2026-11-01 05:40:33
Boooooo! What spooooky times we now live in, with AI rapidly advancing in capabilities and solving more and more major open math problems!
So it seems like a perfect occasion to share yet another podcast. I know I’ve been dropping them like every day, but this is a special one, with Brian Greene for his World Science Festival, recorded in-person when I visited Columbia University a week ago. Note that we don’t talk about OpenAI’s refutation of the Exponential Time Hypothesis because the announcement of that was still two days in the future!
2026-10-31 07:27:34
In my “Mathocalypse” post, I mentioned that my wife Dana—who’s been working on Subhash Khot’s Unique Games Conjecture since ~2009, for the entire time I’ve known her—has for the past few weeks (while on sabbatical at the Simons Institute in Berkeley) been spending essentially all of her time laboring to understand OpenAI’s recent proof of the conjecture. Having now studied the proof closely in collaboration with Subhash Khot himself, Johan Håstad, Dor Minzer, and other colleagues, and (naturally) GPT-6 Astra, Dana probably now understands this crown jewel of OpenAI’s release as well as anyone does. This week, she gave two well-received whiteboard talks on the proof at Simons Institute. So, I and others encouraged her to give the same talks next week at UT Austin when she’s back here, and Dana agreed! Because of the large timely interest, we’re going to do a live Zoom option, and will also record the talk for later sharing on YouTube. Please note: While all are welcome, this is a 2-hour technical talk. The first hour will review key ideas from hardness of approximation, while the second hour will describe the new construction. —SA
Title: The Unique Games Conjecture – Proved (!!?)
Speaker: Dana Moshkovitz (UT Austin)
When: Wednesday Nov. 4, 3:30-5:30pm US Central (with a brief break in the middle)
Where: UT Austin, Gates Dell Complex 6.302. Live Zoom will be available here, and a recording will be available later.
Abstract: The Unique Games Conjecture of Khot says that it is NP-hard, given a system of linear equations of the form xi-xj=bij (mod p) over variables x1…xn, where 99% fraction of the equations can be satisfied, to find an assignment satisfying 1% of the equations (here p is a sufficiently large constant).
This conjecture implies optimal inapproximability results for many optimization problems.
A few weeks ago OpenAI released a writeup with a proof of the Unique Games Conjecture, as well as a Lean formalization of the proof. The writeup, like others released that day, is not written in a way that’s especially readable to human mathematicians.
My goal in this talk is to offer my mental map of the proof, in a way that’s helpful to theoretical computer scientists who are familiar with the area. I think of the innovation as a new code construction, “Hadamard with a noise test.” I’ll sketch how it fits into the NP-hardness reduction. Then I’ll describe the code construction fully and sketch its soundness analysis.
I’ll also point out a couple of ingredients of the proof that are of independent interest, like a simple quadratic that behaves “like a linear,” and a probability bound using a trick with harmonic numbers.
2026-10-27 06:03:37
As always, I strongly recommend 2x speed, which compensates somewhat for my verbal infelicities!
New! More podcasts keep dropping! This one is with the AI alignment researcher Roman Yampolskiy, about … well, AI alignment, plus the Mathocalypse, plus quantum computing, plus whether the universe is a simulation, and I forget what else! Man do the YouTube comments make me despair of humanity though.
Another one that recently dropped, with Sophia Aryan:
The title Curt put next to my head could’ve been in reference to many, many things! But sorry, he just mean AI. He and I start with the Mathacre, of course, but then we get onto the firewall paradox and then Curt starts asking about computational complexity and the Second Law, and then about Integrated Information Theory.
Ah, and another one that just dropped! Man’s Search for Meaning podcast (recorded in-person in Austin), with Yannick Bernard, who asked me about quantum computing, AI, my personal story, grade-skipping, antisemitism, and I don’t even remember what else. I didn’t refuse to answer anything. (Note: this one was recorded over the summer, which is why I so weirdly omit the latest AI math breakthroughs!)
