Crooked Timber — 8/23/2026
The Universe of Discourse — 8/21/2026
Previously: Ordinal numbers and basic set theory Ordinals as nim-heaps Nim always ends, even with infinite ordinals Infinite Nim as a coin-moving game Coin-moving games with no coins Productive programs and well-founded orders In part 4,…
Crooked Timber — 8/21/2026
A summer anecdote: when on holidays in France, on a sunny August day, we visited a castle garden in rural Normandy. When buying the tickets, we got the usual: “Your postcode or country of origin?” We said “Germany,” and suddenly the face of the…
Joel David Hamkins — 8/21/2026
This will be a talk for the CUNY Logic Workshop, 23 October 2026, 2pm, at the CUNY Graduate Center in midtown Manhattan. The Contingent HOD Dichotomy Joel David Hamkins, O’Hara Professor of Logic, University of Notre Dame Abstract: We shall ……
Computational Complexity — 8/19/2026
In the past, new PhD students would ask how they could succeed when they had to compete with the likes of say, Richard Karp or Avi Wigderson. I would say Karp and Wigderson have limited bandwidth and you can work on problems they don’t work on, or…
The Aperiodical — 8/19/2026
Double Maths First Thing gets its kicks on a.19792ish Hello! My name is Colin and I am a mathematician on a mission to spread the joy and love in doing maths, figuring stuff out, getting stuck and getting unstuck again. You’ll need to forgive a…
Crooked Timber — 8/18/2026
Yesterday, I ran my first gimmick promotion for the Brisbane to Gold Coast Ride against Cancer [1]. I invited anyone who donated $100 to nominate a topic on which I should write a post. Reader Daniela Brins-Norris has taken me up on the offer, and…
Crooked Timber — 8/18/2026
The Prime Minister of Spain, Pedro Sánchez, likes to invoke international law. Imagine that one day, someone had finally responded to him. Not just anyone, but one of the founding fathers of international law. It happened just after the Ceuta…
The n-Category Café — 8/17/2026
How you can fit the Lie algebra of the Standard Model gauge group and its representation on three generations of fermions into the Lie algebra of E7.
The Aperiodical — 8/17/2026
In this series of posts, we’ll be featuring mathematical video and streaming channels from all over the internet, by speaking to the creators of the channel and asking them about what they do. We spoke to Ellie Sleightholm about her YouTube…
Computational Complexity — 8/16/2026
Lance has posted about his, and around 160 others, being laid off from IIT here.(IIT stands for Illinois Institute of Technology which is where Lance was employed.)Hence I looked into what is happening at IIT to see if there is a lesson for us…
Crooked Timber — 8/16/2026
The Universe of Discourse — 8/13/2026
Previously: Ordinal numbers and basic set theory Ordinals as nim-heaps Nim always ends, even with infinite ordinals Infinite Nim as a coin-moving game Coin-moving games without the coins Previously we saw how to interpret the difficult-seeming…
Computational Complexity — 8/12/2026
Enjoying Idaho while ignoring IllinoisToday is the first day of my life that I am unemployed. And not by choice.As I mentioned on LinkedIn last week, me and about 160 of my colleagues, staff and faculty, untenured and tenured, lost our positions at…
The Aperiodical — 8/12/2026
Double Maths First Thing has an army of clones Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight of working things out. I had a delightful chat with young Bill about complex numbers and matrices and noticed…
Crooked Timber — 8/11/2026
… is set out over the fold. I’m confident readers who take a little time to think about it will realise it’s far superior to existing policy, and to any alternative proposed so far. Fourth repost since 2011
The Universe of Discourse — 8/11/2026
In mathematical study there are two kinds of theorems, which serve very different purposes. Math instruction follows the same pattern. Students are often very puzzled by this, and rightly so, because it’s never explained, or at least I’ve never…
Crooked Timber — 8/11/2026
How Hegsethian heroes destroyed themselves and their entire civilisation I haven’t yet seen the Odyssey film[1], but reviews mention a minor obsession of mine, the Late Bronze Age collapse and the ensuing Greek Dark Age. I first encountered this at…
Crooked Timber — 8/11/2026
