Crooked Timber — 1/12/2026
For the last year or so, left-leaning UK voters have been subjected to the looming nightmare that Reform – a bunch of xenophobes and welfare-state-slashers – might form the next government. There has been very little silver lining to this. The one…
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…
Crooked Timber — 1/11/2026
Crooked Timber — 1/8/2026
I’ve been asked by a couple of friends, who have signed contracts to write nonfiction trade books, whether I have any advice on how to make sure the book gets written. I think in general non-fiction trade writing is quite a different challenge from…
Crooked Timber — 1/7/2026
In political epistemology, there is a lot of criticism of the metaphor of the “marketplace of ideas,” the thought that people somehow “trade” in arguments or ideas and thereby arrive at true beliefs.* The longer you think about it, the less sense…
The Aperiodical — 1/7/2026
Double Maths First Thing is struggling with its J perms Hello, and happy new year! My name is Colin and I am a mathematician on a mission to spread joy, delight and happiness in not-understanding and then, finally, understanding maths. I’m getting…
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!…
The Aperiodical — 1/6/2026
Here’s some mathematical news from last month we didn’t otherwise report on here. Awards and Honours The European Mathematical Society has awarded the 2025 Fermat prize to Vesselin Dimitrov and Vlad Vicol, “for breakthroughs in number theory,…
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…
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…
The Aperiodical — 1/5/2026
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of December 2025, is now online at The Scribble Board. The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical….
Blog - Logic Matters — 1/4/2026
More than twenty years ago, Robert Brandom wrote Making it Explicit, a 762 page ramble of hand-waving pretentiousness. The sort of philosophical tome I detest. His shortened version Articulating Reasons just exposed how creaky the whole Brandomian…
Crooked Timber — 1/4/2026
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…
Crooked Timber — 1/2/2026
Over the past few days I’ve found myself mulling the question of whether AI will destroy art and literature. Initially, I found myself comforted by a thought, articulated by Carrie Jenkins on bluesky, that since the value of art lies not simply in…
The Aperiodical — 1/2/2026
A conversation about mathematics inspired by a Venn diagram. Presented by Katie Steckles and Peter Rowlett, with special guest Keisha Thompson. Katie mentioned the MathForEquality badges and pins.
Blog - Logic Matters — 1/1/2026
As I have said more than once before, self-publishing was exactly appropriate for the Big Red Logic Books. I am way past the stage of needing the brownie points that are gained by continuing conventional publication. The books are aimed at…
Crooked Timber — 1/1/2026
To all of you – a healthy, flourishing, and meaningful 2026! To the world – I am less sure where to begin, since 2025 was, politically and morally speaking, one of the worst years since long. Let’s hope for peace, definitely. Responsible leaders…
The Aperiodical — 12/31/2025
The UK Government have announced the latest list of honours, and we’ve taken a look for the particularly mathematical entries. Here is the selection for this year – if you spot any more, let us know in the comments and we’ll add to the list. Get…
The Aperiodical — 12/31/2025
Double Maths First Thing is looking for the man with the noses. Hello! My name is Colin and I am a mathematician on a mission to show that maths, proper maths, is a joyful and creative endeavour. I’m also on a mission to shift a stinker of a cold….
Crooked Timber — 12/29/2025
I read a post on one of the social media platforms written by a professor who was sharing his experience with giving away ten percent of his income, after he signed the “Ten percent giving pledge” many years ago. In deciding what or whom to give…
Blog - Logic Matters — 12/28/2025
It was only a bit over six months ago that I was using ChatGPT and Claude as proof-reading assistants as I prepared the second edition of Introducing Category Theory. I certainly found them pretty useful even if far from glitch-free, so I am again…
Blog - Logic Matters — 12/24/2025
Sadly, we still haven’t yet been, as we planned, to the Fra Angelico exhibition at the Palazzo Strozzi and San Marco in Florence. “Momentous and inexpressibly beautiful … a miracle of an event” said the NYT review: others have similarly extolled…
The Aperiodical — 12/24/2025
Double Maths First Thing is not stirring. Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in mathematical creativity. It’s Christmas Eve (babe), which means I probably need to switch off from looking out for…
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.
