Computational Complexity — 7/14/2025
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!…
Crooked Timber — 7/13/2025
The n-Category Café — 7/12/2025
Potential functions from a functorial perspective.
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…
The n-Category Café — 7/12/2025
PDE methods in magnitude, looked at categorically.
The n-Category Café — 7/11/2025
CT2025 conference announcement.
Crooked Timber — 7/11/2025
There’s a great anecdote about Roman Jakobson, the structuralist theorist of language, in Bernard Dionysius Geoghegan’s book, Code: From Information Theory to French Theory. For Jakobson, and for other early structuralist and post-structuralist…
The n-Category Café — 7/11/2025
Feature on Tai-Danae Bradley’s work on categorical linguistics.
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; …
The n-Category Café — 7/10/2025
Stellenbosch University wants to hire a mathematician. Apply before April 30th!
The n-Category Café — 7/10/2025
How do you count rooted planar n-ary trees with a given number of leaves? Use Lagrange inversion!
Crooked Timber — 7/10/2025
Now that the Trump government is relentlessly attacking higher education and abusing its power at the border to arbitrarily refuse entry to scholars, many academics wonder whether it’s still possible to travel to the US for conferences or other…
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….
The Aperiodical — 7/9/2025
Back in 2008, Chaim Goodman-Strauss and Heidi Burgel, together with the late John Conway, wrote a book called The Symmetries of Things, which covered a range of topics around mathematical symmetry and the symmetries of geometric objects. Now the…
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…
The Aperiodical — 7/9/2025
Double Maths First Thing couldn’t possibly comment. Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in engaging with maths, for any reason or for none. I’ve made it back from rehearsal and am feeling a lot…
Crooked Timber — 7/9/2025
I’ve owned this mug for twenty-five years now. Bought in the gift shop of the Metropolitan Opera in New York on my first ever trip to America, which I doubt I shall ever visit again. The mug, in art nouveau style, celebrates Pucchini’s La Bohème,…
Crooked Timber — 7/8/2025
Have they changed, or just become their worst selves While Trump is unpopular with a majority of Americans, his support among Republicans remains solid. That’s despite blatant corruption, fascist policies and a failure to deliver any of the…
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….
The n-Category Café — 7/6/2025
First lecture in a 4.5-hour minicourse on combinatorics with species.
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,…
The Aperiodical — 7/2/2025
Double Maths First Thing could really do with a hot lemon and honey Hello! My name is Colin and I am a mathematician on a mission to shift this blooming cold before the weekend, when I’m meant to be in Peterborough to rehearse for the PRE show in…
The n-Category Café — 7/1/2025
Studying atomic nuclei forces us to quantize the concept of ellipsoid.
The n-Category Café — 7/1/2025
The McGee group is one of the two smallest groups with an outer automorphism that preserves conjugacy classes. My route to understanding this fact was a long and winding one.
Math3ma — 7/1/2025
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 n-Category Café — 7/1/2025
Is the map from the Burnside ring to the representation ring of a finite group usually surjective, or usually not?
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…
The n-Category Café — 6/30/2025
First lecture in a 4.5-hour minicourse on combinatorics with species.
The Aperiodical — 6/30/2025
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 Stephen Welch, of Welch Labs, which among…
Crooked Timber — 6/29/2025
I’ve held off posting this in the hope of coming up with some kind of positive response, but I haven’t got one. When I wrote back in November 2024 that Trump’s dictatorship was a fait accompi there was still plenty of room for people to disagree….
Blog - Logic Matters — 6/29/2025
I have belatedly updated the PDF Appendix to the Study Guide and also the page of links to book notes — 76 of them! — to incorporate some blog posts from last year. And I am now starting to do more homework, as I slowly work up to revising the main…
Crooked Timber — 6/29/2025
Crooked Timber — 6/27/2025
Many thanks to Hannah for her beautiful post on George Eliot’s Silas Marner and the evacuation of moral purpose from the Protestant work ethic. That resonates with Hijacked, my latest book, which traces the history of the work ethic from 17th…
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…
Blog - Logic Matters — 6/26/2025
So here it is, available from today. As with the other Big Red Logic Books, to keep the cost minimal, it is an Amazon-only print-on-demand book, ISBN-10 : 1068346701. And, as with the other Big Red Logic Books, you can still download the latest…
The n-Category Café — 6/26/2025
Second lecture in a 4.5-hour minicourse on combinatorics with species.
