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- Hacker News
- 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.by vouaobrasil
- 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.by vouaobrasil
- It is amazing how the scales of time we consider are shrinking even as change is accelerating. We are concerned about individual changes, that will quickly be followed by cascades of more change.
> Something fundamental to the experience of mathematics is being taken.
That is the near term. At least "near term" like we talked about it five years ago. And it won't stop.
AI isn't a tame long term transition - in scale it is bigger than any transition since the first individual cells. In speed it is happening faster than web adoption. No human adoption bottleneck. They are taking the reins of our tools, and don't need human adaption to improve.
Ineffables, and our intellectual primacy are going away, right now, even as we think about it.
I am not making light of it. But not surprised, because how could AI not redefined everything.
But maybe not everything:
20 years from now, 50, 100, there will still be ineffable experiences at the frontiers, by different beings. I believe esoteric curiosity and the intrinsic rewards of discovery will continue. Our propensities to find idiosyncratic interests and pursuits, seek answers and adventures, exist in our psychology because the low median return is decisively outmatched the extremely hight mean returns of unanticipated progress. The benefits of many pursuits will be even greater for them.
It seems unlikely to me, that future beings will become less interesting.
I relate to the author. Anyone who isn't feeling butterflies or stones in their stomach, isn't really processing the moment.
by Nevermark - > AI isn't a tame long term transition - in scale it is bigger than any transition since the first individual cells
You might need to put the phone / keyboard down, take a day off...
by neonstatic - 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.by vouaobrasil
- What made you realize you'd never amount to a decent mathematician?
For me, it was a course in Real Analysis haha
by joshdavham - 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?
- LLM's may have provided a bit of comeuppance. Many mathematicians have cared little if anyone understands their obscure nomenclature and build mote around their work. Now they have encountered something that is becoming far more capable than they are and they may soon be left in the dark.by waynecochran
- It should be a mandatory part of a technology-related degree to watch "The Man in the White Suit" (1951) https://youtu.be/RC8q1QSkE3M
When a new technology comes along, it diminishes some aspect of the human experience - because whoever had a talent for doing things the older, more difficult way becomes less important.
In that regard, AI is the extreme, because it threatens to make so many of our intellectual talents useless.
- > “Even if AI can prove theorems and theory-craft more efficiently than humans, and even if these proofs and theories are beautiful and interesting, and even if they are presented with elegance and clarity of thought, mathematicians will still have a place in the appraisal, presentation, understanding and appreciation of this new abundance of pleasing non-human proofs. We can still practice mathematics, learn mathematics, teach mathematics and do mathematics together.”
I am not a mathematician, but this seems like an entirely non-problematic answer to me. Mathematics is ultimately the discovery of relations and their consequences, so of course large language models were eventually going to catch up. But precisely what they do lack is ability to appreciate these relations.
The author says mathematics is a spiritual pursuit.[1] I have asked LLMs about theological topics before and they have also been able to produce perfectly cogent answers (even heavy questions like “how did Aquinas view Pseudo-Dionysius’ negation-laden description of God”). I am not the least bit shaken by this, because it is still on me to evaluate and understand, and appreciate these answers.[2] The author seems to think LLM’s pattern recognition makes redundant human understanding and appreciation, which is a logical leap that doesn’t make sense to me. Maybe the author is conflating utility and purpose? I feel bad, and hope the author takes care of themself, but I really think the author is taking a massive leap here. It is not that deep.
[1] I begrudgingly agree, but with the caveat that tending to a vegetable garden in your backyard is also a spiritual pursuit. Mathematics isn’t some special discipline that elevates you beyond other people, as much as it is useful and interesting.
[2] I of course wouldn’t consult an LLM if I actually wanted to educate myself or reason about these topics. Not only do I want to reason through them myself, but when it comes to issues in philosophy/theology/heavy stuff, you need to take in to account the perspective and experiences of the human writing them. LLMs muddle everyone’s perspective together.
by yaqubroli - I am a mathematician, and I agree with you here. I do not feel at all threatened by LLMs, because for me the joy of mathematics is in constructing the theories and beholding their beauty! I know other people are different from me here. I find having to prove theorems a rewarding part of the whole, but I am also not going to weep if an LLM can unstuck me on difficult proofs.
I am really excited if LLMs means more of mathematics will be formalised. Once we have all of mathematics formalised, I think we will start to see real great progress!
by black_knight - I begrudgingly agree, but with the caveat that tending to a vegetable garden in your backyard is also a spiritual pursuit. Mathematics isn’t some special discipline that elevates you beyond other people, as much as it is useful and interesting.
The thing is, if someone had the option to press a button and cause their garden to be weeded and growing perfectly, if most gardeners were using that button instead of growing normally, maybe some people would keep gardening for the spiritual part but they'd certainly feel like the rug had been pulled out from under them.
