The n-Category Café — 3/20/2026
A large language model has very little self-awareness. But it is easy to give it some rudimentary but useful forms of self-awareness using the “plumbing” language.
Computational Complexity — 3/18/2026
Gilles Brassard and Charlie BennettCharlie Bennett and Gilles Brassard will receive the 2025 ACM Turing Award for their work on the foundations of quantum information science, the first Turing award for quantum. Read all about it in The New York…
Crooked Timber — 3/18/2026
Jürgen Habermas has died, at the age of 96, and traditional and social media are full of obituaries and memories. For outsiders, it is maybe hard to gauge the omnipresence of his name in West Germany,* but his influence on democratic theory more…
The Aperiodical — 3/18/2026
Double Maths First Thing is singing powerful songs Hello! My name is Colin and I am a mathematician on a mission to spread the joy, delight and frustration of doing maths. Welcome to episode 50! That’s excitement, not factorial. I enjoyed the…
Computational Complexity — 3/16/2026
(If you live in Montgomery County Maryland OR if you care about Education, you MUST read this guest blog by Daniel Gottesman on Scott Aaronson’s blog HERE.) (This post is a sequel to a prior post on this topic that was here. However, this post is…
Crooked Timber — 3/15/2026
The Aperiodical — 3/15/2026
Can you believe it’s been 10 years since I made the “Is this prime?” game? I sort of can, because I set myself a reminder about it in my calendar. Back in 2016, the game had been played 350,000 times and I wrote a post looking at the collected…
Crooked Timber — 3/14/2026
Third and last part of an article discussing Imperia, the large concrete statue of a semi-fictional medieval sex worker. Part 1 is here and Part 2 is here. A Clandestine Erection Imperia went up in April 1993, and I won’t even try to explain the…
The n-Category Café — 3/12/2026
A category-theoretic approach to “agent frameworks”: that is, frameworks for coordinating “agents” that are large language models.
Crooked Timber — 3/12/2026
It’s the 15th anniversary of the Fukushima nuclear disaster, and any lessons from that event seem to have been forgotten by most. Political leaders of all stripes, from centre-left to far right have been keen to promote nuclear power as at least a…
Crooked Timber — 3/11/2026
I have to admit that I am not at all sure of the date of International Women’s Day. It seemed to be every day of the past week or so. Which perhaps ought to be the case every damn week. So it seems timely to tell you about the current issue (Volume…
The Aperiodical — 3/11/2026
Double Maths First Thing is remembering how icosahedra work. Hello! My name is Colin and I am a mathematician on a mission to spread joy, delight and just satisfaction in doing maths. This week’s excitement was being mentioned (twice!) in a Stand…
The Aperiodical — 3/10/2026
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of February 2026, is now online at Tony’s Maths Blog. The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical….
Computational Complexity — 3/10/2026
Turing Award winner and former Oxford professor Tony Hoare passed away last Thursday at the age of 92. Hoare is famous for quicksort, ALGOL, Hoare logic and so much more. Jim Miles gives his personal reflections.Jill Hoare, Tony Hoare, Jim Miles….
