Crooked Timber — 5/31/2025
Unemployed, I spent a week in April digging a small pond in our back yard. At the time, it was a distraction. Now it is… actually, a different sort of distraction. Because although it’s not a very big pond — about 3 meters by 2, maximum depth about…
The Aperiodical — 5/30/2025
Here’s a round-up of all the mathematical news from the last couple of months we didn’t otherwise cover here. Prizes and Awards The Shaw Prize in Mathematical Sciences 2025 has been awarded to Kenji Fukaya, “for his pioneering work on symplectic…
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…
The Aperiodical — 5/28/2025
Double Maths First Thing shaves newsletters if and only if they don’t shave themselves Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in puzzles, problem-solving and practicing maths. I’m currently wading…
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…
Blog - Logic Matters — 5/25/2025
Charlotte Saluste-Bridoux — the prize-winning young violinist, who has recently joined her teacher Alina Ibragimova as the new second violinist for the spectacularly good Chiaroscuro Quartet — has a fine Schubert CD newly out with her regular duo…
Crooked Timber — 5/25/2025
Blog - Logic Matters — 5/23/2025
Slowly, very slowly, … I would be really annoyed to paperback Introducing Category Theory and then immediately find silly typos or thinkos. So (as I’ve reported before) I have been getting ChatGPT and Claude Sonnet to proofread chapter by chapter….
The Aperiodical — 5/23/2025
It’s been quite a year. We introduced a totally new mathematics degree course, redesigned from the previous version. In addition, restructures and people leaving meant there were fewer of us teaching on the maths degree. All this together means…
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…
The Aperiodical — 5/21/2025
Double Maths First Thing has toothache. Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in figuring things out. And take my mind off of the dental work I had done yesterday. Send ibuprofen and puzzles. Among…
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…
The Aperiodical — 5/19/2025
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 Nils Berglund, whose YouTube channel…
Crooked Timber — 5/19/2025
How far can a government go in harming its own people before it loses support? And what does it mean if this form of harm happens via an attack on public knowledge institutions, from universities to meteorological services, in which expert…
Crooked Timber — 5/18/2025
Blog - Logic Matters — 5/16/2025
A couple of years back, I commented here on most of the papers in Categories for the Working Philosopher, edited by Elaine Landry (OUP). I’ve had occasion to revisit the first piece in the book, ‘The roles of set theories in mathematics’ by Colin…
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…
The Aperiodical — 5/14/2025
Double Maths First Thing wishes it could be formatted as a square Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in figuring things out. The 11yo is doing SATs at the moment, which runs exactly counter to…
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…
Crooked Timber — 5/12/2025
A few weeks ago the historian Perry Anderson published an essay “Regime Change in the West?” in the London Review of Books. Like many of Anderson’s essays this is a wide-ranging splurge full of bon mots and *apercus” delivered from some…
Blog - Logic Matters — 5/12/2025
A week in Amsterdam, mostly to meet up with the digital nomad Daughter, which was of course hugely enjoyable. We have been staying a few hundred yards behind the Concertgebouw, in a quietly so-civilised area, with a great scattering of cafes and…
Crooked Timber — 5/12/2025
More than a month ago, I agreed to an offer to be a visiting scholar at a private US university next year. This was no simple matter because of obligations to my own family and (somewhat more unexpectedly) my department. I have made no public…
Crooked Timber — 5/12/2025
Over the last years, I have edited a volume of papers on the question how to make analytical political philosophy more inclusive, with a particular focus on the debates on economic and ecological inequalities. The starting point was the observation…
Crooked Timber — 5/11/2025
Crooked Timber — 5/9/2025
I watched Attenborough’s latest blockbuster at the cinema last night with my family, and thought I’d collect some thoughts here. First off, it’s wonderfully put together. That’s hardly news with Attenborough. Of course, it’s beautifully shot, and…
The Aperiodical — 5/9/2025
This is a guest post by Martin Whitworth. I am the organiser of Cheltenham MathsJam, and I am a fan of our local Cheltenham Festivals. In addition to successful Jazz, Music and Literature Festivals, they have an annual Science Festival with high…
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…
The Aperiodical — 5/7/2025
Double Maths First Thing will sign autographs, form an orderly queue Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in mathematical practice. Last week, the Pseudorandom Ensemble gave our first…
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…
The Aperiodical — 5/6/2025
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of April 2025, is now online at Reflections and Tangents. The Carnival rounds up maths blog posts from all over the internet, including some from our…
Crooked Timber — 5/4/2025
Blog - Logic Matters — 5/1/2025
We have just booked tickets to see the wondrous Lea Desandre at Wigmore Hall on Tuesday 16 September, singing Dowland and Purcell. It should be an amazing concert. If you haven’t ever seen her perform then this candlelit concert from Rouen three…
Crooked Timber — 4/30/2025
Back in 2022, after my first encounter with ChatGPT, I suggested that it was likely to wipe out large categories of “bullshit jobs”, but unlikely to create mass unemployment. In retrospect, that was probably an overestimate of the likely impact….
