Jean-Pierre Serre's 100th birthday editionprevious:>>16991839
>>17054862I tried to read his book Linear Representations of Finite Groups but it was very difficult because of all the errors
>>17054917The dude is a better mathematician than textbook writer
>NOOOOOOO YOU WERE ONLY SUPPOSED TO GROW SMARTER AND THEN PLATEAU AT A LEVEL JUST BELOW ME.
There was a panel about AI in math>Michael Harris>Peter Scholze>Jacob Tsimerman>Geordie WilliamsonModerated by some DeepMind guyhttps://www.youtube.com/watch?v=H7_d_sgui6o
>>17055513lol, at 10 minutes Scholze says he has never typed anything into an LLM and doesn't use a smartphont. at 11 minutes Michael Harris says LLMs are theft and should be illegal.
>>17055556I mean he's not completely wrong about LLMs. All the top AI companies have ignored every intellectual property and copyright law in existence and then left it to the lawyers to deal with the consequences, if any.
>>17055513This was good. It's charming in a way how aloof Scholze is. Tsimerman is the most clear minded of the group.
>>17055556>Scholze says he has never typed anything into an LLM he's a liar
>>17054862I'd ask this in a physics gen if we had one but alas this board is too full of opinionated schizos to sustain one so I apologize for sloppiness.Consider L^2 or a sufficiently well behaved subspace thereof. The Fourier transform can be expressed as a linear, unitary operator in this space:[eqn]\psi(x) = \hat{\mathcal{F}} \phi(x) = \int_{-\infty}^{\infty} \frac{\exp(-ikx)}{\sqrt{2\pi}}\phi(k) dk[/eqn][math]\hat{\mathcal{F}}^4 = 1 [/math] makes its powers isomorphic to the cyclic group [math]C_4[/math], and it rotates the operators x and p=-id/dx as a 90° rotation. Now the question: obviously (taking the rotation property of (x,p) as the defining feature) a group of operators isomorphic to SO(2) can be identified. What is its infinitesimal generator? Another way of phrasing the same question is, what is the phase space angular momentum operator A such that [math]\hat{\mathcal{F}} = e^{-i\frac{\pi}{2}\hat{A}}[/math]? A sloppy guess would be x id/dp - p id/dx = x^2 + d/dx^2 which would be the quantum HO for omega = hbar = m = 1 (which is a Hermitian operator that commutes with the fourier transform) but I didn't do it properly yet.
>>17055761there's sign errors in there I didn't fix but you get the general idea.
>>17055761>>17055762Nailed it, see Wikipedia, eigenfunctions of F
should I apply to university to learn maths or can I self-learn with chatbots?
>>17056462university, not even a question. You should be around people with the same basic interests and ideally a vast breath of different experiences in your most formative years. Even if a chatbot could replace curriculum (lmfao) it cannot help you grow as a person or intellectually challenge you.
>>17056462the fact that a chatbot will occasionally sperg out and get something completely incorrect with utmost confidence should be enough to tell you it's not a good idea to study material you don't know under one
>>17056462You need to build some fluency yourself or you won't be able to tell when AI is feeding you bullshit as other anons said. I do think it can be an extremely powerful tool for learning though as a supplement to traditional education.
>>17054862Ed Witten's father is 105, apparently.
>>17057041>only 5 years younger than general relativity>last published August 2025fucking hell
This guy was doing ads for OpenAI like 4 months agohttps://x.com/haider1/status/2101368221651869962
In physics one important measure of understanding is the richness of connections you can draw and the number of lenses you can see a problem through. Mathematics always seemed similar in that regard but one thing always trips me up. You guys seem to be bored when something has a lot of properties. Your eyes seem to glaze over when a space is Hilbert, a manifold is Riemannian, etc. I get that it's an old hat and chances are everything worth saying has been said about them. But the same is true for things like the harmonic oscillator or other toy problems and physicists seem to enjoy hearing new or interesting interpretations of these sorts of things. What am I missing?
