Reposted by Joshua ZelinskyDaniel Litt @littmath.bsky.social · 27mextremely concerning that OpenAI has made 3 sign errors—an odd number—upsetting this delicate balance 2203
Joshua Zelinsky @joshuazelinsky.bsky.social · 42mIt seems like for the last few years, the idea of Florida or Texas going blue for an election has been repeatedly floated and it just doesn't happen. Now granted those were for Presidential elections, not Senate, but it still leaves me very skeptical. 010
Joshua Zelinsky @joshuazelinsky.bsky.social · 44m@smbccomics.bsky.social The votey and alt-text from today's comic www.smbc-comics.com/comic/blog combine into what I consider to border on a personal attack.smbc-comics.comSaturday Morning Breakfast Cereal -Saturday Morning Breakfast Cereal - 000
Joshua Zelinsky @joshuazelinsky.bsky.social · 2hCounterexample (albeit not a prominent one): Me. I was in H1. I'll readily say I was egregiously wrong. 040
Reposted by Joshua ZelinskyAndy Craig @andycraig.bsky.social · 20hIt's already illegal. Congress banned it near-unanimously in 2022. That law allows the ban to be lifted only if Russia withdraws from Ukraine. He's simply breaking the law that's already on the books. 5145151368
Reposted by Joshua ZelinskyJulia Curlee @juliacurlee.bsky.social · 22hAnd he tells Ukrainians to find “a new leader.” Russian strikes have killed more than 80 Ukrainians since Wednesday. Today a glide bomb in Zaporizhzhia killed 17, three of them children. Which side is America on? Slava Ukraini.ft.comUS warns Kyiv that strikes on Russia jeopardise intelligence-sharingTrump suggests Volodymyr Zelenskyy should be replaced after Ukraine’s leader criticised diesel deal with Moscow 55115
Joshua Zelinsky @joshuazelinsky.bsky.social · 10/10/2026The article seems to be behind a paywall, so I cannot answer any of that unfortunately. (The problem of many of the questions on the benchmark having problems seems like a pretty serious issue that should have gotten more attention though.) 100
Joshua Zelinsky @joshuazelinsky.bsky.social · 10/10/2026Getting things through careful peer review is important. At the same time, the current peer review system is utterly unsuited for this pace of development. It is similar to how during heights of covid, biologists were much more willing to use/rely on preprints than they normally are. 100
Joshua Zelinsky @joshuazelinsky.bsky.social · 09/10/2026Yeah, I think that's a legitimate criticism. I'm not sure how much of this was carelessness and how much of this was them believing their own hype. 100
Joshua Zelinsky @joshuazelinsky.bsky.social · 09/10/2026About a third are formalized in Lean; I think you may be underestimating how difficult formalization can be. For example, unit distance conjecture's initial formalization project basically halted because there was a lot of needed algebraic number theory that wasn't formalized yet. 100
Joshua Zelinsky @joshuazelinsky.bsky.social · 09/10/2026I'm not sure how much this shows they were careless or unethical; even respected mathematicians release preprints which turn out to be wrong. (I do think though the fact that even Astra was able to find the flaw here does suggest some carelessnes.) 200
Joshua Zelinsky @joshuazelinsky.bsky.social · 09/10/2026I don't want to brag too much about calling it but I called it: bsky.app/profile/josh... bsky.app/profile/josh... 100
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026Seems like he's imagining himself as some sort of Old West sherrif. 000
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026For a broader introduction to the major ideas that doesn't require too much background, I recommend Apostol's "Introduction to Analytic Number Theorey." 011
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026But note there are some typos in Axler's paper so if one needs to use it one needs to be careful (Equation 6.3 there is missing a term). Also, as far as I'm aware, most of this has *not* been Leanified (which someone should really get around to doing). 110
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026More recently, Axler has picked up doing the same sort of thing, with some bounds in nicer or easier in practice to use forms, although some of Axler's involve very heavy computation with only small improvement on Dusart. See math.colgate.edu/~integers/s5...math.colgate.edu 110
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026After R and S's work, there was a bit of a hiatus between the early 1970s and the early 1990s when Dusart started using advanced in analytic number theory + more computational power to make tighter versions of the R/S bounds, but often at the cost of them bounds not kicking in until x is large. 110
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026There are a bunch of related similar products or sums involving primes (such as Merten's theorems en.wikipedia.org/wiki/Mertens... which turns out to be harder to get nice bounds on).en.wikipedia.orgMertens' theorems - Wikipedia 110
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026The bounds on 𝜋(x) though are themselves partially downstream of bounds on what are called Chebyshev's functions en.wikipedia.org/wiki/Chebysh... which turn out to be often helpful and often easier to work with.en.wikipedia.orgChebyshev function - Wikipedia 110
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026For example, using the very weak knowledge of bounds for zeros in the early 1960s, Rosser and Schoenfeld showed that For example, using the very weak showed that if x>1 then 𝜋(x) < (x/log x)(1 + 1.5/log x). If you need explicit counts on the number of primes this sort of thing is helpful. 110
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026This is a pretty good approximation even for small x. For example, 𝜋(100)=25, and 100/ln 100 is about 21.7. Rosser and others found ways of translating where we know there are no zeros of the zeta function into explicit bounds on 𝜋(x). 110
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026Which says that if 𝜋(x) is the number of primes at most x, (e.g., 𝜋(10)=4, since the primes <= 10 are 2, 3, 5 and 7). Then 𝜋(x) is asymptotic to x/log x in the sense that the ratio of their limits approaches 1. (Number theorists write log x to mean natural log.) 110
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026So, the classic papers is there Rosser and Schoenfeld's 1962 paper projecteuclid.org/journals/ill... . But the background here is to first read about the prime number theorem.projecteuclid.orgApproximate formulas for some functions of prime numbersIllinois Journal of Mathematics 110
Reposted by Joshua ZelinskyAstronomer Royal for Scotland | Catherine Heymans @astroroyalscot.bsky.social · 08/10/2026So sad to hear that the iconic, trailblazing, Apollo 11 moon landing software engineering lead, Margaret Hamilton, is no longer with us. Love this image of her, standing next to a print out of the software that landed Buzz Aldrin and Neil Amstrong on the moon! 👩🔬🔭🛰️🧪 ℹ️: www.bbc.co.uk/news/article... 8861237