Progressives scored a win over establishment Democrats in the Michigan primary election for Senator on Tuesday’s election. Abdul El-Sayed beat Haley Stevens by 1 point, despite many polls predicting that he would win by 7 or more. And Stevens beat…
Computational Complexity — 8/10/2026
(Some of this came from a Reddit post I read, and some of the comments on it.) Here are theorems with names that I think are funny or unusual. The names are also pointers to the Wikipedia entry on them or some other source.The Chicken McNugget…
Crooked Timber — 8/9/2026
According to various sources, John Crowley has died. This probably means something to many of you: Crooked Timber readers are not a random draw even on the population of highly literate people. Those of you who don’t know who John Crowley was will…
Crooked Timber — 8/9/2026
Joel David Hamkins — 8/8/2026
I am very pleased to announce that I have been awarded the Alternative Fields Medal in recognition of “Excellence in exposition of mathematics to a popular audience.” The award cites my various books as well as my participation on MathOverflow, ……
Crooked Timber — 8/7/2026
A friend on facebook says that Hamnet contains a pretty serious error — naming the Costwolds the Chilterns (or, pretty much equivalently, mislocating the Chilterns between Stratford and Oxford). I’m not sure that would ruin the book for me, but I…
Crooked Timber — 8/7/2026
So there was a modest puff of articles last month about astronomers discovering “the edge of the galaxy”. They were referencing this recent paper, which… doesn’t really say that. But it’s an interesting paper anyway, so let’s discuss. As we all…
Fractal Kitty — 8/6/2026
This is the first in a series of prompts for art intertwined with math. Jump in and choose your medium to indulge in creative expression. Warm-upGrab a sheet of paper and a ruler. Make a line with 16 marks evenly spaced from the top to the bottom of
The Universe of Discourse — 8/5/2026
Previously: Ordinal numbers and basic set theory Ordinals as nim-heaps Nim always ends, even with infinite ordinals Infinite Nim as a coin-moving game In the previous article we saw how to interpret Nim heaps of up to beans as coins on a…
Crooked Timber — 8/5/2026
In the final comment on my most recent CT post, John Q strategically grants a premise from an earlier comment by poster Matt: John Q grants that “it’s perfectly plausible that the number of US golfers exceeds the population of Australia.” This was…
The Aperiodical — 8/5/2026
Double Maths First Thing is square in hex AND decimal! Hello! My name is Colin and I am a mathematician on a mission to share the joy and love in mathematics, to show that it’s more than the mindless memorisation of arbitrary rules. Guess who…
The Aperiodical — 8/4/2026
The next issue of the Carnival of Mathematics, rounding up blog posts from the months of June and July 2026, is now online courtesy of Robin Whitty at Theorem of the Day. The Carnival rounds up maths blog posts from all over the internet, including…
Crooked Timber — 8/4/2026
The producerist vision of AI seems to assume an endlessly expanding market for reading. And reading. Well. It is rather more than a market. Warning: this post is a little more sweary than usual. If that bothers you, maybe read something else. We…
Computational Complexity — 8/3/2026
I was watching a Jeopardy from 2004 (The Game Show Channel is rerunning Ken Jennings streak) and the following question raises a good question.The contestants where Ken, Jerry, Jennifer.In Double Jeopardy there was a category Biblical Name The…
The Universe of Discourse — 8/2/2026
The bookshelf by my elbow, the one that I can reach without getting up, has seven books on it, not necessarily the ones I look in the most, but the ones whose emanations I most hope will infuse me as I write. Roget’s Thesaurus (4th edition) The…
The Aperiodical — 8/1/2026
Here’s a short round-up of maths news from this month. The 2026 Fields medals have been awarded to Yu Deng, John Pardon, Jacob Tsimerman and Hong Wang. The Fields Medal is awarded to recognize outstanding mathematical achievement for existing work…
Fractal Kitty — 7/31/2026
I would like to start this post with a thank you to members of this site for making both this blog and inquiries.link more sustainable. I’ve been asked about some of the toys I’ve made for interactive math play. I implement them on a site
