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…
The Dark Night of Mathematics
161–170 of 321 posts
Re: The Dark Night of Mathematics
#162I hope that this doesn't mean that you need write proofs while streaming Twitch. ;)
Re: The Dark Night of Mathematics
#163Without knowing anything about the specifics of the conjectures that are falling, I wonder if this affair highlights an issue with the quality of the "open conjectures" that are out there. There are a lot of reasons you might make a conjecture. Perhaps you are motivated by a search for structure: "We suspect that these objects behave like this, therefore we naturally imagine that...". But you might make a conjecture…
The reason the author is upset is not that the conjectures were false, but that an AI settled them. That's why so much of his post is about the loss of the human element.
Re: The Dark Night of Mathematics
#164Every 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…
Normally I'm very sympathetic to the plights of those socially affected by AI, and rarely pass up the opportunity to clown on institutional actors papering over these plights with glib cliches. But in this case, I really feel like this is a case of monkey-brain overriding mathematician-brain.
The greatest accomplishment in my life is my math PhD, earned before AI got useful. I do math-heavy work for my day job, and I care deeply about every craft I practice, to the point that I am almost certainly on the unhealthier end of the spectrum of perfectionism. Yet I both acknowledge rather than deny the impending death of mathematics as we have engaged it for the last couple centuries, and am far more excited than aghast.
I would have to write a whole essay in order to communicate this in a way that is appropriately sensitive, but in a nutshell: We have always been in the business of discovering and understanding math, have we not? Are we going to call it a tragedy rather than a blessing now that the floodgates on both are bursting, just because it makes us feel less special, unique, valuable? It's such a self-serving aesthetic on the beauty of math to me. The author claims there is something profound and spiritual about math, and I agree; it exists prior to and above all of us, human or AI. Whatever way we can tap that beauty is incredible, full stop. This is what I believe.
From the article:
> These developments have triggered some deranged thoughts in me. I have wondered if it is the express goal of these companies to make me kill myself. Am I alone in this paranoia?
The severity of this line caught me off guard. I think the author is genuinely having an emotional-social crisis, and I feel terrible for them, but at this moment they may be having a hard time separating their trauma from their intellectual aesthetic for what math is all about.
Re: The Dark Night of Mathematics
#165Earlier 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…
Their sentence makes perfect sense to me. Science is about knowledge, art is about the process of creation. Conflating the two is just doing a hobby at that point.
Re: The Dark Night of Mathematics
#166Grateful 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.
Why must this result in less joy. Chess has utility in only the most abstract sense, yet people enjoy it. Computers became better than humans, and some dispared, but more still enjoy it. Computers provide insight into the problem, which leads to a greater enjoyment for many people. Instead of finding a move in a complex state and thinking 'I'll never know if that was the best move'. A good chess engine can give a rea…
The parent's point is better articulated as: programming COUPLED with being paid do it is what is now less enjoyable due to AI.
You are free to enjoy pretty much anything but you may not necessarily be paid to do it.
> We are no longer the only world in existence, we are no longer the center of the universe.
Nothing has changed in this regard. We were the centre prior to AI then we still are after it. The human ability to comprehend makes us the centre. The squiggle: 8 means nothing to an ant but to a human it is the number eighth. AI is something only humans comprehend beyond that what does AI matter and to whom would it matter to?
Re: The Dark Night of Mathematics
#167Earlier 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.
We don't live for rockets or the moon, but for ourselves. Anywhere we can go to only at the price of our despair we have no business going to.
Re: The Dark Night of Mathematics
#168Earlier quoted context omitted.
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…
I consider "get paid to do X" to be equivalent to "you get to have your paid job and career as long as you do X". In that case research and papers qualify. Whatever is technically written in the contracts is just surface level bureaucracy. Publish or perish.
Actually, it doesn't. Both math departments I'm familiar with had faculty members who published only to get tenure, and never published again until they retired.
But if they didn't teach (or taught extremely poorly), they got fired, even though they had tenure. If you didn't show up to a scheduled class a number of times, you got in trouble.
I know you weren't saying this, but it's frustrating reading so many comments about mathematicians "getting paid to have fun and good riddance". No - the majority of what they do is teach non-math students. If people here don't like that, by all means dissolve the departments and have the engineering departments teach math.
Re: The Dark Night of Mathematics
#169Have 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…
A year ago, the goal post was that LLMs wouldn't prove anything of worth. The year before that, it was that LLMs wouldn't be able to do math as well as a undergraduate student. Year before that, it was that LLMs wouldn't be able to do math at all. The growth of LLMs has been insane, and it doesn't look like it's going to plateau any time soon.
Re: The Dark Night of Mathematics
#170Grateful 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.
Why must this result in less joy. Chess has utility in only the most abstract sense, yet people enjoy it. Computers became better than humans, and some dispared, but more still enjoy it. Computers provide insight into the problem, which leads to a greater enjoyment for many people. Instead of finding a move in a complex state and thinking 'I'll never know if that was the best move'. A good chess engine can give a rea…
Well I think you answered it:
To become a developer, I disciplined my mind to do impressive and useful things. The resulting feelings were pride and speciality and therefore sometimes joy.
And those feelings are gone now that software engineering has become a low-discipline, low-barrier to entry activity.
Am I immoral or vain for having derived joy from that -- I think is another matter, and one which doesn't resurrect the joy no matter how it's answered