Computational Complexity — 3/8/2026
In my graduate Ramsey Theory class I taught Kruskal’s tree theorem (KTT) which was proven by Joe Kruskal in his PhD thesis in 1960. (Should that be in a graduate Ramsey Theory class? There are not enough people teaching such a course to get a…
Crooked Timber — 3/8/2026
Crooked Timber — 3/8/2026
It’s a truism that every child should be wanted. While there are plenty of exceptions, the birth of an unwanted child often turns out badly for both mother and child (and father, if they are present). Sometimes, once a child is born, the fact that…
The Aperiodical — 3/4/2026
Here’s a short round-up of mathematical and maths-adjacent news from this month. The LMS are seeking Outreach Lecturers, who must work in UK HE mathematics, and will receive a two-year post during which they’re expected to deliver talks to a…
The Aperiodical — 3/4/2026
Double Maths First Thing is spinning plates Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight of doing maths. This week’s “oo!” moment was this lovely observation by Ruud de Rooij, followed by an “oh wow!”…
Computational Complexity — 3/4/2026
In discussions of AI and Mathematics, the discussion often goes to mathematical proofs, such as the the First Proof challenge. So let’s look at the role of proofs in mathematics.Without a proof, you don’t even know whether a theorem is true or…
Crooked Timber — 3/3/2026
She told me she’d be ten minutes late, which was fine. But when it was nearly twenty minutes I messaged – where are you? Shall I walk towards you? My daughter sent a picture of a bit of the state library she was in, people at desks etc. We’re here,…
Computational Complexity — 3/2/2026
Goodhart’s law: When a measure becomes a target, it stops being a measure. I was watching the show Masterminds where Ken Jennings is one of the Masterminds. Here is what happened: Brook Burns (the host): The only vice president in the 20th century…
Crooked Timber — 3/2/2026
These problems are like distant locations that you would hike to. And in the past, you would have to go on a journey. You can lay down trail markers that other people could follow, and you could make maps. AI tools are like taking a helicopter to…
Crooked Timber — 3/1/2026
The Aperiodical — 2/26/2026
A while ago I added a clock to my “Is this prime?” website: it shows you when the Unix time is a prime number of milliseconds. Earlier today I had the thought that it could send you a notification when it’s prime time, so you won’t miss out even if…
Computational Complexity — 2/25/2026
Last week I had the pleasure of meeting Alex Bellos in Oxford. Among other things Bellos writes the Guardian Monday puzzle column. He gave me a copy of his latest book, Puzzle Me Twice, where the obvious answer is not correct. I got more right than…
The Aperiodical — 2/25/2026
Double Maths First Thing is trying to be good. Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight of doing maths. I had an “oo! oo! oo!” moment at MathsJam last week, figuring out a neat solution to a…
Computational Complexity — 2/25/2026
A commenter on this post asked for me (or anyone) to solve the problem without AI:A,B,C,D,E are digits (the poster said A could be 0 but I took A to be nonzero) such thatABCDE + BCDE + CDE + DE + E = 20320.(CLARIFICATION ADDED LATER: We allow two…
Crooked Timber — 2/24/2026
Some Americans have been talking about our shared European culture lately! As CT’s resident American-in-Europe, I feel I must respond. So, here’s a European culture story. (This is Part 2, You can find Part 1 here.) Okay, so Imperia! Big…
Crooked Timber — 2/22/2026
It has been like this for weeks and weeks. And not just in the UK, but across much of Western Europe.
The n-Category Café — 2/22/2026
Making precise the idea that equivalent structures are indistinguishable.
Crooked Timber — 2/21/2026
Not long after Trump took office, I observed that the status of the US as the “indispensable nation” could not be sustained. A year later, the US, considered strictly as a state actor, is already dispensable and has, in fact, been largely dispensed…
Crooked Timber — 2/21/2026
Just north of the Alps, on the border between Germany and Switzerland, lies beautiful Lake Constance. And on the northwest shore of the lake is the lovely small city of Constance, Germany. Constance is well worth a visit. A lot of German cities…
Computational Complexity — 2/18/2026
Computer Science Professor Joseph Halpern passed away on Friday after a long battle with cancer. He was a leader in the mathematical reasoning about knowledge. His paper with Yoram Moses, Knowledge and Common Knowledge in a Distributed Environment,…
The Aperiodical — 2/18/2026
Double Maths First Thing is giving up sacrifice for Lent Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in doing and understanding maths. I’ve given a few classes this week where a student has suddenly lit…
Computational Complexity — 2/15/2026
I sometimes assign open problems as extra credit problems. Some thoughts:1) Do you tell the students the problems are open?YES- it would be unfair for a student to work on something they almost surely won’t get.NO- Some Open Problems are open…
Crooked Timber — 2/15/2026
DEONTOLOGISTICS — 2/14/2026
A couple updates for readers. There will be an impromptu book launch for The Revenge of Reason at Newcastle University on the 25th of February, from 5-7pm in HDB.1.02 in the Henry Daysh Building. I’ll be having a conversation about the book with…
The Aperiodical — 2/13/2026
A conversation about mathematics inspired by a piece of folklore. Presented by Katie Steckles and Peter Rowlett.