Crooked Timber — 12/21/2025
Blog - Logic Matters — 12/19/2025
I have just uploaded a PDF of the current draft of a revised second edition of Introducing Category Theory. I will tinker with the draft over the next few weeks, proof-reading with some help from Gemini this time, but also — more importantly —…
The Aperiodical — 12/19/2025
A conversation about mathematics inspired by a slice of pizza. Presented by Katie Steckles and Peter Rowlett.
Crooked Timber — 12/18/2025
Having watched the film, I thought I’d get Robert Linhart’s book off the shelf and finally read it. I think I bought it in Oxford in the early 80s. To remind you, it depicts Linhart’s experience as a Maoist cadre who has chosen to get a job in a…
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 Aperiodical — 12/17/2025
Double Maths First Thing is not, and has never been, a Grade 2* listed building. Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in learning, understanding and doing maths. I’ve just had an excellent long…
Computational Complexity — 12/14/2025
ONEThe following headline confused me: Trump, 79, Deletes Weird AI Video Shilling Magic Beds (see here). Was Weird Al selling magic beds? Magic beds?! How does that relate to President Trump? What’s going on?The problem is the…
The Aperiodical — 12/14/2025
We chatted to Chris Dawson – the creator of Jigsy, a shape-based puzzle app which we’ve enjoyed playing – to find out more about where it came from and how it was developed. What is Jigsy? A brand new spatial reasoning visual puzzle concept. At its…
Crooked Timber — 12/14/2025
Computational Complexity — 12/13/2025
The playwright Tom Stoppard passed away at the age of 88 on Nov. 29, 2025.ONE) He wrote many plays and some movies. Below I highlight his works whose themes I think will be of interest to my readers (Or at least to me—your mileage may…
Computational Complexity — 12/11/2025
Watching Mathematicians at Work (AI generated)The Smithsonian Natural History Museum has a FossiLab where visitors can peek through windows watching scientists prepare fossils for conservation. Maybe we should have a similar exhibit at math museums…
Crooked Timber — 12/10/2025
I am at the airport in Melbourne (again). I’m sitting in the window eating one of those excellent boxes of kale, broccoli, beans, seeds, peas and a boiled egg that I am grateful are now available at airports. Next to me a father and daughter are…
Crooked Timber — 12/10/2025
My last post described my attempt to generate a report on housework using Deep Research, and the way it came to a crashing halt. Over the fold, I’ve given the summary from the last version before the crash. You can read the whole report here,…
Crooked Timber — 12/9/2025
I’ve long been interested in the topic of housework, as you can see from this CT post, which produced a long and unusually productive discussion thread [fn1]. The issue came up again in relation to the prospects for humanoid robots. It’s also at…
Crooked Timber — 12/7/2025
Blog - Logic Matters — 12/6/2025
I’m still hoping to get a new version of Introducing Category Theory out in January. I want to rewrite the chapter on power objects which is a bit dense, and also carefully read through Part II once more for reader-friendliness: but changes should…
The n-Category Café — 12/4/2025
An introduction to the bioctonionic plane and the mathematics needed to understand it.
Computational Complexity — 12/4/2025
(ADDED LATER- a Sad Note. The older Charles Lin passed away in December of 2025.)In 2001 I supervised Charles Lin’s Master’s Thesis, which was on Private Information Retrieval.In 2025 I supervised Charles Lin’s Master’s Thesis, which was on Ramsey…
Computational Complexity — 12/4/2025
Inspired by Daniel Litt’s X PostStarted asking mathematicians whose career started before the internet if they think Google, email, etc. have sped up the pace of math research. Wide variety of opinions but the broad consensus seems to be “yes,”…
The n-Category Café — 12/3/2025
A complex-analytic perspective on the indefinite integral of 1/x.
Computational Complexity — 12/1/2025
BILL: I honestly do not know whether ChatGPT will make programmers more productive. (I am not touching question of whether it puts programmers out of work. That’s a problem for Future Bill.) Who can I ask? I found two people who disagree on the…
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.