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…
The Aperiodical — 4/30/2025
Double Maths First Thing is HORRIFIED and you should be too. Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight, so obviously I’m going to start with something awful: I recently learned that a “one-year flood”…
Crooked Timber — 4/29/2025
I was not invited to the meeting where the left coordinated their war on water pressure. Sadly, then, it was over before I even knew it was happening. One of those American executive orders (and gosh we’re getting tired of those, even from the…
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…
Crooked Timber — 4/28/2025
Here is a joke. A philosopher goes to a policy committee. Got it? Okay, okay, it’s probably a bad joke. It’s also outdated: these days, many philosophers do go to policy committees. The cliché is that a philosopher sits in the academic ivory tower,…
Crooked Timber — 4/28/2025
I posted this on my (private) Facebook page a few weeks back, just to vent. Since it resonated with quite a few people, I am reposting it here. I thought it was a platitude, but given the sea of self-congratulatory discourse about Europe (here’s an…
Blog - Logic Matters — 4/27/2025
A quite wonderful performance of the Trout Quintet by Patricia Kopatschinskaja, Anastasia Kobekina, and friends, made available by the Gstaad Digital Festival (to watch, you might have to register, but that’s free). Enjoy! The post Schubert on…
Crooked Timber — 4/27/2025
Blog - Logic Matters — 4/26/2025
I have just uploaded a revised version of Introducing Category Theory, which as usual you’ll find linked on the categories page. I will need to do some more proof-reading (with a bit of help from ChatGPT and from my useful new friend Claude). And I…
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…
Blog - Logic Matters — 4/20/2025
A wonderful memory this. Last time we were in Venice, with the Daughter, we visited the Scuola Dalmata (Scuola di San Giorgio degli Schiavoni). Though it’s high up the “must see” lists in the guide books, we were the only people there, and had a…
Blog - Logic Matters — 4/19/2025
I’m getting some very nice comments on a late draft of the categories book. “A rich and thoughtful introduction, both mathematically and philosophically”. “This is extremely readable, with clarity, philosophical depth, and pedagogical structure. It…
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…
The n-Category Café — 4/15/2025
Stellenbosch University wants to hire a mathematician. Apply before April 30th!
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…
The n-Category Café — 4/15/2025
Feature on Tai-Danae Bradley’s work on categorical linguistics.
Computational Complexity — 4/14/2025
I recently read the following theoremDef: A semigroup is a pair ((G,*)) where (G) is a set and * is a binary operation on (G) such that * is associative. NOTE: we do not require an identity element, we do not require inverses, we do not…
Computational Complexity — 4/9/2025
In the recent Signalgate scandal, several senior Trump administration appointees used the Signal app on their phones to discuss an attack on the Houthis. People discussed the risk of the phones being compromised or human factors, such as adding a…
Blog - Logic Matters — 4/9/2025
I am busily proof-reading the category theory notes for typos and thinkos and expositional stumbles (while thinking how to much improve the final chapter). I’ve now reviewed the first 25 chapters, i.e. up to the first Interlude, and you’ll find…
The n-Category Café — 4/8/2025
Studying atomic nuclei forces us to quantize the concept of ellipsoid.
Computational Complexity — 4/7/2025
From November of 2024 to March of 2025 I have gotten email inviting me to speak at conferences and/or submit to journals in the following topics:NOT EVEN CLOSE TO MY FIELD:Addiction Medicine, Behavioral Health and Psychiatry.Looking forward to…
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…
Computational Complexity — 4/1/2025
PDQ ShorPDQ Shor, Peter Shor’s smarter brother, passed away last week. PDQ was a Physicist/Computer Scientist/Mathematician/Astrologer/Psychic at the University of Northern South Dakota in Wakpala.Dr. Phineas Dominic Quincy Shor III, PhD, MBA, BLT,…
Math ∩ Programming — 4/1/2025
It’s April Cools! Last year I wrote about parenting, in 2023 about friendship bracelets. and in 2022 about cocktails. This year it’s a bit of a meandering stroll through some ideas around mutual aid and self-reliance. Maternity wards If you walk…
Computational Complexity — 3/29/2025
I have often began taking a survey and quit in the middle. Why?1) It goes on to long. When I told the surveyors that he may get more people quitting for that reason so he should make it shorter he said, rather rudely, that he is an expert on…
The n-Category Café — 3/27/2025
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.