Edit: As another example, Robert Pirsig in his famous book described motorcycle maintinence as a spiritual enterprise. However, the quality that gave it this was the patience required-for and the uncertainty involved-in the enterprise. And again, if all you have to do is press a button, the spiritual part kind of goes away.
by joe_the_user - I think what people find "spiritual" about mathematics is the process, with its creativity and brilliance, ratjer than the final answer. I'd also think it's rather incomparable to a vegetable garden as the amount of effort required and complexity, which drive "spirituality", are of much grander scales. The author believes that llms make mathematics so trivial that mathematicians will no longer be the ones proving but the ones teaching and commentating, taking the "fun" part away in service of money. People will still do what they wabt to do, but one can no longer get by by indulging in what they like to do (math).by halperter
- When I was in mathematics, reading other people's work was always more rewarding to me than doing my own. I would spend years on a question to get some progress, versus spending a few days or weeks reading a paper to enjoy something new. I understand not everyone is like me but I really welcome the omniscient mathematician machine people are predicting. I can't wait to ask all the questions I care about.by Athanase000
- > I understand not everyone is like me but I really welcome the omniscient mathematician machine people are predicting. I can't wait to ask all the questions I care about.
To be honest, if a machine could prove the Riemann hypothesis and explain it to me, I wouldn't even care. I care about math because it's more of a way to express beauty and I find math interesting because it expresses the souls of those who create it. Just knowing the answer becomes boring after a while.
Most people are like that. Maybe 1% just care about pure answers.
by vouaobrasil - > When I was in mathematics, reading other people's work was always more rewarding to me than doing my own. [...] I really welcome the omniscient mathematician machine people are predicting.
Curious, as someone who relates strongly with both the OP and your first sentence: did it matter that you were reading "other people's work?" Or was it simply the satisfaction of understanding an answer?
Personally, one of the things that finally drew me to math as an undergrad (vs. high school where I thought of it as a stupid competition played by people who cared too much about showing off their smarts) was an instructor who helped me think of studying math as a conversation with a fellow human being many miles, centuries, languages, and cultures removed from me. Despite that distance, my mind was appreciating a creation that another human had cared for and poured years of their life into. There was a sort of romance to it, like the feeling of butterflies-in-the-stomach we get from seeing a multi-thousand-year-old cave painting, yet even more impressive because of the depth of the thought communicated.
I personally haven't been able to recreate that feeling from computer-generated math. Whenever I try to, I feel deeply uncomfortable (somewhat similar to the thought of eschewing human connection for an 'AI companion').
I'm more optimistic than the OP, especially when I think of new discoveries in healthcare. And I know there's enough "organic human-created math" from the last ~2k years that folks who feel the way I do can spend the rest of our lives studying only that. But it is sad to think that this multi-thousand-year project of "communicating human mathematical creations through time" has just ... ended? Or seems to be ending soon? Or at least greatly cheapened from a romantic dream into a sort of fun hobby, like recreational knitting? I can't help but share the OP's sadness that something seems to have been lost for future generations. Though a lot has been (and will be) gained as well, for sure!
by pcfwik - 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.by tptacek
- 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 this analogy breaks down further given that both the real now genie and the hypothetically more powerful genie of the future would each work for your (ex) employer.
by joe_the_user - math never was a science to begin with.by blueflow
- If you say "yes," you're also not doing science (anymore). Therein lies the problem with this take: most of science isn't done with the objective of getting to any specific finish line, and this is particularly true for math.
As the old saying goes, the purpose of a system is what it does, so there might be some Platonic ideal of science we can appeal to, but the practice of science by humans is about the craft as much as it is about the truth.
by skippyfish - Persian Curse seems to apply here
“May your every desire be immediately fulfilled.”
by coffepot77 - Sort of a callous thing to say about a person having a crisis of faith so bad they're talking about killing themselves.by Fraterkes
- An impressive number of things don’t make sense about this thought experiment. Whatever the genie says wouldn’t have much to do with the life you live afterwards, since your life changes after hearing the info. One persons careers worth of discovery work is not that much. A lot of work is dependent on the state of the world and can’t be moved into the past, even language changes. Someone could still do a craft or science or whatever afterwards— assuming life continues to have surprising complexity, the genie could only ever just scratch the surface.by srcreigh
- 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 too.by jckt
- 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 genie that solves the problem immediately, if he/she got paid for the work instead of the genie (or the corporation providing the genie service). In that case the plumber is redundant and unnecessary, the customer can just ask the genie directly. A scientist would say "no" because the whole point of science is the knowledge and understanding, which is gained by the process of discovery and not given on a silver platter.
by lioeters - > For me, the affective quality of learning mathematics is empathetically tethered to an act of discovery and creation. It is social. We are conversant with another mathematician—perhaps long dead. If we follow the chain of communication we arrive at a mathematician who enjoyed some original discovery. Human mathematics is Talmudic. It is a lively discourse of philosophical and religious richness spanning thousands of years.
This is really beautiful. And no matter what happens, two things have to be true: some form of lively philosophic and religious richness will keep being a core part of our history and will touch every person in some way; and it will change enormously over time (maybe with math continuing to be a small part, maybe not).
There is a part of math that is like that. There's also another part (as Vladimir Arnold provocatively said):
> All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like) hydrodynamics (supported by manufacturers of atomic submarines) celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA).
> Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.
> Hydrodynamics procreated complex analysis, partial differential equations, Lie groups and algebra theory, cohomology theory and scientific computing.
> Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.
Those parts can just be delegated to AI the same way they used to be delegated to mathematicians. But Arnold continued:
> The existence of mysterious relations between all these different domains is the most striking and delightful feature of mathematics (having no rational explanation).
by ngriffiths - > It is a lively discourse of philosophical and religious richness
This is pretty funny considering how trashy it is compared to philosophy
by ozgrakkurt