>>17058496Interesting question. I think you're comparing apples to oranges. Mathematical structures like Hilbert spaces, Riemannian manifolds, etc. were developed as a way of formalizing certain widely recurring mathematical motifs: a vector space with a notion of orthogonality, a locally Euclidean space with invariant local angles/distances, etc. It's not a surprise when they appear all over the place because that's pretty much what they were designed to do. A more accurate physical analogy I think would be more general concepts like "phase space" or "entropy" rather than specific physical theories (however simple). Or conversely, a more accurate mathematical analog to something like the harmonic oscillator might be, say, I don't know, the Gaussian.
>>17058652Very interesting perspective! The Gaussian is a peculiar case in general, stupid amount of properties (central limit theorem, fourier transform, ...). If memory serves the N-dimensional analogue is the only correlation-free isotropic random distribution ([math] \rho(\mathbf{x}) = \prod_j \rho(x_j) = \rho(|\mathbf{x}|) [/math]), among other things. You're probably right I am not making as much sense as I would like to, I'm a complete outsider to mathematics as a field. At its core I would love to better understand the kind of guiding principles and mental images mathematicians draw from, I think.
>>17057722professor ching chong says "there is no reason to be this fast"lmaoprofesor bing bong there pretending not to understand power dynamics of economies at all.>gwailo... we must srow down AI
What are some hidden math? Also how do you get into philosophy of math?
Fuck my life
MATHIE ARE YOU OKAY
>Thales Pythagoras Eudoxus Plato Aristotle Euclid Archimedes Apollonius Hipparchus Ptolemy Al-Battani Al-Biruni al-Tusi Descartes Fermat Newton/Leibniz Euler Gauss Lobachevsky/Bolyai Riemann Hilbert.This progressive learning of math and logic makes sense?
>>17059313yep...
>>17059313I like going to r/math because they have one AI containment thread
>>17055556yeah just like how the mnist data set should be illegalall these workers who contributed to writing digits by handHumanity should be illegal too seeing as how we stolen from billions of years of trial and error of other organisms
>>17061100Is it *universally* applicable? Suppose you manage to do this (people have for more or less achieved exactly that for artworks)>take a copyrighted work without permission>train slop with it>prompt slop to produce copyrighted work>take output and use it without creditIs it in the spirit of the law? The only logical consequence is to abolish copyright if so.
>>17056462If you only want to learn mathematics (no intention to make a carrier out of it) then buy textbooks and work through them. Only use AI after you've done the exercises and want a feedback on it.
Stupid question perhaps but: doesn't it already require the axiom of choice to pick a representative from an infinite quotient set? I would suppose you don't always have to (see for example the standard construction of the rational numbers from Z^2, since you can just pick the element with the smallest nonnegative denominator) but I wouldn't be able to give a general answer.
>>17062577a representative for each element in an infinite quotient set I mean.
>>17062577Depends, what do you need to pick a representative for? If you just want to construct the quotient, as long as you are able to describe the "classes", each object of the resulting quotient set can be taken to be the entire "class" iirc, no?
>>17062579I am not a logician myself, but the answer is yes. The statement "Every quotient map [math]X \to X/\sim[/math] has a section" is indeed equivalent to the axiom of choice.However, sometimes the equivalence relation has a "canonical" representative which does not need the choice principle. Very often this is well-orderedness. Your example of [math] \mathbb{Z}^2 [/math] has a clear canonical one namely the reduced fraction.
>>17055556lmfao and those people are supposed to be smart?
>>17055761ask chatgpt
>>17055556>Scholze says he has never typed anything into an LLM and doesn't use a smartphontbased, I envy him
I dont understand what a vector bundle is
>>17063997Locally every point of the bundle looks like the space **times** a vector space. Then there are some other topological formal conditions.The easiest way is to just look at a single point (even though the formal definition uses neigborhourhoods), then a vector bundle assigns to each point on the topological space a vector space. If you are familiar with manifolds you already know the most important example, namely the tangent space. A vector bundle is simply a ""generalization"" of this idea, where instead of the tangent space we attach some other vector space to the base space at each point.