The Aperiodical — 6/26/2025
We do these things, not because they are difficult, but because they are ridiculous– Matt Parker, probably Matt Parker is going to the moon. I mean, not literally. Everyone’s favourite Stand-Up Mathematician is the sort of person who’s more likely…
The Aperiodical — 6/25/2025
Me! On Numberphile! Who would’ve thought it? Earlier this year, Brady Haran visited Newcastle to record a video with some Leverhulme scholars. Luckily for me he had a bit of spare time to record a video with me, so we did one about the Herschel…
The Aperiodical — 6/25/2025
Double Maths First Thing is the Ultimate Answer. Hello! My name is Colin and I am a mathematician on a mission to the moon! But I’m also on a mission to spread joy and delight in doing maths anywhere in the cosmos. Talking of doing maths in strange…
The n-Category Café — 6/24/2025
Todd Trimble and I wrote a paper on characterizing classical groups (and monoids) in terms of their 2-rigs of representations.
Crooked Timber — 6/24/2025
The UK government has signalled its intention to “proscribe” the protest group Palestine Action under anti-terrorism legislation. This will place it in the same legal category as Al Qaeda and Islamic State: it will be illegal to belong to the…
Blog - Logic Matters — 6/23/2025
Back in 2012, the Pavel Haas Quartet recorded a prize-winning Schubert CD including a truly great performance of the Death and the Maiden Quartet. I wrote at the time: The Pavel Haas launch into the quartet with fierce attack and astringent (almost…
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…
The Aperiodical — 6/23/2025
A story In my childhood memories, the lanterns in my hometown always fascinated me – circular palace lanterns, polyhedral colorful lanterns. How did my ancestors achieve the magical transformation from flat to three-dimensional through simple…
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…
Crooked Timber — 6/23/2025
Thursday afternoon I belatedly fulfilled a promise to post a book to Wilcannia. The school day was just finishing and as I left the Post Office I overheard a child around eight years old: Dad, I was so good today I got FIVE stickers. Dad was a…
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…
Crooked Timber — 6/22/2025
Crooked Timber — 6/21/2025
Please consider donating to this fundraising effort (here) to support Helen de Cruz’s family. There is no greater joy for a teacher than to see a student develop and grow; and no more satisfaction to a mentor than to be overshadowed professionally…
Blog - Logic Matters — 6/20/2025
With a mind to building myself a reading list for homework before updating the BML Study Guide, I have been doing some online searches for recent publications on mathematical logic. I asked ChatGPT and Claude in “research” mode too, but they were…
Crooked Timber — 6/20/2025
Hi CT readers, I’m publishing this open letter here so there’s a public record of the letter I’ve co-written and signed about what looks, walks and talks like a good old-fashioned Brussels stitch-up aimed at weakening the EU organisation that…
Crooked Timber — 6/19/2025
Pro-natalism (the idea that people, or rather, women, should have more babies than they choose to do at present) has become an established orthodoxy,[1]. The central claim is that, unless something changes soon, human populations both global and…
Blog - Logic Matters — 6/19/2025
I had luxuriant locks, and the temple was still standing, when I originally started the notes on category theory. But here we are … (according to ChatGPT, channelling its inner Rembrandt). The history of earlier versions is embarrassingly untidy…
Computational Complexity — 6/19/2025
A year ago if I showed you a picture of The Pope wearing a Baseball cap for the Chicago White Sox (or any Amercan team) you would assume it was computer-generated. And you would likely be right. Are there any real pictures of any Pope before Pope…
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…
Blog - Logic Matters — 6/18/2025
For a persuasive way of thinking about what LLMs are up to, read this particularly lucid and sane piece by the philosopher Keith Frankish. The post The game that LLMs are playing appeared first on Logic Matters.