Computational Complexity — 2/12/2026
A reader worried about the future.I am writing this email as a young aspiring researcher/scientist. We live in a period of uncertainty and I have a lot of doubts about the decisions I should make. I’ve always been interested in mathematics and…
Joel David Hamkins — 2/12/2026
I am honored to be invited to give the Owen G. Owens Memorial Lecture at Wayne State University on 16 April 2026, joining a distinguished list of luminaries giving previous Owens lectures, including Gregory Margulis, John Milnor, Mikhael Gromov,…
Joel David Hamkins — 2/11/2026
I have been asked by the ASL to fill in as a last-minute substitute speaker for the ASL session at the upcoming 2026 APA Central Division Meeting in Chicago, February 18-21, 2026, due to a late cancellation of one of … Continue reading →
Computational Complexity — 2/9/2026
(I thought I had already posted this but the blogger system we use says I didn’t. Apologies if I did. Most likely is that I posted something similar. When you blog for X years you forget what you’ve already blogged on.) Historians who study ancient…
Joel David Hamkins — 2/4/2026
This will be a talk at the CUNY Logic Workshop on 13 March 2026, held at the CUNY Graduate Center. Abstract. I shall introduce the elementary theory of surreal arithmetic (SA), a first-order theory that is true in the surreal field when equipped…
Computational Complexity — 2/4/2026
Wandering around maze known as the Computer Science building at Oxford I found the computer science library. Rarely these days do you see a library (and a librarian) devoted to computer science. The librarian found their copy of The Golden Ticket…
Computational Complexity — 2/2/2026
Lance and I had a blog-debate about What to do about students using ChatGPT to do their Homework.Some commenters pointed out that we’ve been here before. I will now list past technologies that looked like they were a problem for student assignments…
Proses.ID — 1/31/2026
I miss writing. That’s a strange thing to say because I’ve been employed as a full-time writer for the past 14 months. And I have…
Proses.ID — 1/31/2026
I’ve been down a rabbit hole for the past few months, obsessed with a single question: “What makes a writing human?” It started, ironically, because…
Computational Complexity — 1/28/2026
The Fighting Temeraire by JWM TurnerA year ago I wrote about an experiment I ran to learn about the modern period of art from ChatGPT. Chatty picked four paintings to discuss and I wrote about Joseph Mallord William Turner’s The Fighting Temeraire….
The n-Category Café — 1/26/2026
David Jaz Myers has some thoughts about Riemann’s functional equation for the zeta function.
Computational Complexity — 1/24/2026
Bogdan Grechuk has written a book Landscapes of 21st Century Mathematics that came out in 2021. There is a revised version coming out soon. The theme is that he takes theorems whose statements can be understood and describes them in 5–10 pages. No…
Computational Complexity — 1/22/2026
I once had a provost who felt that academic departments hindered the university as they tended to silo the faculty. He would argue we should eliminate departments and that would increase cross-disciplinary work. That went nowhere of course.He…
Computational Complexity — 1/20/2026
Students are using ChatGPT to do their HW. Here are things I’ve heard and some of my thoughts on the issue (Lance also added some comments). I have no strong opinions on the issue. Some of what I say here applies to any AI or, for that matter,…
Computational Complexity — 1/14/2026
It’s not every day that one of my open problems is solved, especially one that I asked about over three decades ago. Matt Kovacs-Deak, Daochen Wang and Rain Zimin Yang just posted a paper showing that if you have a Boolean function (f) and two…
Computational Complexity — 1/12/2026
I’m posting from Oxford University where I will be spending the “Hilary Term” (through late March) as a visiting fellow at Magdalen College. If you are relatively local, reach out if you’d like to connect.I plan to get back into research after…
Computational Complexity — 1/12/2026
1) Smells Like… SomethingIn many TV shows having to do with murder (and there are plenty of them), I’ve heard the following exchange: His breath smells like bitter almonds. So he was poisoned with cyanideThey’re either saying bitter…
The n-Category Café — 1/6/2026
Dynkin diagrams have always fascinated me. They are magically potent language — you can do so much with them!…
Computational Complexity — 1/5/2026
2026 will be a year of AI disruption across all of academia. Let’s start by talking about AI is changing how we write research papers. Not the research itself (another post), just about the dissemination thereof.Technology has changed research…
Computational Complexity — 1/3/2026
The Betty White Award goes to people who die at the end of the year— too late to be on those articles with titles like people we lost this year.The point of the award is that news…
Abuse of Notation — 12/24/2025
Everything we do to secure ourselves, every decision we make out of fear of the future, ends up destroying us, ends up making our future a little more bleak — the closer we are to the public ideal of “success”, the farther we go from our own…
Abuse of Notation — 12/24/2025
When the tower crumbles, some will laugh some will cry, some will fall from the top, some will be buried below. When the tower crumbles, better not be around better go all the way down, so you can run away.
