish idealogical humans will do with this technology if they're left unchecked with staggering power and no one to stop them is certainly a big concern though.

Post reply on HN