The Aperiodical — 6/18/2025
Double Maths First Thing is excited about the moon! Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in doing and thinking about maths. Annoyingly, immediately after last week’s issue went out, several…
The Aperiodical — 6/16/2025
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 Ravi Boppana about his channel, Boppana…
Crooked Timber — 6/15/2025
Blog - Logic Matters — 6/14/2025
With a bit of useful proof-reading help from ChatGPT, and rather less from Claude, there’s a new version (2.8b) of ICT downloadable from the categories page. Between them, my friendly AI assistants found perhaps half a dozen straight-up typos per…
Computational Complexity — 6/11/2025
In the June CACM, Micah Beck writes an opinion piece Accept the Consequences where he is quite skeptical of the role of theory in real-world software development, concludingIt is important that we teach practical computer engineering as a field…
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…
Computational Complexity — 6/9/2025
David ZuckermanThe 2025 Gödel Prize has been awarded to Eshan Chattopadhyay and David Zuckerman for their paperExplicit two-source extractors and resilient functionswhich was in STOC 2016 and in the Annals of Math in 2019. We (Bill and Lance) care…
Blog - Logic Matters — 6/8/2025
As the world continues to go to hell in a handcart, let’s just pause for ten minutes to remind ourselves that there is beauty and tenderness … So from a couple of months ago, here are Noa Wildschut and Elisabeth Brauß playing the Three Romances for…
Computational Complexity — 6/4/2025
You can write laws that are very specific, like the US tax code, or open to interpretation like the first amendment. In the literature these are known as rules and standards respectively. In computational complexity, we generally think of…
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…
Computational Complexity — 6/3/2025
(Thanks to David Marcus who sent me the video I point to in point 4 of this post. Tip for young bloggers (if there are any) you can have a half-baked idea for a post and then someone sends you something OR you later have an idea to make it a…
Computational Complexity — 5/28/2025
On Route 1 in Saugus, Massachusetts, about a twenty minute drive from Cambridge, stood the Hilltop Steak House. When I went to graduate school in the late 80’s, Hilltop led all restaurants in the United States by sales (about $30 million in annual…
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.
Computational Complexity — 5/26/2025
(Trivia: What song has the lyric Some are Mathematicians, some are Carpenters’s wives ? It’s not a parody song, though sometimes it’s hard to tell a parody song from a so-called real song.)In my post about Pope Leo XIV I made the following…
Good Fibrations — 5/23/2025
I’ve felt for a long time that automorphisms of curves should control or at least exert serious force on the slopes on their Jacobians. Symmetry forces height, as I’ve written about previously in Models of Formal Groups Laws of Every Height, and…
Computational Complexity — 5/21/2025
On Saturday, I had my last Illinois Tech graduation as dean before I step down at the end of June. The College of Computing had nearly 1600 graduates and I shook many, many hands that morning.After graduation I caught a plane to Washington, DC to…
Fractal Kitty — 5/20/2025
This is the first of a series of guided inquiries in math. If a document is preferred over a blog post, the pdf file is below:Inquiries-Week 1_ Circle ShadingInquiries-Week 1_ Circle Shading.pdf615…
Computational Complexity — 5/20/2025
There have been times when satire has been mistaken for reality. A list of Onion stories that were mistaken for reality (or was it a mistake?) is here. When I say mistaken for reality I mean that a large set of people were fooled.My own…
Computational Complexity — 5/20/2025
The New Pope is Pope Leo XIV (pre-Pope name is Robert Prevost). 1) Pope names are one of the few places we still use Roman Numerals. I saw an article that was probably satirical that Americans prefer Roman Numerals (the numbers Jesus used) over…
Computational Complexity — 5/14/2025
The National Science Foundation was founded on May 10, 1950, 75 years ago last Saturday. No doubt the NSF has seen better days, but first let’s take a look back.At the end of World War II, Vannevar Bush, Director of the Office of Scientific…