Computational Complexity — 12/22/2025
An easy choice for paper of the year, a paper that has nothing to do with randomness, interaction, quantum, circuits or codes. Just a near quadratic improvement in the amount of memory you need to simulate time.Simulating Time with Square-Root…
The n-Category Café — 12/21/2025
There are two ways to stick SU(2) × SU(3) in Spin(10). One is good for physics; the other, alas, is easily obtained using the octonions.
Computational Complexity — 12/17/2025
The Fine Arts BuildingLast week, I partook of the second Fridays open house in the The Fine Arts Building, ten floors of offices all related to the arts and creatives in some way. Art studios of all kinds, from fine art to photography, music…
The n-Category Café — 12/4/2025
An introduction to the bioctonionic plane and the mathematics needed to understand it.
The n-Category Café — 12/3/2025
A complex-analytic perspective on the indefinite integral of 1/x.
Abuse of Notation — 12/1/2025
I should stop doing category theory. What’s the point?
The n-Category Café — 11/30/2025
Tymoczko gave a good talk on the math of music theory.
Math ∩ Programming — 11/17/2025
In an earlier article, I covered the basic technique for performing matrix-vector multiplication in fully homomorphic encryption (FHE), known as the Halevi-Shoup diagonal method. This article covers a more recent method for matrix-matrix…
Joel David Hamkins — 11/12/2025
This will be a talk for the Logic Seminar at the University of Notre Dame, Tuesday 18 November 20215 2pm 125 Hayes-Healy Building. Abstract. I shall introduce what I call the first-order elementary theory of surreal arithmetic, a theory that is…
The n-Category Café — 11/6/2025
Newton’s Principia is famous for his investigations of the inverse square force law for gravity. But he also studied the inverse cube law. Why, and what is so good about this law?
The n-Category Café — 11/4/2025
You can tweak Heisenberg’s equation so that instead of using a commutator it uses an associator! Then it applies to Jordan algebras other than that of self-adjoint complex matrices.
Joel David Hamkins — 11/4/2025
I am honored to be giving the 2025-26 Charles R. DePrima Memorial Lecture for the Mathematics Department of the California Institute of Technology. This lecture series aims to bring mathematical researchers to Caltech to give talks for a primarily…
The n-Category Café — 11/3/2025
Exploiting the secret 4-dimensional symmetry of the Kepler problem to think about the periodic table of elements in a new way.
DEONTOLOGISTICS — 11/1/2025
It’s been a long time coming, but my second book, The Revenge of Reason, is finally available to buy. There are so many things in here that were written or given as talks long ago but never actually published, and it’s nice to know people will…
The n-Category Café — 10/28/2025
Applied Category Theory 2026 is taking place 6–10 July in Tallinn, Estonia, and it’s preceded by the Adjoint School Research Week, 29 June – 3 July.
Math ∩ Programming — 10/19/2025
Polyhedral optimization is a tool used in compilers for optimizing loop nests. While the major compilers that use this implement polyhedral optimizations from scratch,1 there is a generally-applicable open source C library called the Integer Set…
Abuse of Notation — 10/16/2025
In my last post about generality, I tried to show how our ambition to discover ideas that are all-encompassing and eternal makes our worldview crumble, leaving us unable to think clearly even about simple issues with obvious solutions. Today, I…
The n-Category Café — 10/7/2025
I’m trying to better characterize two maximal subgroups of the group of automorphisms of the exceptional Jordan algebra, whose intersection is the Standard Model gauge group.
Math3ma — 9/25/2025
Over the past couple of years, I’ve been learning a little about the world of quantum machine learning (QML) and the sorts of things people are thinking about there. I recently gave an high-level talk on some of these ideas in connection to a…
Math3ma — 9/25/2025
Next up on Good Reads: The Princeton Companion to Mathematics, edited by Fields medalist Timothy Gowers. This book is an exceptional resource! With over 1,000 pages of mathematics explained by the experts for the layperson, it’s like an…
The n-Category Café — 9/16/2025
The octonions have nontrivial inner automorphisms of order 3. Is this related to triality?
