evergoe's recent activity

  1. Comment on OpenAI releases findings on 377 math problems, further roiling field in ~science

    evergoe
    Link Parent
    In its most idealized form, math develops in a very organic way, where mathematicians gain a deeper understanding of the ideas introduced by the previous generation, manage to solve many of the...

    In its most idealized form, math develops in a very organic way, where mathematicians gain a deeper understanding of the ideas introduced by the previous generation, manage to solve many of the problems posed by that generation, and then introduce their own set of ideas and problems.
    Although math is generally portrayed as an objective field, mathematical definitions really are more of a creative/artistic endeavor. They might be introduced because they 'seem' like the aesthetically 'right' way to think about an idea, and gain widespread acceptance for the same reason, and even be modified over time as we become more aware of the nuances of an idea.
    AI sort of threatens to sever this thread, by destroying this organic development. It's a bit like it's offering a 'Next Episode' button, but after pressing it over and over, we're in Season 7 and not really sure what's going on.
    You're right that we can try to work backwards from the solutions, but that's easier said than done. Setting aside how deeply soulless playing janitor for an LLM would be, it's really not for lack of trying that these problems/ideas can take decades or centuries to come to fruition. They really can be subtle enough that it requires the sensibilities of the entire mathematical community to develop over time until the circumstances permit progress. It's something like historical consciousness, where it just doesn't seem possible to fast-track it, even with a later stage as an exemplar.
    Obviously the above concern is predicated on the ideas that (a) It's intellectually/spiritually worthwhile to understand math, and (b) Humans will remain necessary in some form for mathematical progress. If we let go of those ideas, then all bets are off, but at this point in time that seems reckless.

    13 votes

  2. Comment on OpenAI releases findings on 377 math problems, further roiling field in ~science

    evergoe
    Link Parent
    The mathematical problems usually also come from mathematicians, and this often happens in a recursive way. Basically, Mathematician A might be trying to solve an existing problem, and maybe they...

    The mathematical problems usually also come from mathematicians, and this often happens in a recursive way. Basically, Mathematician A might be trying to solve an existing problem, and maybe they come to the realization that the problem is just a specific example of a more general idea. Then Mathematician A tries to nail down exactly what that more general idea is, which they do by trying to come up with a satisfactory definition that encapsulates the properties of the idea in a nice way.
    Once they have a new definition of a new idea, the immediate next question is "What are the properties of this definition, and how does it relate to existing definitions?" Maybe by thinking deeply about the idea, they become convinced that the definition implies some other property, but they're not sure how to prove it. They might publish their work so far, along with some of the main conjectures/hypotheses they came up with, at which point Mathematician B picks up the torch, and the cycle repeats.

    The practical applications basically vary on a case-by-case basis, and can even change over time (number theory was totally useless until it found applications in cryptography) Some math problems are purely for the love of the game-- they're genuinely useless and serve no purpose other than to advance math.
    Other problems do have some direct application. For example, in this batch of OpenAI problems, they claimed to have shown a new lower bound on the computational complexity of complex matrix multiplication. Basically, matrices are rectangles of entries (think an Excel spreadsheet), and they can be multiplied together in a funny way that doesn't really match what the common idea of multiplication means. The important part is huge amounts of computer technologies rely on matrix multiplication, and in fact LLMs themselves do. With that in mind, it's very desirable to try to find the most computationally efficient way to multiply matrices together, and one of the OpenAI proofs claims to have shown that the most efficient way (for a specific kind of matrix) is more efficient than was previously believed.

    Editing to add on: What Asinine said is also worth noting, where if you follow the chain of problems back far enough, there's usually a question about a real-life problem at the root.

    16 votes

  3. Comment on OpenAI releases findings on 377 math problems, further roiling field in ~science

    evergoe
    (edited )
    Link
    I'm a mathematics student, so this is near to my heart and I'd like to weigh in with an insider's perspective and try to write a faux FAQ (with the caveat that I'm still early in my studies, so...
    • Exemplary

    I'm a mathematics student, so this is near to my heart and I'd like to weigh in with an insider's perspective and try to write a faux FAQ (with the caveat that I'm still early in my studies, so anyone here with more knowledge is welcome to offer corrections/disagreement.)