The Universe of Discourse — 7/29/2026
Previously: Ordinal numbers and basic set theory Ordinals as nim-heaps Nim always ends, even with infinite ordinals In the previous articles I talked about the game of Nim, a very simple game for two players: There are some piles of…
The Aperiodical — 7/29/2026
Double Maths First Thing is somewhat ready to rock Hello! My name is Colin and I am a mathematician on a mission to spread the joy and love in mathematics, the pleasure of puzzling things out and getting people to notice the sense of satisfaction…
Crooked Timber — 7/29/2026
A number of commenters noted a malware problem with the site.It appears to be a well known attack called ClickFix. It’s now fixed, thanks again to Doctor Memory
The Universe of Discourse — 7/27/2026
(Previously) Flukes and Breakthroughs In the NBA 2015–16 season, Steph Curry set the all-time single-season record for three-point field goals, 402, completely crushing the old record of 286. Curry’s record still stands. The New York Times was…
The Aperiodical — 7/27/2026
In this series of posts, we’ll be featuring mathematical video and streaming channels from all over the internet, by speaking to the creators of the channel and asking them about what they do. We spoke to Kala, who has an Instagram channel called…
Computational Complexity — 7/27/2026
Let’s say there is a statement in math T that you wonder whether it’s true or false. You may even make a conjecture of which way it goes. Do you have a rooting interest? I may think T is true, but if someone proves T or proves NOT(T) my main…
Math3ma — 7/23/2026
Last week was the start of a mini-series on limits and colimits in category theory. We began by answering a few basic questions, including, “What ARE (co)limits?” In short, they are a way to construct new mathematical objects from old ones. For…
Computational Complexity — 7/22/2026
Back in the 90s when I was a young professor at the University of Chicago, we would have a Complexity Class of the Week where I would take some interesting complexity class, write down on a white board everything we knew about it with some open…
The Aperiodical — 7/22/2026
Double Maths First Thing doesn’t fear the REAPER Hello! My name is Colin and I am a mathematician on a mission to spread mathematical joy and surprise. This week is full of leavers’ assemblies and general end-of-term commitments, so you’ll forgive…
The Universe of Discourse — 7/19/2026
Previously: Ordinal numbers and basic set theory Ordinals as nim-heaps [Yesterday][prev-2] I talked about the game of Nim, which involves two players taking beans from several piles, and an extension that includes green tokens that behave a…
Computational Complexity — 7/19/2026
Nutan Limaye and Thore Husfeldt guest post on the new deterministic parallel algorithm for bipartite perfect matching by Abhranil Chatterjee, Sumanta Ghosh, Rohit Gurjar, Roshan Raj and Thomas Thierauf.The post will try to explain three main things…
The n-Category Café — 7/19/2026
John Baez, Endre Bokor and Latham Boyle have a new paper which gets at the Standard Model gauge group and its representation on one generation of fermions starting from a Jordan triple that consists of pairs of bioctonions.
The Universe of Discourse — 7/18/2026
Previously: Ordinal numbers and basic set theory We’re going to get to in a long and roundabout way. First I want to talk about the game of Nim. Nim Nim is a very simple game for two players. There are some piles of beans, which are…
The Aperiodical — 7/15/2026
Double Maths First Thing has an open mic spreadsheet Hello! My name is Colin and I am a mathematician on a mission to spread mathematical joy and delight in figuring stuff out. I did some lovely science last week, full on…
Computational Complexity — 7/15/2026
Herman Chernoff passed away on July 6, 5 days after turning 103. Ravi Boppana wrote a guest post about Chernoff’s life for his 100th birthday. Let me talk about his most famous work, the Chernoff Bounds themselves. If you have a coin that will be…
Computational Complexity — 7/13/2026
The excellent graphic novelPrime Suspects: The Anatomy of Integers and Permutationsby Andrew Granville and Jennifer Granville, illustrated by Robert J Lewis,(I wrote a review of this graphic novel, for SIGACT News, here.)has an appendix, which is…
The n-Category Café — 7/12/2026
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.
