This is a bigger result, of the form “asked ChatGPT, got a wrong answer, but thinking about it led to a right answer.” And the conjecture was much-discussed but not widely believed.

@antieau.bsky.social · 11h ago

Alex Perry has disproved the period-index conjecture in dimension 3. His period-2, index-8 example is the precise case Ben Williams and I expected but could not prove. Blog: antieau.github.io/2026/08/05/p... Paper: arxiv.org/abs/2608.03684

Ben Antieau and his FRG collaborators have proved that Hodge numbers are invariants of the derived category of a smooth complex projective 4-fold, with a new idea from the fancy version of ChatGPT.

@antieau.bsky.social · 2d ago

GPT-5.6 Sol Extra High proved that derived-equivalent smooth projective complex fourfolds have the same Hodge numbers. The key step: the Mukai pairing shows the topological signature is a derived invariant. antieau.github.io/2026/07/31/h...

Just learned that the root of “onerous” is “onus,” a burden. To exonerate someone was originally to unburden them.

The Odyssey is good. The running discussion of the Sea Peoples is a clever addition.

The blackberries in the field down the street are ripening so we made our first pie of the season. Out of practice, but not a bad start.

Came home from a long trip to find that my sunflowers have boomed and my passion flowers have gone to town.

This is the craziest escalator I’ve ever seen.

For anyone who knows the macaroni and cheese pizza from Ian’s Pizza in Madison, Wisconsin, this is basically the same except a sandwich from a 7-Eleven in Japan.

Overnight flight. R: “Sleep ok?” N: “Like the princess and the pea.” R: “Which one were you?”

Obvious in hindsight, but the auto wrecking place won’t let you out on the yard in sandals.

Help us out with a word game: water wings, firearms, air horns, earth…

Hearing reports that kids these days sign yearbooks with “HAGS” as short-hand for “have a good summer.”

Hope everyone’s been enjoying the conjunction of Venus and Jupiter for the last week or two.

Passion flowers back at it.

Set my phone on top of the car, forgot about it, drove a few blocks to the grocery store, shopped, realized it was missing, found it still there on top of the car. I’m sure I’ve used up all my luck.

@littlejohn.bsky.social @bagofmoons.bsky.social you guys were talking about letting plants grow and seeing what they turn out to be… this wild brassica came up in our potato patch a month ago, and I don’t think I’m going to eat any part of it but it sure looks cool.

Once again found myself writing “by a similar argument…” and then thinking maybe I’d better write out the details just in case, and it turned out to be much more complicated.

If they ever rope me into being department chair, my signature policy will be “no taco bars at work functions.”

Been slacking with my little league posts, sorry. Alice’s team won their last game of the season tonight. She hit a grounder to the first baseman, which pulled him far enough off the bag that she managed to beat him there.

Just learned that palm trees are so called because the leaves look a bit like fingers spreading out from the palm of the hand. This is in Latin (palma), and then both meanings were borrowed into English via Old French much later.

Well they’ve finally reopened the Chambers St. viaduct after probably two years of construction. They closed half the lanes, tore up one side of the road, and then did nothing for a year because they neglected to get permission from the railroad before starting work.

At the Eugene Emeralds game, sitting in the table area way out on the right field line hoping to catch foul balls, and we haven’t had one come to us yet but the fielder did toss one to Alice.

Bird bath next to my office getting some use.

Good earth-shine on the crescent moon as I was taking out the trash.

My colleague turned me on to this site where you can generate all kinds of crazy graph paper. I needed some triangular graph paper to work out a combinatorial thing. incompetech.com/graphpaper/

MathSky: can anyone recommend an undergraduate abstract algebra textbook that does rings before groups?

Autocorrect turned “quartic K3 surface” into “aquatic K3 surface” and now I want to study them.

Bad year for slugs and snails.

Thinking back on being assigned to read Animal Farm in 7th grade (1994). We knew next to nothing about the Soviet Union, certainly no idea who Stalin was, and as far as I remember the teacher didn’t try to explain the allegory. What were we supposed to take from it? A cautionary tale about cliques?

Small victory: the University of Oregon has scrapped plans to have an AI voice read the students' names at graduation. Instead the names will be read by humans.