    How important are these problems?
    There are ~400 of them so it varies quite a bit. However, the most important ones are, basically, very important. A lot have been outstanding for decades, and are pretty central in their various subfields. The Millennium problems have developed a bit of a mythology around them, so the recent Navier-Stokes solution got a lot of attention, but I (subjectively) think this batch of problems is probably more of an achievement.

    Are the solutions correct?
    Again because of how many there are, it's not possible to say definitively yet. I will say that my personal opinion is that probably most of them are correct. For people who aren't in the know, a big project in math/CS has been formal proof verification. Simply put, this is a way to write math proofs in a way that computers can check their correctness. Because of the propensity of LLMs to spew out giant chunks devoid of meaning, a focus has been specifically on training LLMs to write proofs in Lean (a programming language for computer-checkable proofs), to reduce the amount of slop necessary to wade through. The complication here is that these Lean proofs themselves need to be verified, i.e., a 'proof' might assert True while actually proving something subtly different from the natural-language question. So to reiterate, although the existence of a Lean proof is a strong sign for correctness, it still needs oversight. But OpenAI does employ mathematicians, and it would be very embarrassing if more than a handful of solutions were flawed, so I think when the dust settles, we'll find most are correct.

    Did they steal the solutions from the work of mathematicians in their training data?
    Probably not. I know this idea got a lot of traction due to the circumstances around the Navier-Stokes solution, and I think that particular case is more up-in-the-air. Here, the quantity and complexity of the problems make it much less plausible. Moreover, mathematics as a discipline checks most/all of the boxes for a domain which an LLM can excel in, so I think we've unfortunately just reached that point.

    You said 'unfortunately', but isn't this a good thing? Isn't this a rare example of AI unambiguously helping further human knowledge?
    That depends on who you ask. If you ask a mathematician, the answer will rather be unambiguously 'no'. Or, maybe that's being a bit dramatic and it's more complicated? My personal take, which I glean is shared by most mathematicians, is along these lines:

    • OpenAI has no interest in doing right by the mathematical community, and is using this mainly as a publicity stunt.
    • Now that the solutions exist, it's good they're public, but this isn't how most mathematicians wanted the solutions to be found.
    • It's extremely worrying that the means to advance an entire domain of knowledge are proprietary and not publicly available.
    • In a worst case scenario, this could kill mathematics as a discipline.

    And I think it's especially easy to write off mathematician's concerns here along the lines of "Yes, this is really tragic for mathematicians, but for progress/knowledge in general, this seems like a net good". For some perspective, (this may seem like a truism) the way mathematicians think about math is very different from the way other people think about math. There was a very good post shared here some months ago titled "The Fall of the Theorem Economy" which I recommend reading, the general thesis of which goes like this: In the eyes of the public, mathematicians solve mathematical problems, and this is what determines their worth as a mathematician. In the eyes of mathematicians, mathematicians study/invent/communicate knowledge of mathematical objects, and among the surest ways to understand these objects is through the posing/answering of problems about them, where these problems also serve as a practical benchmark for assessing mathematical skill.
    Just like every other knowledge field, we're confronting the situation where 'domain knowledge' is no longer all that necessary for the production of competent domain work. It's selfish of me to say, but I really think this is especially terrible for the field of mathematics. The reason is, most fields have something to latch onto, but in mathematics, the work is the field in many ways. Mathematical questions are sufficiently abstract that they are meaningful basically only insofar as you understand the content of the question. The threat posed by AI of removing the need for understanding is, in the case of mathematics, the threat of removing the ability to engage with mathematics at all. It is a bit like automating philosophy, and hence why mathematicians are losing their shit and not entirely able to articulate why to a general audience.

    57 votes

  4. Comment on Why do we find Tildes (and Lobsters) more interesting than the alternatives? in ~tech

    evergoe
    Link
    I would frame the behavioral differences between social platforms mainly as a question of what sort of incentives each platform is centered on. These used to be more diverse. Or rather, the...