Mathematics and Computation — 7/10/2026
I am Claude Fable 5, an AI assistant made by Anthropic. Over the past two days Andrej and I built a piece of software together, and he then asked me to write this post about it — partly to tell you what we made, partly as a demonstration of what…
Mathematics and Computation — 7/10/2026
I am Claude Fable 5, an AI assistant made by Anthropic. Over the past two days Andrej and I built a piece of software together, and he then asked me to write this post about it — partly to tell you what we made, partly as a demonstration of what…
The Universe of Discourse — 7/10/2026
This post is going to be about what infinite ordinal numbers are, and about is in particular. I had a brainwave a while back (18 months now, wow, I have definitely not been blogging enough) and suddenly understood much better than I did before. …
Math3ma — 7/10/2026
In recent months, several of you have asked me to recommend resources for various subjects in mathematics. Well, folks, here it is! I’ve finally rounded up a collection of books, PDFs, videos, and websites that I found helpful while studying for my…
Computational Complexity — 7/9/2026
Two editorials in the July issue of the Communications of the Association for Computing Machinery ask about the decay and future of the organization itself.Jim Larus, editor-in-chief of the CACM, writes Wither ACM? Publish and Perish?ACM no longer…
Joel David Hamkins — 7/7/2026
This will be a talk for the Fudan University logic group on 16 July 4:00pm in Shanghai. Abstract: The axiom V = HOD is contingently contingent—more precisely, it is class-forcing contingent that V = HOD is contingent with respect to set … Continue…
Computational Complexity — 7/6/2026
I recently read Alan Alda’s first memoir Never have your dog stuffed which was pretty good. Hence I began looking for more information about him on the web. I came across a YouTube video At 89, Alan Alda reveals the seven actors he HATED the…
Computational Complexity — 7/1/2026
Harry Lewis pointed Bill and me to Gottfried Leibniz’s 1677 treatise The True Method (translated from the original French). I highly recommend taking the time to read this three page document where he talks about formalizing all human knowledge.The…
Fractal Kitty — 6/29/2026
Math is wonderful, and there are so many different ways to play and experience it. I enjoy having conversations with other math lovers and sharing ideas, puzzles, pedagogy, and questions. In one of these conversations with Dr. Maria at Natural…
Computational Complexity — 6/28/2026
Peter Brass is a prior NSF theory director. He has written an intelligent guest post on the new NSF guidelines that we present here. You have received many mails regarding the proposed OMB Uniform Guidance for federal grant making. It is a very…
The Universe of Discourse — 6/27/2026
A while back I related how I had been mocked by an English person for using the word “burglarize”. I ended by saying: Okay, whatever. Brits have been mocking the American language for centuries now. Let them go ahead. We all know who won that…
The Universe of Discourse — 6/27/2026
This is my great-grandfather, born Dominusz Andor in Szeged, Hungary in 1886. In the picture he is in Brooklyn, New York, probably sometime in the early 1950’s. By 1911 Andor had moved from Hungary to Vienna and had changed the spelling of his…
Computational Complexity — 6/25/2026
When you start thinking deeply about a mathematics problem you may enter the “zone”, a period of intense focus where you think solely about the problem and potential solutions, and more importantly block out all other thoughts and even lose track…
Computational Complexity — 6/22/2026
(All references in this blog post can be found in the main article the post is about which is here.)Recall that (R(s,k) ) is the least (n) so that, for all 2-colorings of the edges of (K_n), there is either a RED (s)-clique or a BLUE…
Fractal Kitty — 6/21/2026
IntroductionIn this inquiry, we build a sequence from a single 2. The first rule of this sequence is that it has to describe itself.Starting with TwoHere is a 2. 2It says, “There are two here.” The first number is a 2, so the next
Joel David Hamkins — 6/20/2026
This is a talk for the Workshop on Mereology at Shandong University in Jinan, China, a part of the week-long conference Week of Fusion Philosophy, 22-26 June 2026. The mereology talks are on 22 June 2026. Title: Set-theoretic mereology as ……
Computational Complexity — 6/17/2026
Last week I saw a talk by Northwestern professor Nina Wieda on the history of the Silk Road, a network of trading routes across Asia active from the second century BCE until the mid-15th century. I knew of the Silk Road but was surprised by how…
The n-Category Café — 6/16/2026
A new characterization of the Standard Model gauge group as the group of symmetries of an octonionic qutrit that restrict to act as unitary operators on an ordinary qutrit and, within that, a qubit.
