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If you don't think this is creative and intelligent, I believe you have a very flawed idea of both concepts!

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Here's a full exposition without abbreviations acrobat.adobe.com/id/urn:aaid:...

acrobat.adobe.com

Adobe Acrobat

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The exposition is basically an illustrated version of @thomasfbloom.bsky.social's - erdosproblems.com/548#proof-ex... 5/5

erdosproblems.com

548 | Erdős Problems

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The proof was obtained by Astra (in Lean) as part of experiments for FrontierMath Erdos, a new benchmark by Epoch AI Research. epoch.ai/latest/annou...

Now for Lemma 2 proof: We start with marked pairs whose prefixes contain T₁ and miss T. There are C(T₁) − C(T) such pairs, because every rooted copy of T contains T₁. We will turn these into distinct marked pairs missing T₂, discarding at most n! inputs. 3/5

Proof of Lemma 1 (root lemma). 3/

Here are the key lemmas, which are proved in the next two tweets. This image shows how they inductively prove the key counting claim (1) above. 2/

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Ben Golub @bengolub.bsky.social · 19/08/2026

The Erdős–Sós conjecture is a shockingly simple statement about graphs that we did not know was true: a (simple) graph with average degree > t−2 contains every tree on t vertices. A few days ago, OpenAI's Astra proved it as part of an Epoch AI project. Here's a simple exposition. 1/

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I would expect so for a number of reasons. But I think it wouldn't be that informative on the question of how predictive SAT scores are.

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Ben Golub @bengolub.bsky.social · 18/08/2026

There are definitely enough high schoolers in the country who can perform very well in Berkeley calculus classes, and Berkeley is admitting much less mathematically qualified students over them, when they have a tool to do better. Let me know which part I'm getting wrong.

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Ben Golub @bengolub.bsky.social · 18/08/2026

Seems like the current shitshow at the top UCs with a ton of kids not being prepared for college math is pretty cleanly separable from the pandemic?

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Ben Golub @bengolub.bsky.social · 18/08/2026

I'm interested in the views of social scientists who made arguments that standardized tests did not provide a valuable incremental signal of preparedenss in college admissions over HS record. What do they think now? Would love to see some discussion.

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Ben Golub @bengolub.bsky.social · 15/08/2026

No - I don't think so. Very common Ukrainian Jewish last name.

Ben Golub @bengolub.bsky.social · 09/08/2026

I think they're often still pretty nasty at least in my limited observation

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Erzo F.P. Luttmer @erzoluttmer.bsky.social · 09/08/2026

1/5 AEA journals have run a pilot using Refine, and author reactions were overwhelmingly positive: >90% favored incorporating Refine into the editorial process. Think of Refine not as a referee, but as a detailed technical proofreader. @aeajournals.bsky.social #EconSky

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Ben Golub @bengolub.bsky.social · 05/08/2026

YAY - delights me/us to hear this!

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Henry Yuen @henryyuen.bsky.social · 01/08/2026

Some initial thoughts, and a complicated mix of feelings. Wow. I mean, Erdos problems are cool (I genuinely mean that), I didn't know about the Jacobian conjecture before it got disproved. But this newest batch from OpenAI hits home in a way the previous announcements did not.

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Alex Falcone @alexfalcone.bsky.social · 10/06/2026

The place I donate blood gives points that you can exchange for gas cards which means I actually know the current exchange rate of blood for oil. Blood is going for 20.618 times an equivalent amount of oil.

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And similarly no amount of saying " go read these five other things" will change the fact that what is on the page is deceptive relative to what is on the other page. And repeating that the other context matters a lot is not going to change that simple fact of scholarly deception.

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Agreed. But another difference is that Quinn's field is such that it's considered very rude to point out obvious misuse of evidence - being worse than social psychology takes some real effort.

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With Gino, it wasn't the consensus -- it was the in-your-face evidence of dishonesty, just as in Quinn's case. Gino, btw, has ardent defenders TODAY who say exactly what you say - you must study the whole corpus to have a right to judge. So you are very analogous - it's kind of beautiful!

Do you need to study social psychology to know that Francesca Gino is a fraud?

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Let me make an analogy. If someone said that Francesca Gino's research is okay because the studies replicate, they would be completely missing the point about what went wrong with her scholarly practices Your defenses of S have the same quality.

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Just to be clear, the quotation practices were deceptive even fully accepting all the arguments you're making about broader intent. The idea that sufficient understanding of the broader picture would make S's behavior not malpractice is beneath contempt and I'm not going to pretend otherwise.

thank you for amplifying it! I think he is absolutely full of shit (and you too, if you agree)

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Again, I am frankly shocked that people like you are apparently committed this kind of lawyering. Any undergraduate that did what Quinn did with an instructor who was awake would get a terrible grade, and if you deny that you are, forgive me for my bluntness, full of shit.

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Phil Magness (@PhilWMagness) on X

You can read Phil's rebuttal here. I'm convinced based on reading his linked paper that he understands the work he's discussing and CEH here is in my view clearly in the wrong - his piece should certainly not be desk rejected x.com/i/status/206...

x.com

This morning's "defenses" of Quinn Slobodian are trying to paint the misquotations as isolated incidents and accusing me of focusing on narrow technicalities while ignoring his larger argument. False...

What S does can't be fully defended -it's at a minimum EXTREMELY SLOPPY work, even if he has a point on the broader meaning. it's crazy that people will defend what's on the page in Magness's demos

Great response, thanks! I agree this is the weirdest passage and the most ambiguous case of S's behavior. Now let's consider all the other screenshots?

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Wojtek Kopczuk @wwwojtekk.bsky.social · 09/06/2026

To me (someone w/ no dog in this fight) your reply shows you are not a good scholar: rather than publicly confronting the clear evidence of your misrepresenting your sources, you turn to (perhaps correct) personal criticism of Magness. This is the behavior of (bad) politician, not a scholar.

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Unsurprisingly, it's mostly a shrug here except for a few people who pretend it is ok. I'll add another one in this genre that made my jaw drop.

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It's interesting that all the replies have this flavor as opposed to explaining/defending the specific problems with Slobodian's use of sources that are staring us right in the face.

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Interesting that Slobodian being full of shit has hurt your feelings somehow!

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But, just to be clear, no publicly available reply that you can point me to by Slobodian in which he explains these things outside a closed review process.

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Could you point me to where>

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Have his issues been satisfactorily addressed, in your view?

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Fair point! They are related but there's no easy implication.

Then I think we have genuinely different views on a scholar's obligations! I personally could not ignore such an issue, regardless of where the criticism was coming from, and I view this as part of my obligations as a scholar. But I get that some others might not.

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Let's just take it to the object level - do you think Slobodian is a careful, rigorous scholar?

The criticism of his source usage is not in bad faith, so I stopped reading there.

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Analogy: I think Francesca Gino's response to the Harvard process conclusively proves she is a bad scholar, because even if she was framed, a decent scholar would react differently in addressing the trash that got published. I see Slobodian as a similar case of much smaller severity.

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There are many reasonable responses: apologizing for misleading people, explaining how this failure of good practices happened, withdrawing or correcting your article... But dissing the guy for his politics and who pays/rewards him? That's not an honest response.

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