>have to try my half-baked conjectures in le meme counterexample generator before I put them in a paper just to make sure I don't get "scooped" by some biostatisticianI can't wait until normies stop pretending to care about math again.
>>17063974based
>>17054862
I'm beginning to I won't know anything substantial about Topology from this undergraduate topology course.
Any recs to quickly learn the basic concepts of logic? First order of predicate logic mostly but my professor is already on second order and I didn't learn shit in bachelor so I'm behind. Any lectures, textbooks, etc. would be massively appreciated.
>>17066865What have they taught thus far?
>>17066865Intro topology is designed for analysists just like intro calculus is designed for engineers. If you were expecting to learn about coffee cups and donuts then you'll probably have to wait for the next level course.
that thing you're working on?it's already solved
>>17068390Based. I never get why people feel bad that AI solved it instead of people. If anything, it's a sign that AI can do maths, thus accelerate scientific progress and make our lives better (or worse, but it's worth the risk). All the best to OpenAI.
>>17068370Man I wish, I would have loved to learn about uniform structures in undergrad. On a more serious note, intro topology is just intro topology the only "analysis" part is the connection with metric convergence. Manifolds for example are as important in topology as in analysis.Of course you can tailor it more towards analysis but that just depends on the lecturer.For example, I was taught the subspace topology using commutative diagrams, because my professor was a higher cohomology theory tard.
>>17068370>>17068710These days, would be a damn miracle to find an undergrad topology course not oriented towards analysis-prep.
>>17055435All this and for what?
It's overhttps://raw.githubusercontent.com/openai/math/main/overview.pdf
>>17055556>Michael Harris says LLMs are theftbased
>>17068828Yes, the theft is based lol
I left grad school 9 years ago, why haven't you given up on maths and pursued something that will actually bring you success and money instead? read the room, you are no longer required
>Quasi-Riemann hypothesis:Excludes zeta and Dirichlet L-function zeros beyond 7/8. Major progress, although it does not prove full RH.>Hodge conjecture for CM abelian varieties:A major special case, with claimed consequences including Tate for abelian varieties over finite fields.>Hilbert’s tenth problem over \mathbb Q:Settles whether an algorithm can decide if arbitrary polynomial equations have rational solutions.>Unique Games Conjecture:Resolves a central question about how accurately hard optimization problems can be approximated.>Nonsofic groups and Kaplansky counterexamples:Produces groups contradicting several foundational expectations in algebra.>Free group factor isomorphism problem:Claims these fundamental operator algebras are all isomorphic.>Both Mahler conjectures:Settles central convex-geometry questions in every dimension.>Global smoothness of relativistic Vlasov–Maxwell Resolves a major mathematical problem governing plasma dynamics.ummmm math bros?
>AI spergs elected to flood a slow general, begging for attention because all their frog threads have a dozen posts or less>p-pls entertain me /sci/ I am so lonelyI don't think I will. Post math.
can anyone with access reup this shit https://link.springer.com/article/10.1134/S0081543824020111
Not sure where else to ask this, as I'm afraid that bringing it up candidly to my professors may (possibly subconsciously) cause them to write me a less-emphatic recommendation. Lately it seems like all published math will be divided between pre-2026 and post-2026, with post-2026 work essentially having an asterisk by the authors' names to indicate that they should be given significantly less respect/prestige. I'm a math major who's currently applying to graduate school, and am coming to grips with the fact that this would really bother me. Everyone has their own motivations, but personally I am mostly driven by competitiveness and the desire to do difficult things that impress peers (including myself). This, when typed out, certainly comes off as the "wrong reason" to do something, but from what I understand they are similar to the reasons that many mathematicians were drawn to the field.Am I overreacting? Should I bail while I can? Just do a phd since that's what I'm set up for, and spend that time planning my pivot?I know those are impossible questions for a stranger to answer, so I guess I'm mostly just looking to see if anyone feels similarly (or would granted the same facts, but disagrees with my premise).