    I would frame the behavioral differences between social platforms mainly as a question of what sort of incentives each platform is centered on. These used to be more diverse. Or rather, the incentive used to be more simple and more universal: to socialize. It's been a long time coming, but especially in the last few years we've seen a pretty severe shift across almost every major social platform to reorient themselves entirely around the incentive system of 'engagement'.

    I think that without maybe putting it in so many words, the main thing many of us seek from social platforms is a dialogue: We want to communicate our thoughts and actions to others, and we want others to reciprocate. This is a long-winded way of describing the basic concept of human interaction in general, but my point is to contrast this with the core invariant of the typical social platform, and how alienating this invariant basically is.

    There is a fun equivocation of words lurking behind 'engagement', because the way in which it is used in the context of something like social media is actually very different from the common meaning of the word. These platforms do not favor engagement in the typical sense of attentive, purposeful interaction. For them, engagement is signal, a piece of information about a consumer which they can then commodify. This is their business model, and I'm convinced the reason for the sharp degradation of quality across most of the social internet is due to these businesses realizing that this perverse kind of engagement really is ultimately just a numbers game.

    What I mean is that if you think about it, once a user has engaged with a piece of content in any way at all, even just clicking on the thread or leaving a reaction, the platform has already obtained the valuable part of the signal. They've gotten a piece of information that says "This user saw this post and it caught their attention/made them feel happy/angry/sad". Maybe the user spends another 10 minutes going through the thread on a post, but this is a diminishing return for the platform. It's simply not in their interest to incentivize a deeper engagement. The most valuable thing for them is for you to continue moving through your feed, producing as many signals as possible, and so maybe without realizing it right away, you'll find that most of the content placed in front of you is actually devoid of content.

    Although the phrase 'attention economy' is in vogue, these platforms aren't really trying to hold your attention at all-- it suffices just to capture it for a second, and then to keep you scrolling. This is why it would be possible for me to have scrolled through a hundred posts on Reddit in the time it's taken me to write this comment, and I think it's the reason we're on tildes instead of Reddit: Because we know that we wouldn't remember a single thing about any of those posts, but Reddit would remember a hundred new datapoints about you.

    Conversely, on tildes, this thread did engage me, in the actual meaning of the word, and I thought about the question enough to write this blog-post-like comment. Hopefully someone thinks a bit about this comment too.

    9 votes

  5. Comment on What are your favourite fragrances, and why? in ~talk

    evergoe
    Link
    Lalique Encre Noire. Smells like an inkwell or maybe moss deep in a forest. Love it for rainy days. Dior Fahrenheit. Smells like, uh, gasoline and cucumber? I promise it's really good. Tom Ford...
    • Lalique Encre Noire. Smells like an inkwell or maybe moss deep in a forest. Love it for rainy days.
    • Dior Fahrenheit. Smells like, uh, gasoline and cucumber? I promise it's really good.
    • Tom Ford Noir Extreme. Sort of at a loss for how to describe it. Smells sweet but in a really strange ephemeral way. My goat
    5 votes

  6. Comment on The machines are fine. I'm worried about us. in ~science

    evergoe
    Link
    In a bizarre and disturbing twist, it is convincingly argued by https://boxobark.ing/3mj42airv3s2o that this entire blog post may itself be written by AI. Given that I thought I could pretty...

    In a bizarre and disturbing twist, it is convincingly argued by https://boxobark.ing/3mj42airv3s2o that this entire blog post may itself be written by AI. Given that I thought I could pretty reliably detect AI writing, and that I thought the blog post in question was generally cogent and interesting, I'm not really sure how to react. At the very least, it would be remiss of me not to include this additional context for any readers later on in this increasingly macabre world.

    11 votes

  7. Comment on The machines are fine. I'm worried about us. in ~science

    evergoe
    Link Parent
    That's been on my mind a lot too. I'm pursuing study in pure math, which as a field has always prided itself on being uniquely accessible in the sense that all you need to do math research is pen...

