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.
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…
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,…
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…
Crooked Timber — 2/13/2026
I’m not a Rawlsian, though I would admit to certain affinities, and, indeed, I’ve used the device associated with Rawls (though not invented by him) of the veil of ignorance in my own work. But when I disagree with Rawls, I hope I at least take the…
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 →
The Aperiodical — 2/11/2026
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of January 2026, is now online at Letters and Words. The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical….
Crooked Timber — 2/11/2026
Now this Seth… did leave children behind him who imitated his virtues…. They also were the inventors of that peculiar sort of wisdom which is concerned with the heavenly bodies, and their order. And that their inventions might not be lost before…
The Aperiodical — 2/11/2026
Double Maths First Thing still has PRE earworms Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight that comes from engaging whole-heartedly with maths. I’ve been in Peterborough this weekend playing with the…
The Aperiodical — 2/9/2026
Here’s a question that’s been in the back of my head for a while: Starting from 1 and with just the arithmetic operations + – × ÷ available to you , how quickly can you build up to a given target number? You can do this on pen and paper, or even…
The Aperiodical — 2/9/2026
Here’s some mathematical news from last month that we didn’t otherwise report here. Sad news Dr Gladys West, one of the “Hidden Figures” behind developing the maths of GPS, has died. She was 95. (via A. Rivera). Metafilter has a comprehensive post…
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…
Crooked Timber — 2/4/2026
Which jobs will be replaced by AI? Here is a modest proposal.* Replace higher management by AI. Not “management” in the sense of the teamleader who works alongside their colleagues with a bit more responsibility to make decisions and mediate…
The Aperiodical — 2/4/2026
Double Maths First Thing is cranking the handle to bash a stop sign into a boot. Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in mathematical thinking and process. This week, I am mainly recovering from…
Crooked Timber — 2/3/2026
Healthy babies, to be specific. Because worldwide, infant and child mortality has fallen greatly; and is still falling; and will almost certainly continue to fall. In premodern societies, meaning pretty much the entire world before 1820 or so,…
Crooked Timber — 2/3/2026
… to reader and commenter Doctor Memory. We noticed recently that old posts weren’t displaying properly, apparently because we’d used a markup language (Textile) that our current setup doesn’t support. We put out an appeal on Bluesky, and Dr M was…
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…
Crooked Timber — 2/2/2026
My dad genuinely had no interest in music. Well, almost none – he did enjoy novelty songs from time to time, but not really for the music. Our friend Bob, who is otherwise quite sensible, used to try to convince him that listening to music would…
Crooked Timber — 2/1/2026
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…
The Aperiodical — 1/30/2026
A conversation about mathematics and communicating mathematics inspired by a ‘Certified Mathematical Object’ sticker. Presented by Katie Steckles and Peter Rowlett, with special guest Chris Nho from Public-Math.org.
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
Crooked Timber — 1/28/2026
Ever since it became evident that Trump was likely to be re-elected, I’ve been among the most pessimistic of commentators on the likely course of US politics (most recently here for example). I’ve also been nowhere near pessimistic enough. I…
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…
Crooked Timber — 1/26/2026
So the Trump administration has just pulled the US out of the World Health Organization, WHO. WHO is the biggest and most important international health organization. It’s an arm of the United Nations. It’s been around since 1948. Almost every…
Crooked Timber — 1/25/2026
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 — 1/22/2026
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 — 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…
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…
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…
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…
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.
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…
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…
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…
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…
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 —…
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…
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…
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…
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,”…
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…
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?
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…
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…
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…
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…
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…
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…
Fractal Kitty — 10/1/2025
This is the post I’ll update with this year’s Mathober art. Check back and see what’s been added throughout the month. Link, Deviation, PolyhedronStrongly, Digraph Sink, Partial SumNotation (find the sigma)P5.js sketchesLink, Deviation,…
Fractal Kitty — 9/28/2025
Kristin Henry has been providing SciArtSeptember prompts each year. I incorporated all of the prompts into a single sketch this year. 1. Fluid 2. Coral 3. Inertia 4. Diffusion 5. Skeleton 6. Growth 7. Virus 8. Permutation 9. Element 10. Algae 11….
Fractal Kitty — 9/25/2025
Today is math storytelling day, so I thought I would make a visual coloring sheet as a prompt for others. What characters live in this world? What stories are there to tell? What number system would you have? What mathemagical spells would you…
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…
Fractal Kitty — 9/16/2025
Mathober is almost here! I am looking forward to seeing everyone’s creativity and take on this year’s prompts. If you’ve never participated before, now’s the perfect time to jump in!The goal of Mathober is simple: have fun, learn, grow, and play
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 →
Fractal Kitty — 8/26/2025
IntroductionIn this inquiry, triangles are dissected into smaller triangles with vertices labeled as either light (L), medium (M), or dark (D). Any triangles that are LMD triangles are shaded with color. Triangle playLet’s start with a triangle…
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…
Fractal Kitty — 7/11/2025
Haiku + Codewith a second take dance with the first – tethered massorbiting encores .iframe-container { position: relative; width: 100%; height: 0; padding-bottom: 100%; /* 1:1 aspect ratio - square */ overflow: hidden; …
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…
Fractal Kitty — 7/3/2025
IntroductionExplore the reflection and rotation of polygons to discover the patterns that emerge. Polygon PlayLet’s start with a triangle ABC. We can rotate clockwise so that each vertex moves clockwise by one step: We can also reflect (or flip)…