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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

#341

Post by contravariant »

dev_dan_2 wrote: post #54
contravariant wrote: post #39

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 by [deleted] »

henryfjordan wrote: post #21
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…

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

Post by tancop »

majormajor wrote: post #243
CamperBob2 wrote: post #131

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 by alansaber »

kzz102 wrote: post #51
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…

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 by embedding-shape »

alansaber wrote: post #344
kzz102 wrote: 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 by jacobolus »

p1esk wrote: post #311
hananova wrote: post #302

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 by benibela »

yorwba wrote: post #334
unified101 wrote: post #216

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 by chr1 »

IanCal wrote: post #315
kkotak wrote: 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 by largbae »

hn_throwaway_99 wrote: post #272
kkotak wrote: 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.
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