Math ∩ Programming — 5/13/2025
I was inspired to browse some of Edsger Dijkstra’s essays today, and came across his speech, “Under the spell of Leibniz’s Dream”. It’s the sort of personal history I love to read, which gives one person’s sense of the world over a period of…
Joel David Hamkins — 5/12/2025
This will be an online talk for the Leeds Set Theory Seminar, 21 May 2025 1pm BST. Contact the organizers (Hope Duncan) for Teams access. Abstract: One can find in the philosophical research literature surrounding Skolem’s paradox a certain claim,…
Math ∩ Programming — 5/12/2025
Editor’s note: This essay was originally published on Medium on 2016-03-05. I have made minor edits in this republishing and added a few small retrospective notes. 2010–2011 (Year 0) I had just switched my major at Cal Poly State University from…
Computational Complexity — 5/8/2025
I reviewed a paper recently and I had to agree not to use AI in any aspect of the reviewing process. So I didn’t but it felt strange, like I wouldn’t be able to use a calculator to check calculations in a paper. Large language models aren’t perfect…
Computational Complexity — 5/6/2025
In a recent post by Scott (see here or just read my post which includes his post) he listed topis that he conjectured would NOT cause an outrage.I was going to write a long comment in his comments section, which would only be read by people who…
Computational Complexity — 4/30/2025
As someone who has literally written a book on the topic, I have had many people over the years send me their attempts at P v NP proofs. On average, I receive about one a month, but I’ve had seven in the last two weeks. And not just the usual email…
Computational Complexity — 4/28/2025
I wrote this about a month ago but wanted to wait until after the REU PI conference (which was April 21-22-23) to post it. I add a few comments based on what has happened since, which I preface with…
Computational Complexity — 4/23/2025
Right after the election I wrote a post predicting what would happen to higher education under Trump, most of which is coming true, but I had a massive failure of imagination missing the direct attacks on major universities. I won’t detail all the…
Joel David Hamkins — 4/21/2025
I was interviewed by Cody Roux for The Church of Logic podcast—a fascinating sweeping conversation on issues in the philosophy of mathematics and set theory, including what I described as a fundamental dichotomy between two perspectives on the…
Proses.ID — 4/18/2025
lately I’ve been watching a lot of videos on YouTube about China. it’s partly due to all the chaos around Trump’s tariff, but mostly these…
Computational Complexity — 4/16/2025
I’m short on time time this week so I thought it would be good to look back, some 64 years ago, to Dwight Eisenhower’s farewell address. It calls for balance between the industrial-military Complex and the scientific-technological elite. While…
Math ∩ Programming — 4/15/2025
Last month I gave a talk on the HEIR compiler project at the FHE.org conference in Sofia, Bulgaria. The video is on YouTube now, and the slides are public. I plan to write more about HEIR in the coming months, because it’s been an exciting and…
Joel David Hamkins — 4/6/2025
This will be a talk for the conference on Ultrafinitism: Physics, Mathematics, and Philosophy at Columbia University in New York, April 11-13, 2025. Abstract. I shall argue in various respects that ultrafinitism is fruitfully understood from a…
Joel David Hamkins — 4/6/2025
This will be a talk for the Logic Seminar at the Mathematical Institute of the University of Oxford, 29 May 2025 5pm Andrew Wiles Building. Abstract. For a given computably enumerable set $W$, consider the spectrum of assertions of the … Continue…
Fractal Kitty — 4/4/2025
Wow! It’s the 238th Carnival of Mathematics organized by Aperiodical. This has been a fun month with lots of submissions and lots of beautiful math art. To start let’s jump into the number 238 itself.238 is: 2 × 7 × 17.the sum of the
Abuse of Notation — 4/3/2025
Haskell is great. And I want more people to know it, so this is just a quick overview of it’s capabilities, using the code to solve a simple task I saw on Mastodon. The task is the following: Return a list of all combinations (i.e. order doesn’t…