The n-Category Café — 9/16/2025
The octonions have nontrivial inner automorphisms of order 3. Is this related to triality?
Crooked Timber — 9/16/2025
A trolley problem, some personal stuff, a bit of Islamic jurisprudence, and then the Honda. 1) Trolley time. Let’s start with the trolley problem. People proposing trolley problems often do them in two parts. First, there’s the anodyne one…
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
Computational Complexity — 9/15/2025
“I’ll be on vacation so I won’t be checking email.’‘“I can’t be at the meeting since I will be out of town’‘Technology has made it so that:a) You really CAN get email when you are on vacation.b) You really CAN go to a meeting if you are out of town…
Math3ma — 9/15/2025
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…
Crooked Timber — 9/15/2025
You’ve probably heard of the “Peter principle”: that employees get promoted until they reach a job they are no longer good at. And in political philosophy, there is a famous dispute between (the camps of) John Rawls and Jerry Cohen about the…
Crooked Timber — 9/14/2025
This weekend has been dedicated to the “reconstitution historique” of 1653 in Pézenas, when the États generaux of Languedoc met in what is now a small town but was then the seat of the Prince de Conti. So, a capital city back then and also a place…
Blog - Logic Matters — 9/13/2025
What have I been reading this week? I finished The Voyage Home, the most recent in Pat Barker’s wonderful series re-imaging episodes from the Trojan War. This time, it’s Agamemnon’s voyage home after the war, and his death at the hands of…
The n-Category Café — 9/13/2025
Adjoint School guest post by Khyathi Komalan and Andrew Krenz
Crooked Timber — 9/12/2025
I’m working on a first draft of a book arguing against pro-natalism (more precisely, that we shouldn’t be concerned about below-replacement fertility). That entails digging into lots of literature with which I’m not very familiar and I’ve started…
Computational Complexity — 9/11/2025
(After I wrote this post Lance tweeted a pointer to a great talk by Ronald de Wolf with more examples, and also examples of quantum proofs, see here.)I was teaching the prob method for lower bounds on Ramsey Numbers (see my slides here).As often…
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 Aperiodical — 9/10/2025
DMFT turns around, and every now and then it falls apart Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in mathematics. I’m tutoring a bit of Further Core Pure 1 this year, and it was quite instructive to do…
Crooked Timber — 9/9/2025
Mr Magpie has always been a bold friend. He sits at the table with us when we are outside. In the warmer months when we often leave the back door open he walks inside the house, sometimes looking for a snack, but often enough walks all the way…
Crooked Timber — 9/9/2025
I seem to have become CT’s resident moderate techno-optimist. So let me push back a little: here are five things that we’re not going to see between now and 2050. 1) Nobody is going to Mars. Let me refine that a little: nobody is going to Mars and…
Computational Complexity — 9/8/2025
When I first became a professor I had it all planned out, I would do research, teach and supervise students, get tenure and do more research, teach more courses, and supervise more students for the rest of my life. But once I got tenure, instead of…
Crooked Timber — 9/7/2025
Blog - Logic Matters — 9/6/2025
Just before we went off to Zürich, we had our house painted outside (the doors, the windows, and so forth). It took fourteen days, not because we have a mansion but because a lot of preparatory work was needed, cutting out minor rot, repairing,…
Crooked Timber — 9/5/2025
I do these occasional posts about science papers. Some are just for fun. But sometimes — honest! — there’s an underlying connection to the greater Crooked Timber project. This post is one of that sort, because it’s about the limits of…
The Aperiodical — 9/3/2025
The number one component of music that really gets my attention is Brian May plays guitar, but a very close second is clever lyrics. The first morning of 2025’s Talking Maths in Public (TMiP) conference, from waking up, through carving myself a…
The Aperiodical — 9/3/2025
DMFT rocked. Hello! My name is Colin and I am a mathematician, on a renewed mission to spread the joy and delight in maths after a tremendous few days at the Talking Maths in Public conference. I listed some highlights here, and decided that rather…
Computational Complexity — 9/2/2025
Coding Style Is ImportantDoes coding style matter? We teach students how to write code and about algorithms. But, do we discuss coding style? Some people may say that style is just personal preference. But, there is undoubtedly good style and bad…
The Aperiodical — 9/2/2025
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of August 2025, is now online at Flying Colours Maths. The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical….