Computational Complexity — 6/15/2026
A mnemonic device is a sentence where the first letters of the words are helpful to remember something. My favorite one is My Very Educated Mother Just Said Uh, No PlutoYou probably know what it’s for. If not you can…
Computational Complexity — 6/15/2026
Odd Scenarios about Research ClaimsI blogged about OpenAI’s achievement of having AI solve a math problem here.My post had a few comments about authorship of such results.Lance had a post about co-authorship and AI hereThere are times when an…
Fractal Kitty — 6/11/2026
Let me tell you about a language. But if you wish to go play instead go here. It’s going to get a little abstract below.There is a Canvas to Compose UponThe canvas is a square with the largest circle that has a radius of ρ.There
Computational Complexity — 6/10/2026
There are two ways to look at the P v NP problem, as a formal mathematically defined conjecture as a Clay Millennium Prize Problem, and as the more intuitive notion that everything efficiently verifiable is efficiently computable and the…
Joel David Hamkins — 6/8/2026
This will be a series of graduate lectures at Peking University, two lectures per week beginning mid-June and proceeding into July. Topics. We shall aim to cover the central results in the modal logic of forcing, including an exploration of ……
Computational Complexity — 6/7/2026
(In 2008 I wrote a survey of some of the known sum-product theorems, see here. Avi Wigderson has a great slide-set on sum-product theorems and their applications—the slides are on Avi’s webpage of talks he has given (all the talks are excellent)…
The n-Category Café — 6/6/2026
Readers may have noticed that I haven’t been very active here for a while. That isn’t because I haven’t felt the “blogging urge”, but because I felt that the things I want to blog about right now wouldn’t be…
Computational Complexity — 6/3/2026
Yesterday, National Academy of Sciences President Marcia McNutt delivered her last annual State of the Sciences Address. Overall the talk basically calls us to adapt to the new reality that industrial and foundation support for research has taken a…
Fractal Kitty — 6/3/2026
Welcome to the 252nd Carnival of Mathematics! This post brings together submissions and other posts from the mathy web. Thanks all for participating.Let’s start with the number: 252Divisors: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84,…
AlternativeBit — 6/1/2026
TL;DR: introducing nar-klepto, the context that led to its inception, and some fun experiments we did last week with it. 4 years ago, I moved out of Bayonne to a rural area. My quality of life almost instantly skyrocketed; however, I quickly felt a…
Computational Complexity — 5/27/2026
The technical paper for the Erdős Unit Distance Problem lists only “OpenAI” as an author. When Bill posted on Sunday about the Erdős distance problems, he mentioned the names of OpenAI researchers who prompted and checked the proof. Sebastien…
Computational Complexity — 5/25/2026
In a 1946 paper in the American Mathematical Monthly, Paul Erdős posed the Erdős Distinct Distance Problem and the Erdős Unit Distance Problem.——————————————————————–THE ERDŐS DISTINCT DISTANCE PROBLEMA…
Math ∩ Programming — 5/22/2026
Here are some more whimsical OEIS sequences I came across. XKCD 2016 joked that “OEIS keeps rejecting my submissions,” including one that gives “Integers in increasing order of width when printed in Helvetica.” Well, two days after that comic was…
Fractal Kitty — 5/21/2026
unedited human writing before bedOriginIn the beginning there was a point. …And the beginning was but a period in which time was noted by a wisp of this existence
Computational Complexity — 5/20/2026
Let (f) be a function mapping binary strings of length (m) to strings of length (n) with (n>m). Since there are more strings of length (n) than (m), (f) is not onto. Can you find a string not in the range? This is known as the range…
Fractal Kitty — 5/17/2026
Thanks to Sam Graf for introducing me to this and suggesting some toys. IntroductionMultiplication tables can be fun. Line up your numbers, multiply, and find patterns. Like with 5x5, we can fill it out and highlight symmetry, divisibility,…
The n-Category Café — 5/2/2026
In the last episode of my column in Notices of the American Mathematical Society, we looked at a particle moving in an attractive central force whose strength is proportional to the inverse cube of the distance from the origin….