>>17069311Just bail now, the glory of having citation metrics and stuff is all over, which may be a good thing for maths but not for your motivation. No idea where you should go though, maybe become a tech bro.
>>17069311You forget a crucial point about academia: people talk. I know of professors who have a radiant H-index by the standards of their community who, outside of the very well known clique of people citing each other in a circle, are not as highly regarded as their numbers would suggest.
>>17069311You should be ashamed that these are your motivations.
>>17069320NTA but why exactly? It's natural for a human to feel that way. Do you think scientists and mathematicians should somehow be superhuman? Why do you expect anyone to meet such a standard? Do you simply hate others?
How is Arnold's ODE for a first into to DE. I am a math grad but I have never studied applied math or physics except for CS.
>>17069352Well I certainly hate you. How about you tell me where you are right now and we can "compete" for who's going to be the least raped. I think I already know the answer.
Some guys did a panel after the 400 openai proofs droppedhttps://www.youtube.com/watch?v=voDtZqijetw
>>17069511tl;dr? or tl:dl?
>Math before>You are poor but do it for the love of the game>Math now>You are poor but AI sucks the fun out of everything I’m tired boss. Should have done quant or shit years ago.
>>17069539Literally how does AI suck the fun out of anything?
>>17069565Some of us actually enjoy solving problems ourselves. It's a triple digit IQ thing, you wouldn't get it.
>>17069572And how exactly does AI stop you from doing that?
>>17069587Becuase a big part of the appeal is solving something no one else has done before.Even if it's a trivial problem that's been over looked.Now you can just say Computer solve for X.
>>17069311You've picked about the worst possible place to ask a question like this, the schizoid AI doomerism you see here really is not representative of people actually in the field.>Lately it seems like all published math will be divided between pre-2026 and post-2026, with post-2026 work essentially having an asterisk by the authors' names to indicate that they should be given significantly less respect/prestige.You were right to not bring this up to your letter-writers, because it's completely retarded, with all due respect. You're projecting a degree of your own prestige-hunting onto the field that it simply doesn't have.>Everyone has their own motivations, but personally I am mostly driven by competitiveness and the desire to do difficult things that impress peers (including myself).At least you're honest with it, I suppose. Even before AI there's no glory in math. Other mathematicians aren't going to bask in your radiance because you published in Annals once. If your ultimate goal is to just be a BMOC then I'd suggest becoming the resident mathfag at some tech startup or something.
>>17069593 You could always work on something no one has ever solved or will ever care about. But you're a narcissist, so you'd rather solve something that gets you status and recognition than actually engage with a problem out of curiosity or for the sake of science, technology and philosophy.
>>17069646>You could always work on something no one has ever solved or will ever care aboutliterally the vast bulk of "vibemathed" lmfao
>OpenAI dumps a bunch of papers, with about 1 out of every 7 including a lean proof>Lean proof is a mechanical translation of natural language proof the model arrived atSo, how does anyone verify that the translation is accurate, and that the assumptions the proof was derived from are the correct ones for framing the problem? I'm not a mathematician, but even as a code monkey I find myself needing to fix AI hallucinations at work.
>>17069698In principle, the whole idea with Lean is that you only need to check that the initial statement is correct, which is orders of magnitude easier than constructing a proof or even checking the proof yourself, formalizing each step with a library of existing theorems is what it is designed to do. It is not remotely foolproof and bugs have been found that allow you to "prove" any false statement. People say they've been fixed but of course an LLM is exactly the software you would dream up to find and exploit new ones when incentivized to produce a Lean cert.
Saw the OpenAI announcement today. I'm not smart enough to know if this is a big deal or not. It seems like a big deal. Can someone fill me in?
