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…
Crooked Timber — 11/16/2025
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…
The Aperiodical — 11/12/2025
Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight of getting stuck into maths. Let’s start with a lovely quote from Karen Uhlenbeck: “I think you can’t do mathematics without the ability to concentrate. But…
Crooked Timber — 11/10/2025
107 years ago*, the guns fell silent on the Western Front, marking a temporary and partial end to the Great War which began in 1914, and has continued, in one form or another, ever since. I once hoped that I would live to see a peaceful world, but…
Crooked Timber — 11/10/2025
With another COP starting today, and the question of climate change having played no role at all in the Dutch elections recently, and, well, for a zillion different reasons – it seems like a good time to ask the question: what books can help to…
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…
Crooked Timber — 11/10/2025
If you’ve ever been at a Dutch PhD ceremony, you’ve come across the toga – which is, unfortunately not a Greek or Roman toga as pictured here. Instead, it’s a kind of black gown, made from heavy cloth, with velvet facings, accompanied by a white…
Crooked Timber — 11/9/2025
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:Clean coded in p5js with p5sound - enjoy in fullscreen. Click here for the visual with music - (CW: Strobing…
The Aperiodical — 11/7/2025
A conversation about mathematics inspired by a 3D wooden puzzle. Presented by Katie Steckles and Peter Rowlett, with special guest Grant Sanderson.
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?
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…
Crooked Timber — 11/5/2025
Death comes for us all. We are outlived, as Barkandji man Woddy Harris would have it, by Mother Nature, who holds us in something that I think he would liken to ‘eternity’. By what logic, then, must Mother Nature also die? The Barkandji in…
The Aperiodical — 11/5/2025
Double Maths First Thing is disappointed that it’s not that sort of plot you’re meant to remember. Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight in doing maths, even if today I am slightly despondent…
Crooked Timber — 11/4/2025
I’ve been visiting family in Germany, with only a phone, so I couldn’t post on Sunday. But here are some crows from Hamburg.
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 Aperiodical — 11/3/2025
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of October 2025, is now online at Theorem of the Day. The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical….
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…
Crooked Timber — 10/31/2025
In the Wilcannia cemetery a lot of plastic is on display. This cemetery is an important local monument not because it celebrates the working class, because it doesn’t. Unlike in Broken Hill, there are no tourist guides to the cemetery, no famous…
Crooked Timber — 10/30/2025
“An ELECTIVE DESPOTISM was not the government we fought for; but one which should not only be founded on free principles, but in which the powers of government should be so divided and balanced among several bodies of magistracy, as that no one…
Crooked Timber — 10/29/2025
Bit of a joke there. What the paper is about is, we found a new planet, about 18.2 light years away. That means that we’re seeing the planet as it appeared 18.2 years ago, in the summer of 2007. Summer 2007: the first iPhone had just hit the…
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 Aperiodical — 10/29/2025
Double Maths First Thing is brought to you by ibuprofen and grandparents taking the kids Hello! My name is Colin and I am a mathematician on a mission to share and spread the joy in doing maths for its own sake. It’s half term down here in Dorset,…
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…
Crooked Timber — 10/26/2025
Crooked Timber — 10/24/2025
On the longer time scale that we feel in nature, the violence of colonial capitalism seems almost fleeting. ‘Mother Nature will outlast all of this’, Barkandji man Woddy Harris told me, gesturing across his hometown of Wilcannia, two hours’ drive…
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…
The Aperiodical — 10/22/2025
Double Maths First Thing is beautiful, it’s simple and it’s wrong Hello! My name is Colin and I am a mathematician on a mission to share the joy and love that comes from doing maths. As the amazing Jo Sibley says, if you love someone, set them a…
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…
The Aperiodical — 10/20/2025
Somehow, I’ve been awarded the MEGA grant, from Matt Parker and Talking Maths in Public, for a ridiculous public maths project. I’d better get on that, then! My plan is to go to the beach and use great big cookie cutters in the shape of the spectre…
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…
Crooked Timber — 10/19/2025
Crooked Timber — 10/19/2025
Within ten minutes I regretted my decision to walk to Creedon Street in the outback town of Broken Hill. At first, I thought it was the shoes. Stupid things I’d bought on the internet, they were little more than plastic-coated cardboard soles…
Computational Complexity — 10/18/2025
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 Theory.These are different people. To celebrate the second one’s thesis, I took…
Blog - Logic Matters — 10/16/2025
Briefly, Thomas Forster tells me that he has acquired funding for two studentships in Wellington NZ (a delightful place!) for students who want to do a Ph.D. in set theory, in particular working with him on NF or perhaps some adjacent topic. He has…
Crooked Timber — 10/16/2025
One of the big puzzles in the last months, for those observing the politics in the US and elsewhere, is this: why is there apparently so little protest against the attacks on democracy and the rule of law, and why does it happen in some but not…
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….
