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The Dark Night of Mathematics

kirwinhampshire.substack.com

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Re: The Dark Night of Mathematics

#131

Post by lioeters »

c7b wrote: post #107

The endangered art form of human mathematics is one thing. Another thing is that there seems to be little concern for whether a theorem was created using a documented open-weights model or some unknown model in a web chat. If you want to make the case that the journey of creating the proof is part of doing mathematics, then you should also document that path and make it reproducible, as science should always be. Ther…

There's a parallel with open source software (FOSS), that you don't really control the software if you don't have the source code.

Being given only the generated proof (or disproof) is like having the binary artifact as an executable. Sure you can use it to solve or build further on top of it, but without the source code - the understanding of the steps to build the binary - you can't build it yourself, and you don't actually own it. If you want to adjust or extend something in the proof, you have to go back to a third party to implement it and generate another artifact for you.

We need a Stallman for mathematics with uncompromising integrity, to shout from the rooftops for a "free and open-source math movement" (FOSM). Even if the biggest AI companies go bankrupt, we still need to be able to bootstrap all the math from the source code.

Re: The Dark Night of Mathematics

#132

Post by zemvpferreira »

discreteevent wrote: post #16
zemvpferreira wrote: post #10

This is what locking yourself away in an ivory tower gets you. Do things ‘for beauty’ and watch as they are automated and commoditized by the people who depend on them for their continued wellbeing, reduced to a hobby or sport. But the reduction began when you yourself started putting more importance on your enjoyment of the process over the value being provided to your customers.

> But the reduction began when you yourself started putting more importance on your enjoyment of the process over the value being provided to your customers. Why would you make this comment? Is it envy? They were able to do things only some people can do. They enjoyed what they did and it provided value. Now the fun has been taken out of it and you seem to be saying that they deserve to have no fun? What should they…

Because I’ve often been with professors in math, literature, arts who pride themselves on a certain intellectual purity that makes them a cut above, while living on wages paid by the taxpayer. Suddenly the golem of basic market dynamics comes for them and these extremely smart people are struck by the unfairness and bruteness of it all. Whole careers having fun publishing useless nothings, funded by people sowing soccer balls and scrubbing toilets. I have nothing against having fun while doing your job, I have it often. But I have a job first to serve society, not myself.

Re: The Dark Night of Mathematics

#133

Post by BeetleB »

bonoboTP wrote: post #89
singpolyma3 wrote: post #84

> Mathematicians are paid to prove theorems lol who is paying for this? Mathematicians are generally paid to do other things and get to do this kind of work as a side effect.

In academia they are paid to produce papers (and get some chores done like teaching), hopefully ones that can result in bombastic press releases, or winning awards. On a more abstract level they are paid to bring funding and prestige to the university, but that often goes through the route of papers. And papers often involve proving theorems.

Actually, no. They are hired to do research but not paid for it. They get a 9 month salary to teach, not for research.

They have to publish papers to get tenure but the university doesn't pay most math faculty for it.

If they want to get paid for research they apply for grants and get the max of a third more salary.

Most other departments make getting grant money a prerequisite for tenure. Math departments typically don't.

So in most math departments faculty members don't bother with grants. Usually only a minority of them do because they want more money.

They're not paid to do research.

Re: The Dark Night of Mathematics

#134

Post by groos »

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 synthesis and unification, and the discovery of new modes of mathematical thought will still require mathematicians.

Re: The Dark Night of Mathematics

#135

Post by MinimalAction »

tidojo wrote: post #108
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…

you can’t climb to the moon, you need rockets for that. In the hands of great researchers, AI will accelerate and propel human knowledge far beyond what we could achieve with pencil and paper alone.

True, but many of us have grown identifying ourselves with the kind of work we do, the discoveries that follow from our hard work. Even in the case of rockets, we designed the rockets! Here, I've to let the oracle take care of things while I'm robbed of that delight of discovery.

Re: The Dark Night of Mathematics

#136

Post by marifjeren »

Grateful for this essay. Made me feel seen.

Someone said:

> No one is stopping you from doing what you enjoy.

But that's wrong. LLMs are creating an environment in which some things are no longer enjoyable.

For example there is less joy to be had in learning a programming language in 2026 than there was in 2016, because there is less utility in it now.

Re: The Dark Night of Mathematics

#137

Post by tptacek »

lioeters wrote: post #82
tptacek wrote: post #22

One way to differentiate between an art or a craft and a science is that if a genie appeared and offered to trivialize all the discovery work of your career and simply give you the answers today, and you'd say "no", you're probably not doing science.

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…

No, I think you're pretty overconfident here. A plumber is not in fact thrilled by the genie who permanently resolves all the world's plumbing problems.

I also kind of love the subtext in these responses that there is something suspect about crafts.

Re: The Dark Night of Mathematics

#139

Post by practal »

I actually think it is just the dawn of mathematics. During the last few days I discussed a few questions about abstraction logic [1] with AI that I was wondering about for quite some time (years), but didn't have the time + energy + in-depth expertise, there were like, 4 related questions; it positively solved 3 for me in the way I expected, but couldn't power through before; and for the fourth it proved to me that answering this question would imply solving a known open problem. And I know that it answered all of those questions correctly because I asked it to provide me with Isabelle/HOL proofs for it.

If you are interested in mathematics because it can model things precisely, and you want precise answers about these models, and you want to know how it is all connected (Langlands anyone?), AI is fantastic news. There is plenty of new and interesting and beautiful and elegant mathematics to be had this way, as well.

This is not a time to be scared or frightened. This is a time to be excited as fuck.

There will always be open questions. Now, there will be actually many more of them, because many more people will be asking questions.

[1] http://abstractionlogic.com

Re: The Dark Night of Mathematics

#140

Post by spiresofagartha »

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.

I don't get it. Do you feel good or bad about that? Is that the way you tell you're empathetic to the author?
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