Crooked Timber — 8/31/2025
Looking at the facts, there’s no reasonable conclusion except that US democracy is done for. But rather than face facts, I’m turning to fiction. So, here’s a story about the collapse of Trumpism, crony capitalism and the AI/crypto bubble. Fiction…
Crooked Timber — 8/31/2025
Blog - Logic Matters — 8/30/2025
It is difficult to believe that Hugh Mellor died over five years ago: he was a very generous and loyal friend, and still much missed. And I have been thinking about him particularly this week, prompted by Tim Crane’s newly published biographical…
The n-Category Café — 8/30/2025
All equivalences are generated by just the strict, literally surjective ones.
Crooked Timber — 8/29/2025
I was recently part of an online discussion that asked this question. People were talking about industry, democracy, civil society, world leadership, you name it. But nobody was asking the obvious question: when, in fact, will the sun set on the…
Computational Complexity — 8/27/2025
This will be one of a series of posts that I’ve always wanted to write but I needed to wait until I was no longer an academic administrator.Logic is critical to proving theorems but it’s the wrong way to argue for resources.When I was such an…
The Aperiodical — 8/27/2025
Double Maths First Thing is at about 3.5/5 on the ready-to-rock-o-meter HELLO $CURRENT_LOCATION! Sorry, hang on, the show isn’t until tonight. Let me switch off rock god mode and try again. Hello! My name is Colin and I am a mathematician on a…
Crooked Timber — 8/27/2025
People are wondering how Trump could get away with nationalizing 10% of Intel, with plans to acquire more corporate assets for the Federal government, while hardly hearing a peep from other Republicans. Isn’t this socialism, which is anathema to…
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…
The Aperiodical — 8/25/2025
Books. Every self-respecting mathematician’s floor has a pile of them, some half-read, others to re-read, some merely providing structural support. In The Mathematician’s Library, Thomas K. Briggs considers an alternative approach to the…
Crooked Timber — 8/25/2025
My friend was bitten by a dog this summer. For British readers: being bitten by a dog elsewhere in the world isn’t merely painful, scary and shocking. It brings with it a real possibility of rabies. For non-British reader – really, I’m not making…
Computational Complexity — 8/24/2025
(This post was inspired by George Foreman, who passed away March 21, 2025, at the age of 76.)About 10 years ago I asked my classWhat is the best invention or tech advance of the last 50 years?Here are the answers I got NOT ranked.1) The internet….
Crooked Timber — 8/24/2025
Blog - Logic Matters — 8/23/2025
It is time to face the book problem again. We had to clear a whole floor-to-ceiling bay of bookshelves so our plumber could drop new pipework down at the back of the bay (long boring story). And we forced ourselves to be selective about what to…
Crooked Timber — 8/22/2025
I managed to time things perfectly – I had a conference in Manchester after day one of the Cheltenham festival, which our friend Bob hasn’t missed since 1953, so we all went to see the first day of Gloucestershire v Hampshire (starring Wisconsin’s…
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 →
Computational Complexity — 8/20/2025
I’ve heard this story from a few places. A father watches Back to the Future II with his kid. The 1989 movie view of 2015 looks entirely different when in fact not much has changed except for the fashion and the lack of mobile phones. This is…
The Aperiodical — 8/20/2025
Double Maths First Thing is looking forward to the cricket Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight of doing maths, solving puzzles, and feeling really clever about it. This week, we’re planning to…
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…
Computational Complexity — 8/18/2025
Tom Lehrer passed away on July 26, 2025, at the age of 97. I wrote a blog-obit here. One of my readers read the post and went down a rabbit hole (or did he?), which lead to a blog post about rabbit holes here. A few more notes about Tom L.1) When…
The n-Category Café — 8/15/2025
This week, 50 category theorists and software engineers working on “safeguarded AI” are meeting in Bristol.
