bbeonx

(a) vim is super powerful (b) vim is way faster to edit, navigate, etc (c) it really doesn't matter that much

do the thing you enjoy :)

Maybe it's because I'm not working in the workforce (grad student), but I find my best workflow is to fight and argue with my agents throughout the entire process. Often times, since the agent is such a sycophant, I end up arguing with myself...I actually find this useful because it gets me to think about the other side of a problem and poke holes in it. This is not fast, but it is effective.

I mean, of course, if you make the benefit of the result itself large enough than yes, by all means; I'm sure Terry would agree: if there was some algebraic geometry proof that could be used to build a life-saving drug, then I don't think folks would have a problem with using AI to prove it. But most math isn't like this. Most math has very little immediate effect on the real world.

There is a tradeoff that is implicit in this entire discussion: if I can go out and use a result to do a thing much much better/faster/easier than I could yesterday, like a real and useful thing in the real world, then the result itself has value. The cost incurred by swarm solving that individual problem is relatively low and isolated, and the value added is clear, so great, we should do it! But if proving a result only allows us to apply it to more mathematical questions, then there isn't really value added aside from our own value we place in the results, and that value comes from our understanding. So now, swarm solving random math problems is taking away our opportunity to solve these things ourselves.

And people who don't have math backgrounds will poo poo this whole "opportunity to solve problems ourselves" stance, but it is 100% the way mathers think about this stuff. When I was a math major in undergrad I actually had a friend who told me that he didn't want to give me hints on a difficult homework problem because he wanted me to have the opportunity to solve it myself. Like, his _present_ to me was to give me an opportunity to solve a hard but rewarding problem.

It's both. Some math has applications. Some math doesn't. Many mathematicians are interested in mathematical beauty, in solving problems, and playing with puzzles.

None of the results from October 6, as far as I know, have direct real-world applications today. We can't go build a better thing, or make a faster thing, etc. I might be missing something (I'm not an expert in any of the fields). I don't think most folks would have a problem with solving a bottleneck problem that let us flux a capacitor at 2x efficiency, or whatever.

I also think this is hard for a lot of folks who are in fields that heavily apply math to come to terms with. I do not think that programming and practicing mathematics are the same: many (most?) mathematicians are closer to a composer than a programmer: all three are making things, but there is much more emphasis on elegance and cleverness in mathematics than in programming.

But again, it's not binary, and a lot of the discussion does try to take a black-or-white view of it. It's tradeoffs all the way down.

For what it's worth, I think this quote from the article sums up my position best:

"To me, someone who chooses a worthwhile problem, obtains a proof completely using AI, understands it thoroughly, and uses it to develop interesting further questions or directions has made a substantial mathematical contribution. I would give that person substantial credit even if they supplied no new ingredient in the original proof. Choosing worthwhile problems may end up mattering more than producing proofs."

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".

It seems like you might be inventing a form of non-monotonic logic. Check out answer set programming, it actually does exactly what you want of "unlearning" facts that you've learned. Not sure if it helps in your particular instance, but it's very cool stuff and IIRC there is an implementation that extends datalog. https://en.wikipedia.org/wiki/Answer_set_programming

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.

there are some things that clearly exist that are really hard to nail down with definitions; once we get into anything social, we are kinda playing with that territory. everything is so fuzzy that our normal way of defining things breaks down. so saying precisely what gender _is_ is going to be almost impossible. but there are definitely roles and traits that are highly correlated with a person's birth sex that are distinct from their birth sex. there can even be genetic reasons why those correlations emerged. but they are still distinct.

as evidence, what it _means_ to be a man, woman, etc, differs from society to society. if you ask me to quantify this precisely, i will struggle. but it's plain for all to see.

sorry, is this in response to my post? in which case, this is exactly the distinction i'm making. the entire argument is whether or not there _is_ a distinction; my point is that this guy just, a priori, decides gender doesn't exist. but there is plenty of evidence that it does. there are plenty of social traits associated with sex that differ across different cultures: pink used to be a manly color, now it's a feminine color; "be a man" doesn't literally mean "make sure your sex is male"; etc. there are traits that are heavily correlated with a person's sex that are culturally reinforced, and this is distinct from their sex.

yeah, the argument is ridiculous; like, formally, it is ridiculous. i also disagree with the sentiment and conclusions of the argument, but the actual form of the argument is garbage: "i introduce an axiom that says there is no gender and therefore the distinction between sex and gender doesn't exist".

the first post was a swipe, i'll grant you. probably shouldn't have said it. it was a knee-jerk reaction to a structurally fallacious argument that leaves no room for discussion: "i reject your stance not based on reason, evidence, or anything that you can interact with, but based on an new presupposition i've just now decided is true". though i'll admit the severity of my knee jerking was probably amplified by some of the other opinions he holds.

the second post is actually about (a) me having understanding for a position of someone i disagree with harshly, and (b) the logical structure of an argument, not the underlying topic itself. it was in reference to the content of the link that was posted.

anyway, mods can take it down, i get why the rules are there. you're also right to ask folks to keep it clean. but i stand by it; dude just seems to have a trifecta of awful traits and i'm so so so tired of super rich tech dudes ruining the world.

[flagged]

wait this is kinda brilliant tho

sigh how are so many brilliant people this stupid?

Thank. Too much word, me try read but no more tokens.

this is true, "black" has been used in racist ways, but it got rehabbed and reclaimed in the 60s and 70s.

but more to the point, it is not currently used in a racist manner by the vast majority of the US, and certainly does not carry the same connotations as "yellow", so not really comparable imo

"yellowsky" sounds racist because calling asians "yellow" is racist.

"whitesky" sounds racist because...well, i don't know if you're a big history buff but in the US white-people-only gatherings were always suuuuper racist.

agreed...i think it's fine to keep up with what the corporate world is doing, but these projects bring me real joy