OK, despite the title of this post, short break from “The Topic.” Here’s an absolute masterpiece of mathematical exposition, from the “Polylog” YouTube channel, which tells the story of the determination of Busy Beaver values through spectacular animations. I play cameo roles in the video, although I embarrass myself (as the video silently points out) by transposing two digits in the value of BB(5)…!
Just for old times’ sake, a short podcast about quantum computing with Danny Li.
And, coming soon (not on YouTube quite yet): a conversation about the Mathacre with celebrated physics popularizer (and character on The Big Bang Theory) Brian Greene, recorded in-person in NYC during my recent trip to speak in the math department at Columbia University!
And to preempt the inevitable comments about it: yes, my students just came to my office to tell me that an OpenAI model has now refuted the Exponential Time Hypothesis, by giving an algorithm to solve 3SAT in an amount of time that scales roughly like exp(n/√log(n)). Even as we struggle to digest the previous courses, the endless buffet continues!
2026-10-26 05:54:26
Someone writing an article for the Israeli press about “people abroad who love Israel but might be worried” emailed me the following questions:
“1. What is something about Israel that you admire/appreciate over the years?
2. What are you worried the most about Israel these days?”
So I replied as follows:
“It’s hard to know where to start with either of your questions! But briefly:
Tiny Israel standing up for itself, against an often hostile and unjust world, is a huge part of what’s given me the self-confidence to stand up for myself in my own life. That was true even before I had visited Israel or spent significant time there, gazed across the desert at the still-clear ruins of the Roman siege of Masada, staggered overwhelmed out of Yad Vashem into the sunlight of Jerusalem, tasted the hummus or pomegranate juice or ice cream with blended fruit, befriended or had academic collaborations with dozens of Israelis, or married an Israeli woman.
My fear is merely the ‘obvious’ one — that, in response to the staggering hostility directed against the ‘Jew among the nations,’ Israel will become more and more belligerent, isolated, and right-wing. It will get demographically overwhelmed by those who don’t want to work or serve in the army, while hundreds of thousands of secular educated Israelis leave. It will be internally divided almost to the point of civil war. It will repudiate the liberal-democratic vision of Herzl and Ben-Gurion, of world-class universities and making the deserts bloom, for the swaggering, theocratic vision of Smotrich and Ben-Gvir, of chasing Palestinians from their olive groves. It will become more and more like the hateful caricature of itself that the anti-Israel people in the West always imagined. And then, having been internally weakened in all of these ways, it will finally be destroyed by its external enemies, who will never have rested the whole time, who never once wavered in their dream of a second Holocaust.
I hope and pray that in the upcoming election, the Israeli voters make optimistic choices that repudiate these fears.”
As I’ll do more and more with political posts, I’m leaving the comments off. Why? Because my remaining life is too short to spend it battling an endless parade of trolls and griefers, leftists and rightists and just nihilists, who might or might not be AI.
2026-10-21 13:13:08
Today, I take a break from your regularly-scheduled AI mathocalypse programming to urge my American readers to vote in the Congressional midterms, early if possible, if you haven’t already. Especially if your state faces one or more major contests, as does my adopted home state of Texas.
Me, I voted straight-ticket Democrat today, as I’ve done in every election since I became eligible over a quarter-century ago (except for when I vote-swapped with someone from another state).
So yes, I voted for the guy who studied theology a short walk from my house, and who seems to have really internalized the whole Jesus thing about kindness to everyone—
—over his sneering, thuggish, cartoonishly mafia-like opponent. Fingers crossed that Talarico pulls off a historic upset for our state (he’s currently a 2-to-1 favorite in the prediction markets).