>>17069717It's a big deal but no one will know exactly how big for months while experts check their claims. We also have no reason to believe their claims about how much compute it took or how many problems they failed to solve, which has huge implications for how impressive the results are.
>>17069511>mfw being filmed without consent
>>17069515>math isn't about results, its about math frameworks reee
>>17069515>this is fantastic! congrats to openai
>>17069316>>17069318>>17069320>>17069599This is literally just a copied post from /r/math. What happened to the quality of this general. Go to proofsandprompts if youre this fucking retarded.
>>17070020> What happened to the quality of this general. People foolishly assume good faith posts while the board is being raided.
>>17055556>Michael Harris says LLMs are theft and should be illegal.how is he wrong? at least in how LLMs are being used now and not some theoretical fantasy world where these companies actually respected copyrights, they are theft
>>17070072nta but you're fucking retarded. Training is not plagiarism and this has been found to be the case in even the very first frivolous lawsuits from years ago. It's only in some smaller cases in European countries that rulings against AI corporations occurred, and even in those it's exceptions like song lyrics where even memorization could be considered reproduction.Calling it plagiarism let alone "theft" as if legal fact is braindead. Plagiarism concerns misrepresenting another person's work or ideas as one's own. The AI cases concern statutory rights of reproduction, distribution, and derivative use; you're not seeing those models claiming to have proved unramified GLC, it's just all-around fucking retarded and legally illiterate
>>17069572It's a double-digit IQ thing to doomerpost about AI on 4chan instead of doing math.
>>17070100Yeah, I don't really care whatever extremely stupid precedent they set says. I don't think many would argue Dodge v. Ford was a good ruling, even though it is the basis of corporate America. In hindsight it fucking sucks and we all know it. Enjoy your world where no one wants to write books anymore because they can just be trained on or fed into a prompt and reworded to the point they can be considered transformative and then resold.
>>17069717Yeah it's absolutely a big deal, nobody except schizo undergrads on 4chan are denying this. What is legitimately a problem is that the repo just contains the results and very terse proof papers, and none of the research artifacts the agents created. And just from my personal experience with GPT ever since getting access to a free Pro subscription through my institution, it really does feel very obtuse at times. Like thinking logs aren't showing up (probably to prevent distillation) and some replies read like what you'd see in the Encyclopedia of Mathematical Sciences. Just really terse and difficult to follow; you can kind of prompt yourself to better explanations but more human-readable output generally seems to be an issue right now. They're undeniably capable though.
>>17070140Well then just admit to being a lowly shitposting activist and don't obscure it behind faux legal reasoning to pretend your immature seethe has any valid basis. It's also not just about one precedent or one legal system, the training argument holds up in most courts around the world for a good reason. >fed into a prompt and reworded to the point they can be considered transformative and then resoldYou know that there are thousands of trash, derivative textbooks out there, hell with the dawn of the internet it was common practice of textbook authors to copy sections from Wikipedia and edit the Wiki article before publishing of the book. Spend any time at university and you'll go through several trash courses where the prof is shilling his shitty botched-together textbook.If anything, chatlogs with these AI services are subpoenable material. AI doesn't create a copyright loophole. You just do not understand what training means and what copyright infringement is. You don't have copyright on a specific explanation or a proof. People will create slop textbooks at a greater scale thanks to AI, so what? Just don't read it. Stop being such an alarmist depressed bitch lmfao
>>17070183>You know that there are thousands of trash, derivative textbooks out thereCool. Scams exist therefore ...let's make it super trivial for scammers to make more? What a compelling argument. I've yet to see a single good use out of this technology that wasn't either some throw away novelty, or automating away deep intellectual pursuits or just a tool for straight up fraud like indian scam ads and impersonations. But it's all okay because 60 year old boomers who can't navigate a smartphone said so?AI creates all kinds of chaos and violates trust and base core assumptions we have held for decades. Everyone who made software since nearly its inception operated under the assumption that a compiled binary was a safe way to protect their source code because the amount of work required to reverse engineer it would be many years worth of tedious labor. That assumption no longer holds and has extreme ramifications. Carefully constructed legal agreements over decades between the corporate world and FOSS developers are being violated in very serious ways. For example, a programmer who pours years of work into his software and licenses it, even with a cuck license, usually expects attribution as per the license. The attribution being at least part of the reason they are willing to be so permissive with it. But the AI slopper can hit the copy button, shit out a rust rewrite of the same fucking program in an afternoon and pretend they made it, bypassing attribution entirely while hiding behind the plausible deniability of the soup of the dataset.Anyone who thinks being able to build training data on works they do not own is either complicit in the fraud or a retard that has not even thought long about any of the consequences.