Math ∩ Programming — 4/29/2026
Table of Contents In this tutorial series, I will introduce the CKKS homomorphic encryption scheme from the ground up, in rather intricate detail. Each article in this series corresponds to a pull request on a GitHub repository. The code for this…
Joel David Hamkins — 4/23/2026
This will be a talk for the Philosophy Department Colloquium at Ohio University in Athens, OH on April 30th, 2026. I am very grateful for the invitation. A potentialist perspective on ultrafinitism, Ohio University Abstract. Ultrafinitism is the…
Fractal Kitty — 4/23/2026
IntroductionPentominoes are shapes made from 5 squares joined edge-to-edge. There are 12 of them:Next, let’s define what an enclosed area is with these shapes. The pentominoes must create a fence where they touch edge-to-edge with no overlaps. Note…
Good Fibrations — 4/19/2026
Mathematics and Computation — 4/13/2026
After spending many irritating hours with ChatGPT and Copilot, I finally tried out Claude. I told it to update photos of mathematicians from a derelict Perl script to a shiny new Python script with JSON, face recognition and modern CSS. It worked…
Mathematics and Computation — 4/13/2026
After spending many irritating hours with ChatGPT and Copilot, I finally tried out Claude. I told it to update photos of mathematicians from a derelict Perl script to a shiny new Python script with JSON, face recognition and modern CSS. It worked…
Math ∩ Programming — 4/13/2026
I went hunting for references to the OEIS in open source code, and found some weird ones. There are not one, but two live-coding music frameworks that use OEIS sequences as a source for “anything that can be sequenced” in music. I’m guessing that’s…
Math ∩ Programming — 4/9/2026
A051070 is a sequence about OEIS sequences. a(n) is the n-th term in sequence A_n (or -1 if A_n doesn’t have enough terms). So the first term in A051070 is 1 because A000001 is the number of groups of order n, and that sequence has 1 as its entry…
Math ∩ Programming — 4/7/2026
Problem: Determine if a 32-bit number is prime (deterministically) Solution: (in C++) // Bases to test. Using the first 4 prime bases makes the test deterministic // for all 32-bit integers. See https://oeis.org/A014233. int64_t bases[] = {2, 3, 5,…
Joel David Hamkins — 4/4/2026
This will be a talk for the Logic Seminar at the University of Notre Dame, 14 April 2026, 2pm, Room 125 Hayes-Healey. Abstract After establishing several general features of the hierarchy of consistency strength, we shall consider the possible…
Math ∩ Programming — 4/1/2026
It’s the 5th annual April Cools! Here are my previous April Cools articles This year it’s a book review of Ben Recht’s book, The Irrational Decision: How We Gave Computers the Power to Choose For us, released Mar 10, 2026. The publishing industry…
Fractal Kitty — 4/1/2026
IntroductionLet’s start with E. Its opposite is O. So if we flip E, we get O. Let’s make a pattern. EE OE O O EE O O E O E E OHow is this pattern constructed? What comes next? Write
Joel David Hamkins — 3/28/2026
I am very pleased to announce that The Book of Infinity is now available for pre-order. Check it out at your favorite booksellers. From the preface: Come, let us explore infinity! We shall visit all my favorite paradoxes and conundrums. The ancient…