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026I'm not sure why you think those two comments are in contrast? 110
Reposted by Joshua ZelinskyMicah @rincewind.run · 07/10/2026he’s got a 30% approval rating and this one is ridiculous even for him, you craven sycophant 341716179
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026Many of these have Lean checks, and a lot of mathematicians stayed up last night with coffee and these; quasi-RH and and UGC both look correct right now and those are 2 of the biggest. I wouldn't be surprised if 1-3 are in error, but I'd be surprised if more than 10 are in error. 021
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026Also, this batch has no cryptography relevant things except for very tangential: There's speculation they are waiting to release those (or may not release at all) for security reasons. 040
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026For your "records" neither Jeff nor I are rationalists, just mathematicians who know about their own field. If I had any bias to "defend" Jeff here it would be because he's a nice guy and many years ago when I was in high school he helped me get my first paper published. 000
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026Incidentally, do you understand what it means for math to be verified in Lean? 000
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026But that you are unwilling/unable to listen to subject matter experts here and think that shaming them makes sense is a failure on your part about how to understand the world around you. Instead maybe consider that possibly, if all the experts disagree with you, it might be because you are wrong. 0100
Joshua Zelinsky @joshuazelinsky.bsky.social · 08/10/2026I didn't "used to do math," I'm a mathematician. (Heck, if you want you can read my latest preprint: arxiv.org/abs/2609.36068 , although I will note my student did about 90% of that.)arxiv.orgStrongly Pseudoperfect NumbersA positive integer $n$ is said to be strongly pseudoperfect if there is a subset $S$ of the positive divisors of $n$ such that $d \in S$ if and only if $n/d \in S$, and $\sum_{d \in S} d = 2n$. We con... 150
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026Then I'm missing something basic here. In what way do you think it will become more nuanced? 100
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026Quasi-RH and many of the others have Lean proofs. In the case of Quasi-RH some analytic num theorists stayed up last night with just it and a pot of coffee and looked it over. I wouldn't be surprised if 1 or 2 of these have subtle errors, but the situation you are envisioning looks unlikely. 100
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026Well, they do have more processing power, and that matters. But LLMs have gotten better and more efficient. You can for example do math with Kimi now that a model twice its size could not do earlier. (I've used Claude to do non-trivial math but not anything remotely this extreme.) 000
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026Having not read it (and it being outside my expertise), I have no idea but that looks like some sort of raw calculation or constructions details that should be in an appendix. That doesn't make it "slop" though. 220
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026You are I suspect drastically underestimating the size of the search spaces involved. You cannot just brute force your way through to proofs like this. And if you could, people would be able to do this without LLMs. 100
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026But Zach's statement isn't about some sort of claim about "Is this a good thing?" or even "should we support this." The entire point is that he's focusing on the factual level of what is going on, not any reaction to it. 180
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026I think everyone agrees that the level of readability for these papers is highly variable. 000
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026That may be part of it, but it is I think also combining with a general ideological reaction against anything related with LLMs, which while it has some definitely justiifed elements, is causing people to behave much less rationally where this is concerned. 010
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026Well, we're surprisingly bad about this sort of thing. When someone drops what looks like a really good result, we'll sometimes start gushing over it, and then a few days or weeks later we'll be like "Oh, wait, what about that step?" and then it will fall apart. 110
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026Yeah, this is very much not a foolproof method, just one that works pretty decently. 110
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026I'm not sure what counterpoint you are thinking here, or why you think this is helpful. I'm a mathematician (you can directly verify from my name), Jeff, who you are replying to a prominent recently retired mathematician, and the quasi-RH proof was verified with Lean code. 120
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026That's true, but checking math really takes time to do carefully. For example, I'm refereeing a paper now where I've had the paper for 3 months and it just takes that long. No one is checking all the subtle details of a problem in 2 or 3 hours. 010
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026Or people who don't know much about math, and don't know who to listen to. I do think though that even non-math people have at least heard of RH and so should be able to understand that quasi-RH is a big deal. 150
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026Well, they were trained on massive amounts of human writing. 000
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026Right, so when you do this, you tell the AI you want to find a hole. And then if it finds what it claims to be one you check it. This is not foolproof at all, but works surprisingly well. (And if anything, it will sometimes weirdly something is a hole where it follows from a standard argument.) 110
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026It looks like about half of them have Lean code (including a lot of the more prominent ones like quasi-RH, so they may have prioritized Leaning the biggest ones), but at the risk of sounding like an AI, you may be right to pushback here. 030
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026But despite that, my guess is that at least one of them will turn out to have some error (722 is just a lot of problems), and that then people who don't want to deal with/admit what is going on will blow up that 1 or 2 like it somehow undermines everything. 150
Joshua Zelinsky @joshuazelinsky.bsky.social · 07/10/2026As a rule of thumb, if you want to check an OpenAI proof, run it through Claude and make sure it knows it came from OpenAI. If you want to check an Anthropic proof, do the reverse with ChatGPT. They seem to be more inclined to find potential errors with their rivals. 210
