bbeonx

I don't know if this will happen in math, but in other fields where computers have outstripped humans (chess and poker, for instance), there's been a loss of creativity, but there have also been other forms of creativity that take its place. There was a period of reeling where we had to figure out what it meant to just be able to know answers to the question that made the game fun, but there's also a moment of realization: just because a computer says something doesn't mean we can't make it our own. Using poker solvers to find creative non-equilibrium strategies can still be fun: the ingenuity comes from using the tools to think out side the box. Or, finding a nicer set of abstractions that explains why a strategy does a certain thing, and then starting to notice it showing up other places.

For math, just because we know a thing is "TRUE" doesn't mean the investigation is done. The folks that love math are driven by solving puzzles, and the puzzle is still there, only changed: instead of being "is this true?", the puzzle is now "why is this true?" Building theories, finding nicer proofs, etc: there is still plenty of room for creativity.

But in the meantime, it really is tragic that so many young minds have had their work stripped away from them.

No matter how cheap it is, people will never be able to come anywhere close to affording what giant corporations can.

omg this is brilliant i was IMMEDIATELY tilting my face off

i was talking to opus the other night about the polio vaccine related stuff (i had been arguing with one of those people who claims the polio vaccine didn't work so i figured i'd use it as an excuse to brush up on some bio/history). i asked it to explain how polio virus was isolated pre PCR and claude hard killed my session citing security reasons (it was talking about stool samples ffs LOL)

i think there are a few reasons.

- lean proofs are hard, and a lot of the time there is so much mathematical machinery that folks are working on that you would need to not only prove your result, but also all of the machinery that your subfield it is built on. it would be infeasible for many authors to do all of this work (this might be a major part of multiple careers, and when there are 5 folks in your entire subfield, the payoff is not really worth it)

- human proofs are readable, and can illustrate concepts better than lean proofs. human proofs give insights into how to think about a type of problem, and this is often the most valuable part of a proof/result.

- lean proofs are often very difficult to read; while they give you a "verified" check mark, they do not necessarily improve the bounds of human understanding if that makes sense.

lol yeah we're doomed

i can kinda get how a glp-1 can be a miracle drug for weight: if we assume that simple molecular fixes to problems will eventually be found by evolution, then when we change our environment rapidly (e.g., with cheap bountiful calories) then this presents an opportunity for a miracle drug, since evolution will take some time to find the fix.

but for something like reducing disease infection, i find it a lot harder to understand why we don't create this naturally unless there is some equal-but-opposite cost that we'd incur, or if there is not actually as big of a benefit as we believe (or if this is all just colinear with the weight loss stuff).

note: i have no background in any of this and have no idea what i'm talking about

these might not be 100% complete, but i think this does a reaaalllly good job at capturing the vast majority of mathematics.

i'm sure you could come up with another breakdown, but these also have the benefit of tracking roughly with history. numbers and geometry (euclid), then eventually algebra. probability was a fundamentally new way of looking at the world. analysis comes via newton/leibniz and then dynamics tries to tackle complex systems (kinda where newton left off, e.g., 3-body problem type stuff).

also: dimension reduction is not a bad thing. this is like a decomposition: we can decompose so much of what research mathematics is doing into 6 different basis elements. that's pretty darn neat.

(edit: liebnitz -> leibniz)

agreed! it's funny, i'm returning to some of the maths i studied in undergrad with a bit more "worldly" knowledge (if you can call comp sci academia knowledge "worldly"), and i'm seeing that so so much of the stuff that was confusing was actually just trying to frame really intuitive properties. of course, the language to do so rigorously can be very dense and terse and difficult to get through, but at the end of the day, mathematicians are often trying to do some very simple things.

for example, intuitively, i and j are _basically_ the same "shape" as one another, and f and c and s and v are _basically_ the same "shape" as each other, but the two sets of shapes are definitely _not_ the same as one another...to quantify this and actually capture it in math you gotta do topology, and once you get past the point set stuff it gets real abstract real fast. but they really just wanna say "hey, my donut kinda looks like my coffee mug".

yeah, i've studied a lot of math and a lot of cs, and stats is tough. part of the problem is the terminology, and just giving a ton of complex machinery without telling you what it's actually doing. i've never learned that way, and it is very easy to feel like you're doing some sort of dark magic.

also, probability theory vs statistics is an important distinction: prob theory is a nice clean mathematical subject, while statistics is almost the philosophy of applying probability theory to the world.

i mean, the headline statistic can be misleading, but you gotta dig in and wrestle with the details. just like anything, we cannot boil down complex things to single numbers and expect any sort of meaningful signal. we gotta roll up our sleeves, look at definitions, think about what our actual questions are, how we might answer those questions through measurements and observations, and what the confounders are. i think a common issue folks have with stats is that they expect a tidy answer, and it just doesn't do that: it's more of a way to prove the world...the results still need some interpretation.

> At the time, my professor closed the final lecture with dramatic words (I'm paraphrasing slightly):

>>> And now you've learned that almost all interesting problems are undecidable and of the remaining ones, almost all are NP-hard. For the project of computer science, that puts the final nail in the coffin.

> Sheesh. Not sure if everyone got such a dire framing but that would explain.

Honestly, this is what makes computer science fun.

is it?

I think I'd put it this way: if I could flip a switch tomorrow and the AI boom was done, I probably would. The negative effects just super duper outweigh the fact that coders are more efficient. But since it exists, I'm going to use it. Hacking on my own small projects isn't using that many resources. But the benefit simply isn't worth the cost, as much as I personally love using LLMs.