Joel David Hamkins — 9/10/2025
Recently I had the pleasure to give a talk at the Conference on the occasion of Jörg Brendle’s 60th birthday at Kobe University in Japan, and I was invited to make remarks at the conference banquet given in his honor. … Continue reading →
Joel David Hamkins — 8/20/2025
This will be a talk for the Conference on the occasion of Jörg Brendle’s 60th birthday at Kobe University in Kobe, Japan, 2-5 September 2025. Many years ago, I was a JSPS Fellow at Kobe University, at the same time … Continue reading →
Joel David Hamkins — 8/18/2025
This will be a talk I shall give for the History and Philosophy of Science (HPS) Colloquium at the University of Notre Dame, 17 October 2025, 12:30-1:30 pm, 201 O’Shaughnessy Hall. Did Turing ever halt? Abstract. Alan Turing’s 1936 paper … Continue…
Math ∩ Programming — 7/25/2025
On Monday, July 14th 2025, I hosted a mini-workshop on homomorphic encryption at Google’s Portland, Oregon office. Though Portland is a small city, it’s becoming a hub for homomorphic encryption. Intel and Google both have a presence here, as well…
Math ∩ Programming — 7/18/2025
I work on homomorphic encryption (HE or FHE for “fully” homomorphic encryption) and I have written a lot about it on this blog (see the relevant tag). This article is a collection of short answers to questions I see on various threads and news…
Joel David Hamkins — 7/16/2025
This will be a talk for the Fudan Logic Seminar at Fudan University, to be followed immediately by two talks for the Fudan Logic student seminar, forming a mini-conference for the logic group on 23 July 2025. Abstract. I shall … Continue reading →
Joel David Hamkins — 7/14/2025
This will be a talk for the Seminar on Frontier Issues in Logic and Philosophy The First Forum on Logic and Philosophy 逻辑与哲学前沿问题研究”学术研讨会暨第一届逻辑与哲学论坛 Changchun, China, 18-20 July 2025 Pointwise definable end-extensions of models of arithmetic and set…
Joel David Hamkins — 7/9/2025
This will be a lecture series on the Philosophy of Mathematics at Fudan University in Shanghai, China, 30 June – 25 July 2025, as a part of the International Summer School program at Fudan University. Lectures given by Ruizhi Yang … Continue…
Joel David Hamkins — 7/9/2025
This will be a talk for the International Conference on the Philosophy of Mathematics, held at Lanzhou University, China, 25-27 July 2025. How the continuum hypothesis might have been a fundamental axiom Abstract. I shall describe a…
Joel David Hamkins — 6/23/2025
This will be a talk for the Conference on Infinity, a collaborative meeting of logicians and specialists in Chinese philosophy here at Peking University, 24 June 2025, in the philosophy department. Abstract. I shall lay out a spectrum of…
DEONTOLOGISTICS — 6/22/2025
Here’s a recent thread on philosophy of AI from Twitter/X, in which I address rather popular arguments made by Emily Bender and others to the effect that LLM outputs are strictly speaking meaningless. I think these argument are flawed, as I explain…
Joel David Hamkins — 6/11/2025
This will be a lecture series at Peking University in Beijing in June 2025. Announcement at Peking University Course abstract. This will be a series of advanced lectures on set theory, treating diverse topics and particularly those illustrating how…
Abuse of Notation — 5/27/2025
title: A monad layout: microblog category: microblog tags: programming haskell — A monad is when you know how to convert $M (M a)$ to $M a$, but not $M a$ to $a$.
Abuse of Notation — 5/27/2025
The level of progress in programming language design: Shortly after the first ever programming language was created, it’s author said that the language’s whole paradigm is flawed and we should do functional programming instead*. That was 46 years…
Abuse of Notation — 5/27/2025
I want to forget Gaza. I want to forget the pain. I want to forget all dumb jokes, old song lyrics. I want to forget that most things ever happened, as remembering makes everything tedious. Forces you to become a bureaucrat of your memories, to…
Abuse of Notation — 5/27/2025
Every time you eat mushrooms, I have to try them too. Cause, if the mushrooms turn out to be poisonous and you die of slow and painful dead, I will die as well. I once dreamed that I was dying, You were beside me, I turned to you and said, “I don’t…
Abuse of Notation — 5/27/2025
The road I walk is new. It’s made not of stone, but dirt. There are no road signs yet. And no bridges to cover the rivers. The road I walk is new, so people think that it is hard. “How do swim?” “Don’t you get dirty?” “How do you cope with all that…
Abuse of Notation — 5/27/2025
Out for a walk I let go and let the city dissolve me.