Computational Complexity — 11/24/2025
Last week we had a talk by Purdue philosophy professor Eamon Duede Tail Novelty, Knowledge Collapse, and Useful Frictions in Science. In part of the talk he argued that if AI makes writing technical papers easier, researchers will write up small…
Blog - Logic Matters — 11/22/2025
Not the best few weeks. Old people have health issues. Who knew? We were planning to go to Italy in a week or so, in particular to see the wonderful-sounding Fra Angelico exhibition at Palazzo Strozzi. Hopefully we will still be able to catch that…
Computational Complexity — 11/20/2025
Carmichael Numbers are the bane of probabilistic primality algorithms. You have to go through extra steps just to handle these relatively rare numbers. But did you know that the Miller-Rabin algorithm not only determines the compositeness of…
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…
Computational Complexity — 11/16/2025
Since there is now a CCC Test-of-Time Award, see here, (CCC stands for Computational Complexity Conference), I decided to look at other Test-of-Time awards in computer science.Below is a list of various computer science Test-of-Time awards, along…
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…
Computational Complexity — 11/12/2025
In 2016, in the pre-transformer times, Georgia Tech professor Ashok Goel gave a prescient TEDx Talk on an AI teaching assistant for his large online Artificial Intelligence course. Students would ask questions to an online forum, and fellow…
Computational Complexity — 11/10/2025
A friend of mine told me that in the last six months, the last grandchild of one of our former presidents (who had already passed away) died.I tried to deduce who it was without checking the web directly. For example, I looked up when various…
Computational Complexity — 11/6/2025
We’re seeing an attack on capitalism on both ends of the political spectrum with with the election of Democratic Socialist Zhoran Mamdani as mayor of New York, and Donald Trump trying to direct the economy through tariffs, less independency of the…
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.
Computational Complexity — 11/4/2025
The following excerpt from Abrahim Ladha’s comment on Lance’s post aboutAI and intro theory caught my attention:—————————BEGIN EXCERPTNot just with AI, but in theory and math courses, there have always been Bart Simpsonlevel…
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.
Blog - Logic Matters — 11/1/2025
I’m slowly working on a corrected update of Introducing Category Theory, perhaps for early in the new year. But you can today download a new PDF version, without any of the revised content, but now with the bookmarks for chapters and sections…
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…
Computational Complexity — 10/31/2025
The advances in artificial intelligence have changed the way we think about computing. For today’s post, how nonuniformity plays a much larger role than I previously believed.First, some background. Circuit complexity gives a different, more…
Blog - Logic Matters — 10/29/2025
We were supposed to be in Bergamo for a few days. But when it came near the time, neither of us were feeling up to going — was it a recurrence of Covid? It was a rather good thing that we didn’t set off, as whatever virus it was led to sudden…
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.
Computational Complexity — 10/27/2025
I sometimes give the following advice for research which I label Bill’s Bad Advice. We will later see who it might be good advice for. Spoiler alert: the number of people for whom it is good advice is shrinking but might include Lance especially…
Computational Complexity — 10/23/2025
This fall, for the first time at Illinois Tech, I’m teaching Introduction to Theory of Computation. While I’ve taught a variation of this course a couple dozen times, I last taught this class Spring 2016 at Georgia Tech. Intro Theory is a course…
Computational Complexity — 10/21/2025
Several people emailed me that September 16, 2025—written as 9-16-25 in the US—represents the integer side lengths of a right triangle.9-16-25 is the only such triple that is also a valid date. This kind of mathematical alignment only happens…
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…
Computational Complexity — 10/15/2025
Each fall I try to predict the theory computer science faculty job market to come and give suggestions to those going after them. Get set for a rocky ride, with AI’s disruption of computer science, fiscal stress at universities, and new U.S….
Computational Complexity — 10/8/2025
A few comments to last week’s post Computers Don’t Want suggested that human brains are just advanced computers, yet still possess agency and desires. But are we just Turing machines? I wrote about this question before but let’s revisit in the…
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.
Abuse of Notation — 9/27/2025
“My life is like a prison” I wrote this in my personal website when I was 14. I was quite correct in pinpointing the problem, pinpointing how I, and many other people, felt, but I was off at identifying the cause — I thought, that I was kept in…
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?
The n-Category Café — 9/13/2025
Adjoint School guest post by Khyathi Komalan and Andrew Krenz
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 →
The n-Category Café — 8/30/2025
All equivalences are generated by just the strict, literally surjective ones.
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…
The n-Category Café — 8/15/2025
This week, 50 category theorists and software engineers working on “safeguarded AI” are meeting in Bristol.
The n-Category Café — 8/5/2025
Comparing two mathematical notions of diversity.
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 $a$.