Computational Complexity — 8/13/2025
Last month the New York Times highlighted some AI generated short movies, including Total Pixel Space, by Jacob Adler that gets philosophical about information, à la infinite monkeys. It imagines the finite number of images and video that contain…
The Aperiodical — 8/13/2025
Double Maths First Thing feels like this rubber band is getting longer. Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in maths. This week I’m mainly on childcare duty and watching the calendar until I can…
Computational Complexity — 8/10/2025
NICK: I read and enjoyed your blog post on Tom L (see here). I then spent 40 minutes down a rabbithole listening to his music on YouTube.BILL: You call that a rabbit hole?! A while back I spent 3 hours reading questions and answers on quora…
Blog - Logic Matters — 8/9/2025
Five days in Zürich, mostly to have quality time with The Daughter. Hence more hours have been spent in long lunches and dinners, and strolling, and stops for mother/daughter shopping, than in ticking off the tourist top ten must-sees. Which has…
Computational Complexity — 8/7/2025
AI and VacationI’m back from my German vacation. This was my first AI vacation, by which I mean how I used AI to navigate a foreign country. Taking a picture of a hand-written menu board, not just to translate the dishes, but to get a description…
Math3ma — 8/7/2025
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…
The Aperiodical — 8/6/2025
Double Maths First Thing keeps getting bumped to the next room Hello! My name is Colin and I am a mathematician on a mission to spread delight and joy in mathematical thinking and practice. This week, the kids are at a sailing course. I’ve never…
The n-Category Café — 8/5/2025
Comparing two mathematical notions of diversity.
Computational Complexity — 8/5/2025
A guest post by Eric Allender prompted by an (incorrect) P ≠ NP proof recently published in Springer Nature’s Frontiers of Computer Science.For a time, I served as Editor-in-Chief of ACM Transactions on Computation Theory, and in this role I had to…
The Aperiodical — 8/4/2025
Welcome to the 241st Carnival of Mathematics, hosted here at the home of the Carnival, The Aperiodical. The Aperiodical is a shared blog written and curated by Katie Steckles (me), Christian Lawson-Perfect and Peter Rowlett, where we share…
The n-Category Café — 8/2/2025
I hear that Jack Morava died on August 1, 2025.
Blog - Logic Matters — 7/31/2025
I hadn’t planned to return to Introducing Formal Logic just yet. But the last week or so I’ve found myself tinkering with the opening chapters. And, sad to relate, I’ve been enjoying the tinkering. So I might continue doing just that. The first…
Computational Complexity — 7/29/2025
Tom Lehrer passed away on Saturday July 26 at the age of 97. (For other obits see this collection of ten obits here.)He worked in both of my fields of interest: Parody Songs and Mathematics. 1) He got a BA in Mathematics from Harvard, magna cum…
Computational Complexity — 7/29/2025
UMCP has a building named The Francis Scott Key BuildingSTUDENT: How much money did Francis Scott Key give to have a building named after him?BILL: He didn’t give money. He wrote The Star Spangled Banner.STUDENT: I get it! He left the royalties!…
Computational Complexity — 7/28/2025
I am curious how AI or humans can do on the following question.I have listed out the nominees for Prez and VP (Vice Prez) since 1976 and put them in two categories.What criteria did I use?The criteria is about their lives. So it’s not going to be…
Computational Complexity — 7/28/2025
In a prior post I asked what criteria I used to place Prez and VP nominees since 1976 into two groups. In the book Abundance I read that since 1984 all of the Democratic nominees for Prez and VP except Tim Walz had gone to law school. I decided to…
The n-Category Café — 7/28/2025
Can the Duflo isomorphism explain the extra 1/2 in the Hamiltonian for the quantum harmonic oscillator?
The n-Category Café — 7/25/2025
Kevin Coulembier has come out with a paper claiming to prove some conjectures on 2-rigs that Todd Trimble, Joe Moeller and I made.
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…
The n-Category Café — 7/25/2025
Announcing the Clowder Project: a wiki and reference work for category theory built using the same general infrastructure and tag system of the Stacks Project.
The n-Category Café — 7/25/2025
Todd Trimble and I wrote a paper on characterizing classical groups (and monoids) in terms of their 2-rigs of representations.