The Texas Republicans did everything they possibly could to make this choice easy for me, by being corrupt, conspiratorial, racist, and Taliban-like even by the jaw-droppingly debased standards of MAGA in 2026. As I draw breath, I could never vote for a slate one of whose candidates attacked UT students for the crime of being visibly Southeast Asian while cheering their school’s football victory from the stands—and whose other candidates could barely bring themselves to condemn this knuckle-dragging racist, for fear of angering their base. (It’s like, didn’t you want immigrants to assimilate to American culture? What more could these kids possibly do, short of skin bleach?)
All the same, this was also the first US election in my lifetime where I felt like my vote was genuinely in play—especially when I listened to Talarico’s condemnations of Israel, for having the temerity to fight the same kind of war any random other nation would’ve fought had it been attacked as Israel was on October 7. When Hasan Piker came to speak to a cheering crowd here at UT Austin, I actually wrote to someone I know in the Talarico campaign, to ask whether Talarico would show enough balls to condemn Piker’s many antisemitic and anti-American statements, and renounce his support. My contact was nice enough to reply to me, saying: don’t worry, James is taking care to be far away from Austin during Piker’s visit, so he won’t need to engage at all!
So then, this is my candidate: the guy who’s strategically silent on the wildly-popular streamer who’d gladly see my Israeli family members raped and beheaded, rather than campaigning with that streamer like Abdul El-Sayed did in Michigan. I unironically believe that, for Talarico, it took genuine moral courage to resist the whole momentum of his party’s youth even to this extent.
To earn my vote in the near future under these circumstances, all a Texas Republican would need to do is be somewhat sane or reasonable. He or she might affirm, for example, that racism is bad, that abortion is a woman’s choice, that Christianity is not the state religion of the US, that Covid vaccines work, that human emissions are worryingly changing the earth’s climate, and/or that Joe Biden won in 2020, while still being arbitrarily right-wing on taxes and other stuff. He or she could then simply wait for the Democrats to descend fully into the worldview of the masked hooligans who are currently setting France’s beautiful cities aflame, terrorizing its shopkeepers, and looting as many Louis Vuitton handbags as they can carry … all for Palestine, of course, and for the death of global capitalism, and for the violent overthrow of the scheming, money-grubbing, hook-nosed, international Talmudic … err, I mean “Zionists.”
What I’m trying to say is, it was a genuine achievement on the part of the Texas Republicans to fail to earn a single vote from me this cycle.
2026-10-20 05:07:12
As I announced on this blog a couple weeks ago, I’m teaching a new course this semester at UT Austin, entitled AI Alignment Theory. To call such a course “timely” seems like an understatement; this is the first course I’ve ever taught for which multiple gargantuan developments relevant to the course have happened while I was teaching it.
Since AI alignment is still a field with no standard textbook (although that might be changing), no accepted body of mathematical theory, etc. etc., the way we’ve been running the course is like a humanities discussion seminar, albeit one that happens to be in a CS department and to include technical results from time to time. Basically, in each class session, a student “rapporteur” gives a talk on an AI alignment reading—which include “ancient” readings (from way back in 2016), “modern” readings (from, say, last week), and everything in between—and then we freely discuss and debate whatever was presented, with my own role mostly limited to that of gadfly (occasionally I’ll do a mini-lecture on some technical concept).
Anyway, two weeks ago, I promised a list of the papers and other writings that we’ve been discussing, as well as student “rapporteur reports” on those papers, which cover not only the papers themselves, but the students’ thoughts about the papers and (anonymized) summaries of points raised during our class discussion. People have been bugging me for that ever since.
Since I am to please, here you are, without further ado! I’ll continue to update the list as the semester progresses, so that this post can serve as a central public repository for the course.
(More readings TBD, until the semester ends!)
Thanks to my TA, Lin Lin Lee, for her help in getting all of this together.
Update: I welcome elevated discussion of these papers and rapporteur reports in the comment section; some of the students might chime in too! Because of the connection to an academic class, though, in this post I’ll be especially ruthless in keeping out nonconstructive or off-topic comments.