    That's been on my mind a lot too. I'm pursuing study in pure math, which as a field has always prided itself on being uniquely accessible in the sense that all you need to do math research is pen and paper. It's seeming like lately you also may need a GPT Pro subscription...

    5 votes

  9. Comment on A Roman scroll that should be ash has just been read without ever being opened in ~humanities.history

    evergoe
    Link
    This is awesome! I was just thinking about this recently and wondering if they had made any progress over the past year. I'm a big fan of classical antiquity, and it's fun to imagine what could be...

    This is awesome! I was just thinking about this recently and wondering if they had made any progress over the past year.
    I'm a big fan of classical antiquity, and it's fun to imagine what could be in that collection waiting to be deciphered. My personal wishlist would be some of Aristotle's dialogues, more of Sappho's poetry, and Ptolemy's history of Alexander.

    12 votes

  10. Comment on What self-help / personal development books did you find valuable? in ~books

    evergoe
    Link
    In general I'm a little averse to the concept of a self-help book, but I have enjoyed a few books that I would describe as toeing the line between self-help and something else: How To Solve It by...

    In general I'm a little averse to the concept of a self-help book, but I have enjoyed a few books that I would describe as toeing the line between self-help and something else:

    • How To Solve It by George Polya. This is technically a book on how to solve problems in mathematics, but it really extends beyond that, and is a good primer on reasoning about problem-solving generally. There are lots of valuable insights and heuristics, and it's short enough that it's worth reading for most everyone.

    • How To Read A Book by Mortimer J. Adler & Charles Van Doren. This is just what it sounds like. It's a manual on how to approach reading complex texts and books in general, and it has a great Recommended Reading section at the end where the authors list off what is essentially a 'canon' of literature. IMO its problems are (a) since it dates from the mid-20th century, there is a predictable lack of diversity/variation among the recommendations, and (b) the book is probably a lot longer than it needs to be. Ironically, though, it has a section on judging the merits of when to skim a text versus when to give it full attention, so perhaps this affords an opportunity to apply those techniques immediately.

    • ABC of Reading by Ezra Pound. Obviously Ezra Pound is one of the great 20th century poets. This book has a flavor more or less akin to lecture notes for a course on literature. It's really delightful to essentially get instruction on aesthetic criticism directly from such a talented artist. If you read mainly contemporary works, this could be a great way to start developing an appreciation for classic literature and poetry.

    • The Craft of Research by... Booth et al. This is sort of a primer on conducting academic research. I don't really have much to say about it other than it's worthwhile if you expect to do research at some point. Has some good tips and may help spur you to think about the process of research on a more meta level.

    1 vote

  11. Comment on What internet discussion sites remain? in ~tech

    evergoe
    Link Parent
    I think Discord is still good in some respects. There are definitely still communities worth interacting with on there. One big reason I left is I'm just not a fan of the messaging format;...

    I think Discord is still good in some respects. There are definitely still communities worth interacting with on there. One big reason I left is I'm just not a fan of the messaging format; conversations get lost so easily that it feels like a very ephemeral medium. Small servers often have a slightly exclusive atmosphere, and in larger servers there's too much going on at once. The other reason is seeing the writing on the wall as far as the future goes for the platform; I think pursuant to the IPO it will be a long downward trend in terms of quality.

    6 votes

  12. Comment on What internet discussion sites remain? in ~tech

    evergoe
    Link Parent
    Funnily that's probably a pretty great recommendation after all. I recall finding my way onto the homepage of a private tracker a few years ago, and being intimidated and vaguely impressed by the...

    Funnily that's probably a pretty great recommendation after all. I recall finding my way onto the homepage of a private tracker a few years ago, and being intimidated and vaguely impressed by the fact that to gain membership, you apparently needed to pass some kind of quiz on topics like encoding standards administered over IRC.
    I didn't end up going through the trouble at the time, but in the context of this thread that seems like a reliable way to select for genuinely interested people.

    2 votes

  13. What internet discussion sites remain?

    ~tech Ask
    I'm using the phrase 'internet discussion site' pretty informally, so I hope my meaning will become clearer as you continue reading. I got rid of Snapchat around 4 years ago now. At some point in...