>>17068454but can the AI prove the result?
>>17070210Let me name a few more.Everyone who is losing their job to AI is having an existential crisis. No one stands to gain anything at all except the ultrawealthy. It completely undoes the benefits of the industrial revolution by devaluing the ingenuity of man. Many are losing desire to do the things they once loved. Mathematicians look like they're about to start jumping out of buildings. They dedicated their entire lives to a pursuit of obscure and arcane knowledge, regardless of whether they did it for prestige or whatever, they deliberately chose the harder path when they could have gone into finance and made fuckloads, which speaks to how devastating this is for them and their purpose.FOSS developers are closing themselves off from the world to combat the mountains of AI generated pull requests. It is killing the last way juniors were getting trained; through the mentorship of these developers and the communal pursuit of building open source software. FOSS itself is on its deathbed. The open internet philosophy following after universities (its birthplace) is on its deathbed.Oh, and do you like competitive video games? Well, you're not going to for long. Cheaters will now be able to reverse engineer anti-cheats and figure out all of the ways cheats are detected from the perspective of the client, meaning the only way anti-cheats will be able to operate will be from the server side looking at the data the client is sending. This used to always be a mixed approach but a lot more power is now going to shift in favor of the cheater.Developers are not going to tolerate their sourcecode being decompiled so they're going to shift towards cloud gaming.There are just nearly unlimited ways this fucks up literally everything if you just sit down and think. How exactly does this help the world become a better place? Ignoring the grandiose claims about curing cancer with puppy dogs and rainbows, everything is just getting worse around us.
No of course I don't like "competitive" video games fuck off
>>17070224>pick the weakest claim of the group and discard it outright without even trying to refute it while ignoring every other argumentI forget which fallacy this is, care to remind me?
>>17070227I don't care about Reddit nonsense like logical fallacies I just hate competition go do one.
Listen I'm sorry, I actually agree with the thrust of your argument and shouldn't have said that. I've been having 30 years of bad days in a row and decided to take it out on an innocent person just because they used a word I dislike.
>>17059588Missing Tarski.
Some people may be retarded some of tbe time, but all peoplevwon't be retarded all the time. We're entering a new era, but it will be fine.
This might be a longshot, but is there a reason why there is not much discussion (online) around the Baum-Connes conjecture disproof? I am not in C^* algebras but a related field and I thought it was a pretty important conjecture.
>>17070262A new era of machine assisted retardation.
Three, six nine.Twelve, fifteen, eighteen.Twenty-one, twenty-four, twenty-seven.Thirty.
>>17070321It just hasn't been a very hot field for a while. There were some poeple working on it in my department, but they were usually looked at us dying breed.
>>17054917Math is for midwits who specialize in only one field.
>>17055513AI > Maths
Maths is the most useless thing there is.
If you haven't been cited by an AGI, you're basically a non-mathematician.https://citedbyagi.com/
>>17070862It's funny because it's mostly true. Math is both the most important thing for any civilization to progress beyond sticks and stones and it's also one of the least important things currently because there's more maths than ever in history of mankind yet very little genuine, major progress, if we exclude AI that is, humanity's only hope.
I wonder what all the tourists will do when the hype ends and they need to find a new personality
I wonder what all the buckbroken fake mathtards will do when AI conquers the galaxy and they need to find a new personality
