Joel David Hamkins — 4/4/2026
This will be a talk for the Logic Seminar at the University of Notre Dame, 14 April 2026, 2pm, Room 125 Hayes-Healey. Abstract After establishing several general features of the hierarchy of consistency strength, we shall consider the possible…
Blog - Logic Matters — 4/2/2026
Well, that all took rather longer than expected … A lot of repairing and filling and preparation (the joys of a late Victorian house). But at last the miniature room that counts as my study is redecorated. A carpet remains to be laid in ten days,…
Computational Complexity — 4/1/2026
I blogged about Pope Leo XIV here. Pope Leo XIV has an undergraduate degree in mathematics. He saw my post and asked for my help with his latest encyclical. LEO: Let’s have lunch together at Popeyes.BILL: Why Popeyes?LEO: The name is Pope-yes so I…
The Aperiodical — 4/1/2026
Double Maths First Thing insists it’s March 32nd Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight in mathematical thinking. After the clock change and a trip to that London – we chanced on a Rob Eastaway…
Math ∩ Programming — 4/1/2026
It’s the 5th annual April Cools! Here are my previous April Cools articles This year it’s a book review of Ben Recht’s book, The Irrational Decision: How We Gave Computers the Power to Choose For us, released Mar 10, 2026. The publishing industry…
Fractal Kitty — 4/1/2026
IntroductionLet’s start with E. Its opposite is O. So if we flip E, we get O. Let’s make a pattern. EE OE O O EE O O E O E E OHow is this pattern constructed? What comes next? Write
Crooked Timber — 3/30/2026
As I approach formal retirement from my academic job, I’m still thinking about ideas in my main theoretical field of decision theory. But I’ve largely lost interest in publishing journal articles, leaving the chore of dealing with Manuscript…
Computational Complexity — 3/29/2026
Occasionally I run into what I consider fun problems in complexity, that require just a little bit of out of the box thinking. They require some background in theory, but nothing too deep. Some of these problems have been mentioned before on my…
Joel David Hamkins — 3/28/2026
I am very pleased to announce that The Book of Infinity is now available for pre-order. Check it out at your favorite booksellers. From the preface: Come, let us explore infinity! We shall visit all my favorite paradoxes and conundrums. The ancient…
The n-Category Café — 3/27/2026
Slides for a talk on features of the octonionic projective plane.
Blog - Logic Matters — 3/25/2026
Some of my very favourite paintings are Annunciations … the stunning Leonardo and Botticelli in the Uffizi, the lovely small painting from a predella by Domenico Veneziano close to home in the Fitzwilliam, the wonderful Filippo Lippi in the…
Computational Complexity — 3/25/2026
High table dinner at MagdalenMy time in Oxford has come to an end and I head back to Chicago this week. I was a visiting Fellow at Magdalen (pronounced “maudlin”) College for the Hilary Term.There’s a six week break between the eight-week Hilary…
The Aperiodical — 3/25/2026
Double Maths First Thing saw two shooting stars last night Hello! My name is Colin and I am a mathematician on a mission to spread the joy of thinking mathematically, solving problems and generally doing creative things with one’s brain. Such as,…
Computational Complexity — 3/22/2026
If I get an email offering me a $1000 for I DON”T KNOW SINCE I ignore it and don’t even bother looking for other signs it is a scam. If I get an email offering me $100 I may look more carefully and often they are legit (most common is to give a…
Crooked Timber — 3/22/2026
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.
Fractal Kitty — 3/20/2026
When I create art, I do so for many reasons. Some of these are:to engage in an expression of beingto explore a concept or experiment with an ideato grow as a person through creativity and struggleto immerse myself in a spiritual actto have a coping
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…
Blog - Logic Matters — 3/16/2026
In the last couple of years, Dirk Hoffmann has published English translations of two of his books which originally appeared in German. In 2024, he gave us Gödel’s Incompleteness Theorems (Springer), which I will discuss in a future post. And then…
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…
Blog - Logic Matters — 3/4/2026
Some good things come out of America — Dvořák’s String Quintet Op. 97, for example, written while he was staying with a Czech-speaking community in Iowa for the summer of 1893. And there was a quite joyous performance a few days ago at Wigmore Hall…
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
Blog - Logic Matters — 2/28/2026
As I said some weeks ago, I am slowly revising my Introduction to Gödel’s Theorems; I am still only about a third of the way through. I haven’t yet spotted any real horrors, but I’ve found some ways of re-arranging the material for the better, and…
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.
