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The Dark Night of Mathematics

kirwinhampshire.substack.com

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Re: The Dark Night of Mathematics

#251

Post by thrance »

d_burfoot wrote: post #92

Every single knowledge worker is going to face this kind of crisis. It will be worse for people who cared deeply about their craft, but the crisis will have the same shape. The way through is to change the way you relate to your work, and to appreciate the fact that you can now produce far more output. Mathematicians should realize: instead of spending decades on individual theorems, you can now create whole new subf…

> The way through is to change the way you relate to your work, and to appreciate the fact that you can now produce far more output.

Yeah, just like artisans enjoyed being turned into assembly line workers in the industrial revolution. There was a movie starring Charlie Chaplin about how awesome that was.

If AI is truly useful for knowledge work, that will mean a huge downgrade to working conditions for knowledge workers, whose skills are no longer as valuable. And these workers will be alienated from their craft, just like artisans were.

Re: The Dark Night of Mathematics

#252

Post by cubefox »

amarka wrote: post #208
cubefox wrote: post #187

Earlier quoted context omitted.

> There is something about mathematical discovery (progress, advancement, creation) which is vital to the spiritual, experiential quality of doing mathematics. The creation (or even the pursuit) of novel mathematics is one way that humans have historically accessed the ineffable and encountered the divine and mystical.

“ one way that humans have historically accessed the ineffable” that’s my question, what about the other ways that have been automated away. Is there something special about mathematics or is it the authors first encounter with obsolescence?

The automatic dishwasher has replaced the human dishwasher, but I highly doubt that dishwashing was one way that humans have historically accessed the ineffable.

Re: The Dark Night of Mathematics

#253

Post by cubefox »

RhysU wrote: post #116

> The creation (or even the pursuit) of novel mathematics is one way that humans have historically accessed the ineffable and encountered the divine and mystical. Would a mathematician please unpack this for me? A theorem is the opposite of ineffable. A conjecture may be ineffable but its pursuit reifies it. I am missing something.

No answer so far... Go ask the author on his blog!

Re: The Dark Night of Mathematics

#254

Post by FacelessJim »

I think that this new paradigm in mathematics will allow for more math being born out of curiosity and creativity. Many mathematicians have built their career around hyper specialization, and are now the most threatened because LLM excel in hyper specialization. I see it as a boon in a sense because it will bring forward the generalists. LLM will allow to much more effectively explore and discover new mathematics spanning across fields while retaining the specialist depths. Humans can still be at the helm, the focus just need to shift from cranking out technical proofs to more playful connections.

Re: The Dark Night of Mathematics

#255

Post by shibaprasadb »

marifjeren wrote: post #136

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.

I get what you are saying, but your joy shouldn't always be utility-driven IMO.

Re: The Dark Night of Mathematics

#256

Post by RhysU »

cubefox wrote: post #253
RhysU wrote: post #116

> The creation (or even the pursuit) of novel mathematics is one way that humans have historically accessed the ineffable and encountered the divine and mystical. Would a mathematician please unpack this for me? A theorem is the opposite of ineffable. A conjecture may be ineffable but its pursuit reifies it. I am missing something.

No answer so far... Go ask the author on his blog!

Done

Re: The Dark Night of Mathematics

#257

Post by xorcist »

tptacek wrote: post #191
xorcist wrote: post #180

Earlier quoted context omitted.

That thought experiment says more about your thoughts on plumbers than anything else.

I live in Chicagoland, which has the largest water reclamation facility on Earth in order to prevent the entire region's basements from flooding under storm water pressure. It doesn't work, and I have multiple times had the pleasure of watching from my basement stairs as plumbers waded through raw sewage to clear obstructions in the lines at my house. It's a tough job that requires a lot of skill and nobody is doing…

Thank you for proving my point by fixating on the raw sewage part.

Contrary to what you think, no plumber would abstain from fixing plumbing permanently, even if it meant no more wading through said sewage.

Re: The Dark Night of Mathematics

#258

Post by justanotherjoe »

skeledrew wrote: post #209
jknoepfler wrote: post #100

Earlier quoted context omitted.

The history of mathematics is tightly coupled to spirituality... some more famous examples off the top of my head are Cantor, Euclid, and Euler, but there are probably hundreds of examples of folks who explicitly tied their faith to their research. I definitely don't think there's anything inconsistent with mathematical and theological thinking. That actually strikes me as a very strange idea?

Would those persons mentioned have found themselves in a state of crisis if they were alive today? And it still doesn't touch on the core question: what does math and spirituality really have in common (beyond the extrinsic connection someone may make because they're emotionally overwhelmed by the "beauty" of the golden ratio appearing in nature, for example)?

Probably they wouldn't be. A lot of this is people catastrophizing. Probably already somewhat unhappy even before.

Regarding spirituality i think it's more about math itself than math as a discipline. Math might be divine. Even if math is divine, i think doing math doesnt make you more spiritual.

Re: The Dark Night of Mathematics

#259

Post by abanana »

kensai wrote: post #250
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…

"like... programmers enjoy the act of typing lines of text into a file on their computer" ehm, no!

Yes exactly, that jumps out as a strange thing to say. The enjoyable part of programming is the puzzle, the act of figuring out how to solve the problem elegantly and well.

Although I can't speak for artists, surely the joy of painting is in the creation of a piece of art they can be proud of?

Enjoyment in work is generally about taking pride in the end result, not in the repetitive mechanical part.

Re: The Dark Night of Mathematics

#260

Post by frognumber »

Jtarii wrote: post #99
d_burfoot wrote: post #92

Every single knowledge worker is going to face this kind of crisis. It will be worse for people who cared deeply about their craft, but the crisis will have the same shape. The way through is to change the way you relate to your work, and to appreciate the fact that you can now produce far more output. Mathematicians should realize: instead of spending decades on individual theorems, you can now create whole new subf…

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…

> Taking a helicopter to the top of Everest is not as rewarding as climbing the mountain.

I don't think this is a fair comparison. New tools take you higher. I'll never climb Everest. A good comparison is:

- Climbing your local mountain

- Helicopter to the top of Everest

- Spacecraft to the moon

If a helicopter just saved you a trip up, you'd be right, but it can take you places you wouldn't otherwise go.

I created a new field of mathematics just yesterday, coincidentally. It wasn't a very good field of mathematics, though.

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