The Aperiodical — 10/15/2025
Double Maths First Thing almost forgot to put this line in! Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight of doing mathematical things. This week I am mainly getting to grips with reluctantly becoming…
The Aperiodical — 10/14/2025
I was asked recently by a first-year maths undergrad student if I could recommend any books on problem-solving, as they were hoping to develop their problem-solving skills. Asking around some maths communication colleagues has resulted in an…
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 Aperiodical — 10/8/2025
DMFT is grateful for the last minute. Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight of doing maths and solving problems. Today I went to a school in Poole to talk about my career in maths and computing…
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.
Blog - Logic Matters — 10/6/2025
An accessible, very readable, well-motivated, zestful book on ordinal analysis and proof theory would be a very good thing to have. Arai’s Ordinal Analysis with an Introduction to Proof Theory isn’t it. By a country mile. (I was asked for a…
Computational Complexity — 10/5/2025
You used AI in your work. Do you hide it or brag about it? 1) In 2002 there was a movie Simone about an actress who is really an AI. The Wikipedia entry tells the entire plot. I saved time by reading it in two minutes rather than watching it in 2…
Blog - Logic Matters — 10/4/2025
Most of the writing I have actually done this last week or so has been in tinkering with the category theory notes. For, sad to relate, I still find myself occasionally working through them. Until yesterday, however, it has just been a matter of…
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,…
Computational Complexity — 10/1/2025
I read through the new book If Anyone Builds It, Everyone Dies by Eliezer Yudkowsky and Nate Soares. “It” refers to Artificial Super Intelligence (ASI). A very short version of the authors’ argument: You can view advanced AI as though it has its…
Computational Complexity — 9/29/2025
Martin Kruskal was born Sept 28, 1925 and passed away on Dec 26, 2006, at the age of 81 (we did two posts for his memorial, here and here). Today, Sept 28, 2025, is his 100th birthday. His son Clyde Kruskal wrote today’s blog post as a tribute to…
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….
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…
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…
Computational Complexity — 9/25/2025
A few weeks ago I took an Uber to a regional airport and was picked up by a Tesla. The driver used FSD, so-called Full Self-Driving, never touching the steering wheel during the entire trip. Should you tip a driver who just sits there? In the end I…
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…
Computational Complexity — 9/23/2025
STUDENT: What did you do before the web to find papers?BILL: We went to the library and copied papers to read later.STUDENT: Did you read them later?BILL: Well, uh,hmm, …BILL to a professor in his 80’s: What did you do before copy…
Blog - Logic Matters — 9/20/2025
A great couple of days in London. The high point, a quite outstanding evening at Wigmore Hall — the wondrous Lea Desandre and Thomas Dunford (and the Jupiter ensemble) performing Dowland and Purcell. Their new CD is terrific, and the live version…
Computational Complexity — 9/17/2025
When announcing Open-AI’s latest release last month, Sam Altman said “GPT-5 is the first time that it really feels like talking to an expert in any topic, like a PhD-level expert.” Before we discuss whether GPT-5 got there, what does “PhD-Level…
The n-Category Café — 9/16/2025
The octonions have nontrivial inner automorphisms of order 3. Is this related to triality?
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…
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
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 →
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…
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,…
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…
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.
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…
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…
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….
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…
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…
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.
The n-Category Café — 8/2/2025
I hear that Jack Morava died on August 1, 2025.
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
Did you know that Lawvere did classified work on arms control in the 1960s, back when he was writing his thesis?
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…