Computational Complexity — 3/26/2025
In 2012 I wrote a blog post about the growing influence of Massively Open Online Courses, or MOOCs.John Hennessey, president of Stanford, gave the CRA keynote address arguing that MOOCs will save universities. He puts the untenable costs of…
Fractal Kitty — 3/25/2025
In January, I kicked off a journey of reflection and growth at the Recurse Center (RC) – a retreat where you work at the edge of your abilities with wonderful peers to pair program, study with, and grow. My goals in participating were to learn and…
Computational Complexity — 3/24/2025
The issue of whether to record lectures or post slides or more generally how much material to give to the students is a new question (the last 20 years?) but I do have an anecdote from 1978.I was taking an applied math course on Mathematical…
The n-Category Café — 3/20/2025
A talk about some striking mathematical images.
The n-Category Café — 3/20/2025
I’m giving a talk next Friday, March 14th, at 9 am Pacific Daylight time here in California. You’re all invited! (Note that Daylight Savings Time starts March 9th, so do your calculations carefully if you do them before then.)…
Computational Complexity — 3/19/2025
With care you can explain major ideas and results in computational complexity to the general public, like the P v NP problem, zero-knowledge proofs, the PCP theorem and Shor’s factoring algorithms in a way that a curious non-scientist can find…
Proses.ID — 3/17/2025
What is reality? It might seem like a straightforward question, but Ursula Franklin, a pioneering thinker in technology and society, saw it as layered and…
Computational Complexity — 3/17/2025
I had been meaning to write a post-COVID post for a while, buta) Are we finally post COVID? (I think so)b) Are the long term affects of COVID (society not health) known yet?However, Lance wrote a post-COVID post (see here) which inspired me to do…
Computational Complexity — 3/14/2025
A long time ago I made up the question (are questions ever really made up?)What is the least number that looks prime but isn’t?It was not quite a joke in that it has an answer despite being non-rigorous.My answer is 91:Dividing by 2,3,5,11 have…
Computational Complexity — 3/12/2025
As we hit five years from when the world shut down, lots of discussions on how Covid has changed society. What about academia and computer science?It’s a challenging question to ask as Covid is not the only major change in the last five years….
The n-Category Café — 3/12/2025
CT2025 conference announcement.
Abuse of Notation — 3/10/2025
Last week I learned that Robert Paul Wolff, the philosopher who got interested in anarchism and marxism, died and I wanted to write something dedicated to him — this was the first reason I started writing this. The second one, was to finally finish…
Joel David Hamkins — 3/6/2025
This will be a talk for the Panglobal Algebra and Logic seminar at the University of Colorado Boulder, March 12, 2025, 3:30pm MDT The talk will be available live on Zoom. Contact the organizers for access. Abstract. I shall introduce … Continue…
Joel David Hamkins — 3/6/2025
I am honored to be giving the 2025 William Reinhardt Memorial Lecture at the University of Colorado Boulder, March 11, 2025. How we might have taken the Continuum Hypothesis as a fundamental axiom, necessary for mathematics Abstract. I shall…
The n-Category Café — 3/5/2025
Is the map from the Burnside ring to the representation ring of a finite group usually surjective, or usually not?
Computational Complexity — 3/5/2025
On February 20th we got the news from the National Science Foundation Algorithms Foundations Team that long-time NSF program director Tracy Kimbrel, was leaving the NSF, and not by choice.Along with many others in part-time status at NSF, my…
Abuse of Notation — 3/5/2025
At the Agda headquaters: “OK, guys, so our user pool consists only of folks who already know Haskell and Emacs Is there a way to narrow it down more?” “I got it, what if we allow unicode, so they also have to also know Latex ?” “Brilliant!”
Abuse of Notation — 3/5/2025
I don’t want to lose the human in me, I don’t want to have to see the world through their ways. I don’t want to have to feel through their point of view, To be locked inside it like an alien in a space suit. I don’t have to lose the human in me….
Computational Complexity — 3/3/2025
Karp turned 90 in January of 2025. I searched to see if there is a 90th Birthday Conference for him. I did not find one (is there one?). For which years do we have celebratory birthday conferences?Here are some conferences in honor of 60th…
The n-Category Café — 2/26/2025
PDE methods in magnitude, looked at categorically.
The n-Category Café — 2/26/2025
Potential functions from a functorial perspective.
The n-Category Café — 2/26/2025
Who are the applied category theorists working on AI, and what are they doing?
Math ∩ Programming — 2/23/2025
My four-year-old son has declared 36 to be the best number. His reason: 36 is the only number (he knows of) that is both a square and a staircase number AND an up-and-down-staircase number. “Staircase numbers” are what he calls triangular numbers…
Good Fibrations — 2/14/2025
Here’s something enticing and strange: there are two “cut and paste” invariants of the same group which are equal to dual zeta values! the euler characteristic ( \chi(SL_2(\mathbb{Z})) = \zeta(-1), ) and the tamagawa measure of (…
Fractal Kitty — 2/11/2025
On winter solstice I had my personal “new-year” and I started an experimental journal of self. My motivation was to see if my experiences and awareness change through the type of journaling that I do. Will tallying the days that I glimpse the moon,…