The n-Category Café — 7/25/2025
Did you know that Lawvere did classified work on arms control in the 1960s, back when he was writing his thesis?
The n-Category Café — 7/24/2025
First lecture in a 4.5-hour minicourse on combinatorics with species.
The n-Category Café — 7/24/2025
Second lecture in a 4.5-hour minicourse on combinatorics with species.
The n-Category Café — 7/24/2025
First lecture in a 4.5-hour minicourse on combinatorics with species.
The n-Category Café — 7/24/2025
How do you count rooted planar n-ary trees with a given number of leaves? Use Lagrange inversion!
Blog - Logic Matters — 7/23/2025
At Wigmore Hall a few days ago, a predictably superb concert. Beethoven’s String Quartet No. 13 in B flat Op. 130 with a (take-no-prisoners) Grosse Fuge Op. 133, followed by the Brahms Piano Quintet in F minor Op. 34, with the plangent tones of the…
Computational Complexity — 7/22/2025
A new prize:The Trevisan Prize, in honor of Luca Trevisan, who died in 2024 (blog obit is here, open problems column in his honor is here), has been announced. The link is here. The deadline for notification of intent is July 31 which is…
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…
Computational Complexity — 7/16/2025
Douglas Hofstadter first published Gödel, Escher, Bach: an Eternal Golden Braid in 1979 and my then high school self tried, and failed, to read though the entire book. It focused on the contradictions, with Kurt Gödel’s incompleteness theorems, M….
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 →
Blog - Logic Matters — 7/15/2025
The first mini Amazon review of the new edition of Introducing Category Theory arrives: five stars. Simultaneously, the first report of a typo (§2.9(b), “its homomorphism needs to be included” should read “its identity homomorphism needs to be…
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…
Blog - Logic Matters — 7/12/2025
I have written before about the pleasure of serendipitous finds in charity second-hand bookshops. It isn’t the matter of saving a few pounds (or of giving the money to a charity rather than a chain bookstore); that’s nice, to be sure, but it…
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; …
Computational Complexity — 7/9/2025
I had an epiphany reading an article in the Trenton Times when I lived in New Jersey at the turn of the century. The article interviewed companies along a certain street lobbying for a new bus route so their employees could more easily get to work….
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…
Computational Complexity — 7/6/2025
We denote the busy beaver function by BB.BB(n) is the max time a Turing machine of size n takes to halt on the empty string.(A particular model of TM and a notion of size has become standardized.)BB(n) grows faster than any computable function….
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)…
Computational Complexity — 7/2/2025
A new dean has taken my place, and I have returned to the professoriate at Illinois Tech, ending thirteen years in administration, six as dean and seven as department chair at Georgia Tech. I won’t rule out more administrative roles in the future,…
Blog - Logic Matters — 7/1/2025
In a previous book note, and also in the Appendix to the Guide, there is a review of Shashi Mohan Srivastava’s earlier A Course on Mathematical Logic. Parts of that book, as I say, could make useful supplementary/revision reading. So I was…
Computational Complexity — 7/1/2025
(I wrote this post a while back so its no longer NEW. More important— if there has been a follow-up to the story that is not in my post, let me know.) We have something NEW and something OLD about the Pythagorean Theorem. Now all we need is…
Computational Complexity — 6/26/2025
Alberto Fraile and Daniel Fernández guest post on random walks generated by the distribution of prime numbers.In our recent papers, we explored the sequence of prime numbers by defining “random walks” governed by simple algorithms applied to their…
Computational Complexity — 6/23/2025
The Univ of MD at College Park holds a HS Math Competition every year. At the reception for the winners Professor Larry Washington points to many past people who did well on the exam. Two stand out for different reasons:1) Serge Brin did well on…
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…
Computational Complexity — 6/18/2025
As the entire Fulbright board resigned last week and as the program that promotes international visits for US researchers, and vice-versa, may not survive the Trump administration, I thought I would recount some memories from my Fulbright…
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…
Fractal Kitty — 6/3/2025
IntroductionIn this activity, we’ll explore patterns by finding the remainders when Fibonacci numbers are divided by other numbers.ModuloSometimes, the most interesting part of dividing numbers is what’s left over—the remainder. This is where…
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.