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The Dark Night of Mathematics

kirwinhampshire.substack.com

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Re: The Dark Night of Mathematics

#231

Post by vouaobrasil »

oytis wrote: post #115
lioeters wrote: post #82

Earlier quoted context omitted.

Not even wrong. Real scientists say "yes" to the genie with all the answers? And artists and crafts people don't? The entire statement is nonsense, and offers no insight into art or science. It's almost like a language model generated a plausible sentence that is grammatically correct but has no relation to the real world. Perhaps if the analogy was between science and engineering.. A plumber would say "yes" to the g…

One should differentiate between "working in academia" and "doing science" here. Science is fundamentally about the curiosity, the desire to know, not the process of getting there. If we can now know anything we want, we have an age of unimaginable abundance before us. I think it's more likely though that we will just be able to know more things than before and/or maybe learning new things faster - which is a good th…

No way. Science is not just about the desire to know. Almost all scientists I know (and I've met hundreds) care deeply about the joy of working out the problems themselves rather than just knowing the answers. The joy of finding that mental spark on your own to solve a problem - that's what makes it worthwhile. Just knowing everything right away is boring. If it were not, I'd just spend all the time in a library reading the work of others.

Re: The Dark Night of Mathematics

#232

Post by vouaobrasil »

satvikpendem wrote: post #155
jckt wrote: post #35

Earlier quoted context omitted.

Disregarding the competing definitions of “science”, a significant value in mathematical work is “the journey”. The truth or falsehood of individual results are rarely as important as the machinery developed to deliver it. If all the genie did was tell you something was true or false, the only learning you gain is to backtrack and develop the machinery yourself. To a certain extent this is true of the other sciences…

Maybe the genie provides full proofs of each result. So will the journey still matter? For a true mathematician it should not.

Of course it does because the joy of math is discovering something yourself. At some point you just want to stare at a blank sheet of paper, start with a premise and go on a journey. Are you a mathematician or scientist? I am and just typing "tell me the proof of this result" sounds immensely boring to me.

Have you ever played a video game with an "invincibility cheat"? Boring. But you do get to the end and "solve the game".

Re: The Dark Night of Mathematics

#233

Post by vouaobrasil »

oytis wrote: post #83
joe_the_user wrote: post #70

Earlier quoted context omitted.

The only "fields" where a genie appearing and doing all your work for you are fields (jobs) where you only about the money at the end. There are some fields where a serious practitioner might be happy to have a genie do all the "grunt work" (though what people that is varies - I'm not sure what "discovery work" means here but it doesn't matter since present AI promises to do everything in the future if not now). And…

Wouldn't it be great if we had a cure for cancer, working fusion energy or at least a proof for P vs NP even if no human had a joy of discovering it?

Would it if it meant that the entire joy of creating art was mostly gone from the world because the social value of it was diminished? Not really. And all that technology is not free. It needs rare earth mining, land usage, and habitat destruction that will likely cause even more cancer, mental problems, health problems, etc.

Re: The Dark Night of Mathematics

#234

Post by vouaobrasil »

drivebyhooting wrote: post #15

Well for me the twilight had already come when I realized I’d never amount to a decent mathematician. Maybe this is rather a common experience? LLMs just democratized that process.

The whole point of math is to just have fun discovering things. You might be able to discover math with an LLM, but you'll never be a mathematician if you don't do it yourself. LLMs don't democratize anything. They just let you spew out results that aren't particularly impressive if you can't even understand what the hell you're creating.

Re: The Dark Night of Mathematics

#235

Post by vouaobrasil »

MinimalAction wrote: post #146

I feel seen and heard. I'm conflicted in feeling there's now a lot more to do with AI, but also if it ain't me doing most of it, where's the fun in that? Days feel meaningless, and don't know who will pay for what I want to do, after all these years of heavy training.

Exactly. We should preserve a society where at least some people have a chance of doing what they love, especially if they have a talent for it. AI is eliminating that, whether or not people can find other jobs.

Re: The Dark Night of Mathematics

#236

Post by vouaobrasil »

kevinalexbrown wrote: post #38

It’s ok to mourn the loss of a frontier and also support the thing driving that loss. The way it looks, the generation of mathematical results will become less and less of a human endeavor. There’s a way that’s sad even if on the whole it is a huge leap for society. This was a great article, and I applaud the author for acknowledging this head on.

Is it a leap for society? I'd argue that society is better off if it's mostly people doing things and feeling like they are valued. What is the end result? Endless surplus, where we have the cure for every disease, but are useless masses of flesh consuming endless entertainment? Sounds like a fucking zoo and not a life worth living.

Re: The Dark Night of Mathematics

#237

Post by vouaobrasil »

groos wrote: post #134

Have LLMs produced something novel like Cantor's diagonalization procedure once was? Come up with new concepts like set theory once was and axiomatized it? Is there any indication or evidence LLMs can do this? If not, I would wager mathematicians are still going to be a profession in the future. Maybe not as theorem provers in a particular axiomatized system where LLMs can be effective tools but the wider project of…

Poeple once thought that it was ridiculous that a computer could beat a 1600 player in chess. Then they put it at master. Then international master. They still thought it was ludicrous that a computer would beat a grandmaster or the world champion.

Oh wait.

Re: The Dark Night of Mathematics

#238

Post by soulofmischief »

satvikpendem wrote: post #148
Jtarii wrote: post #99

Earlier quoted context omitted.

The creation is the actually enjoyable part. Taking a helicopter to the top of Everest is not as rewarding as climbing the mountain. You are completely discrediting the joy humans derive from actually -doing- the work, and not just, telling someone else to do the work. There is a reason artists hate AI, its because they enjoy the actual act of painting, like mathematicians enjoy the act of proving theorems and progra…

Jobs are not generally meant to be enjoyable (although that is a benefit if so), they are meant to get work done. It's funny seeing office workers here on HN have this sort of opinion and contrasting that with blue collar workers, ask a miner or house builder how fun their job is.

Then they should take up less of our lives.

Re: The Dark Night of Mathematics

#239

Post by vouaobrasil »

skeledrew wrote: post #98

This is the first I've ever heard math connected to the spiritual. For all my life it has been this rigorous thing grounded in reality in such a way that only people who think a certain way could even approach. Now those people are having this strange "crisis" because AI is being more rigorous than humans I guess. I find it... wild. My, but how the mighty have fallen.

Almost all mathematicians I know admit to feeling spiritual about discovery in the mathematical world. Engineers are taught the rigorous thing but it goes way beyond that. In fact, I bet a lot of people find some satisfaction in their work that goes beyond the practical. Artists, etc. That's what AI threatens because it destroys strong communities of people who value such work.

Re: The Dark Night of Mathematics

#240

Post by vouaobrasil »

amarka wrote: post #182

Apologies is this is a simpleton question, but how does this differ than most of the mechanical work previously done by hand, but is now automated?

It differs because LLMs can and will eventually make inferences, even if they're not truly intelligent. They can do things that one can't predict ahead of time. In that regard, it's very different than asking a computer to multiply together two degree twenty polynomials. I could do it by hand theoretically in a completely mechanical fashion, but AI can do some basic inferences.
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