Abuse of Notation — 2/22/2026
In the 19th century, Copernicus, Newton, Galilei et al pushed a revolutionary new idea that reshaped the way we think… but no, it’s not talking about cosmology, but about theology. This idea, (which was also the real reason they were in so much…
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…
Blog - Logic Matters — 2/18/2026
It is time at last to redecorate my small but now rather depressingly shabby study. Already books from the top shelves are piled in a hallway, and the rest are covered in plastic sheeting as I start tackling the late Victorian ceiling (which isn’t…
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,…
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…
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…
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…
Fractal Kitty — 2/6/2026
Whether you call this triangle Pascal’s triangle, Binomial Expansion Coefficients, Yang Hui’s triangle, or any other name, it is beautiful.Finding patterns in this triangle is fun - from counting numbers, to looking at parity (even/odd-ness), to…
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…
Fractal Kitty — 1/29/2026
Have you ever been to a quilt store and bought fabric without a plan? You just saw the pretty colors and patterns and went for it? Well, I did - with a jelly roll of white, beige, grays, and black with mathy patterns (Note: A jelly roll is a roll
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….
Blog - Logic Matters — 1/26/2026
So far — but then I am still in the foothills, tinkering with early chapters — I have found just a couple of minor expositional stumbles in An Introduction to Gödel’s Theorems. I have spotted, though, quite a few places where I can make the text…
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,…
Blog - Logic Matters — 1/19/2026
I didn’t at all intend to return to my Introduction to Gödel’s Theorems (which I’ve not really read for a dozen years, apart from correcting a small handful of typos in the PDF). But I had occasion to look something up, and — hey, ho! — I’ve found…
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…
Blog - Logic Matters — 1/13/2026
There comes a tipping point, when the prospect of yet another round of proof-reading becomes intolerable and you think, dammit, the book as it is will now just have to do! So I have drawn a line, put the latest version of Introducing Category…
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!…
Blog - Logic Matters — 1/5/2026
The first issue of the new Journal for the Philosophy of Mathematics appeared back in September 2024. A second issue, now edited by Alex Paseau, has now appeared, just a day before the end of 2025. This is a collection of just seven, again mostly…
Fractal Kitty — 1/1/2026
Happy New Year! It’s time for Genuary 2026! I am not sure how many prompts I will do (or combine), but I hope to share my code and progress here. I hope to get at least 5-10 done this year with a mix of different languages and approaches.
Fractal Kitty — 12/31/2025
IntroductionIn this inquiry, we explore chords, which are lines drawn across circles, using different rules to create various patterns, curves, and shapes. This inquiry will be different from those in the Inquiries Series in that it will be more…
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.
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.
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.
Fractal Kitty — 12/2/2025
December Adventure was started by Eli_oat at Oatmeal. I love seeing what others do this month - here is a log of logs.This December, I plan to make a generative quilt, play with origami, doodle some mossy mandalas, set up next year’s journal, and…
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…
Fractal Kitty — 11/8/2025
A coded poem and trackThe Track:Initiated on a piano, and realized on an OP-1 Field. somewhere here0:00/101.302857142857151×The Visual:Human coded in p5js with p5sound - enjoy in fullscreen. Click here for the visual with music - (CW: Strobing…
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?
Fractal Kitty — 11/6/2025
IntroductionIn this inquiry, nodes are connected one at a time. How many lines can you draw before a triangle emerges?Starting with FourLet’s start with four nodes - draw them on a sheet of paper. How many lines (called edges) can you draw before a…
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.