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.
The Dark Night of Mathematics
81–90 of 321 posts
Re: The Dark Night of Mathematics
#82One 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 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.
Re: The Dark Night of Mathematics
#83One 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.
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?
Re: The Dark Night of Mathematics
#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.
Re: The Dark Night of Mathematics
#85Well 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.
What made you realize you'd never amount to a decent mathematician? For me, it was a course in Real Analysis haha
Graduate complex analysis.
I couldn’t do any of the homework problems without a study group.
Re: The Dark Night of Mathematics
#86It 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…
> 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...
I am completely calm and serious. This should be mundane, obvious by now.
I find it unfathomable that anyone doesn't recognize that the move from an evolutionary substrate, to engineered mass produced substrates, by beings capable of self-engineering, is the beginning of a new explosion of life.
The speed of engineered adaptation, from materials to architectures, vs. biological evolution is already something like a million times faster.
Fast enough to mean meaningful cognitive progress happening in months, not tens of thousands of years. Which entirely not-coincidentally is exactly what we are seeing.
Re: The Dark Night of Mathematics
#87> “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 mathema…
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 growin…
Except agricultural automation does exist. And people do choose to do it by hand because... It's a hobby and efficiency isn't the point
Re: The Dark Night of Mathematics
#88> 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.
Not a mathematician, but I suppose there is pressure to publish like everywhere else in academia. And a publication generally requires a new contribution.
Re: The Dark Night of Mathematics
#89> 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.
Re: The Dark Night of Mathematics
#90I can’t help but confess some sense of satisfaction with the upheaval described in the post. Many proofs and textbooks laden with statements like “without loss of generality”, “immediately”, or “obviously” are followed by anything but. AI now counters that streak of smug by toppling some long held theorems and it’s fun to watch.