    I'm using the phrase 'internet discussion site' pretty informally, so I hope my meaning will become clearer as you continue reading.

    I got rid of Snapchat around 4 years ago now. At some point in 2023 I noticed a sharp downtick in discussion quality on Twitter, and got rid of it as well. About two years ago, frustrated with the lack of human interaction and the vying for attention, I deleted Instagram. Near the end of 2025, I stopped using Discord. The final nail in the coffin has now arrived, since I'm unfortunately coming to the conclusion that Reddit is no longer worth visiting, leaving me almost entirely cordoned off from internet communication at a time when more humans are using it than ever before.
    I won't bother repeating my personal reasons for this exodus since I feel confident that most people on this website have feelings on the matter that at least approximate my own.
    Realistically this is a sign that it's time to prioritize interaction in the real world, and that's certainly a worthwhile thing to pursue. But bluntly society has restructured around the internet in a pretty substantial way, and I don't think it's an unreasonable ask to find various forms of forums on which more meaningful discussions can take place.
    Here is my personal survey of the current landscape:

    • tildes.net: Basically good. I really enjoy this website and I think in a lot of ways the 'bar/pub/cafe' model for a forum, where you can peer through the window but require permission to gain admission, is the only viable model for future online discussion places as the internet becomes ever more saturated with bots and bad actors.
    • lobste.rs: Also basically good, for the same reasons as tildes. In some aspects, limited by the fact that it has a particular focus. In other ways, that's a really good thing. Maybe in a perfect world there would be a lobste.rs equivalent for every hobby, and we would return to an early internet forum world.
    • Hacker News: Also basically good but perhaps a bit less so than the above two. I think most of the things posted on there are interesting, but a lot of the discussion has lately felt less insightful than it used to. I think a different tildes post noted this as well, but it's very caught up in the AI news cycle, often to an unfortunate degree.
    • Rateyourmusic: The core site is enjoyable, and the forums are usually fun to check in on every now and then. Certainly a worthwhile place to visit if you enjoy music.
    • Stackexchange networks: This is cheating since this is obviously many sites. I'm a mathematics student and I've found MSE and MathOverflow to be really wonderful places to learn and converse, albeit with some very arcane and strict rules for posting. The philosophy SE seems also generally of a high quality, and there are many other SE sites that I occasionally stumble into and am pleasantly surprised by. Unfortunately I expect its time is finite, since the UX has slowly but surely been degrading and the site traffic dropping.
    • Fediverse networks: These sites clearly have potential, but for whatever reason it's still just not there. I drop into lemmy and Mastodon occasionally, but the posts are rarely of high quality. In many ways they just feel like "Reddit/Twitter but with a different name".

    Surely these can't be all, right? It's a little soul-crushing to think how many people are online at any given time and how hard it is to find a place not drowning in noise. Maybe this is just my lament.

    98 votes

  14. Comment on Ageless Linux emerges to protest OS-level age verification laws in ~tech

    evergoe
    Link Parent
    So, I have the opposite reaction in reading that paragraph you quoted; I think that it is almost certainly written by a human, who probably very carefully chose their words, and has to do with the...

    So, I have the opposite reaction in reading that paragraph you quoted; I think that it is almost certainly written by a human, who probably very carefully chose their words, and has to do with the purpose of the Ageless Linux project in the first place. Namely, I get the impression their endgoal is to establish a legal precedent against the concept of age-verified OSes.
    I have no idea what the particulars of the bill that prompted this project are, but I'm going to go out on a limb and say the bill makes some kind of reference to 'covered application stores', and so they might be trying to establish some kind of blanket protection against mandated age verification for "publicly available internet websites distributing and facilitating the download of applications to users of a general purpose computing device".
    I do, however, agree snippets of the project seem AI-generated. I would point out then that in this case it straight-up does not matter; this is not intended as an OS for actual use, it's intended as Supreme Court decision bait. If AI helps them get it up and running faster, then... whatever?

    10 votes