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 Aperiodical --- 4/16/2025
Double Maths First Thing doesn’t look an issue older than 1F Hello! My name is Colin and I am a mathematician on a mission to spread joy in the creativity and beauty of maths, in the delight of figuring things out and asking more questions. This...
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...
Crooked Timber --- 4/14/2025
And then the light of an older heaven was in my eyesand when my vision cleared, I saw Titans. — Alan Moore Today’s Occasional Paper comes to us from the James Webb Space Telescope. So let’s start with some basics: nothing can travel faster than...
“When numbers have meaning it makes it a lot easier for me” vs “I over think the given information and confuse myself”: do engineering students prefer maths questions in context?
The Aperiodical --- 4/14/2025
In 1693, Christiaan Huygens was struggling to learn the new calculus developed by his former student Gottfried Leibniz. He wrote to Leibniz asking for “any important problems where they should be used, so that this give me desire to study them”....
Crooked Timber --- 4/13/2025
Crooked Timber --- 4/13/2025
Thanks to James Wimberley for prompting me to write this, and alerting me to the data on China’s emissions Most of the news these days is bad, and that’s true of the climate. Even as climatic disasters worsen, the Trump regime is doing its best to...
The Aperiodical --- 4/10/2025
This is a guest post by Elinor, who’s been collecting her favourite maths art from the month of March. March is a month of change in the UK: the days get longer, the temperature is slowly creeping upwards, and we start to believe that spring may be...
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 Aperiodical --- 4/9/2025
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of March 2025, is now online at Fractal Kitty. The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See...
The Aperiodical --- 4/9/2025
Double Maths First Thing only exports lost puffins Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight, and to find excuses to do interesting maths. (If you could use an interesting mathematician — for the...
The n-Category Café --- 4/8/2025
Studying atomic nuclei forces us to quantize the concept of ellipsoid.
Crooked Timber --- 4/7/2025
With collapsing stock markets, retirement portfolios, and consumer confidence, there is an all-too-human tendency to focus on the economic effects of tariffs by their critics: they are a tax on consumption, they will raise inflation, reduce...
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...
The hierarchy of consistency strengths for membership in a computably enumerable set, Oxford Logic Seminar, May 2025
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
Crooked Timber --- 4/6/2025
Blog - Logic Matters --- 4/5/2025
My good friend, the logician Thomas Forster, tells me that he once shared an office with Giovanna Corsi, who at one point shared an office with Jean van Heijenoort, who was Trotsky’s personal secretary in the 1930s …. The post Four handshakes from...
Blog - Logic Matters --- 4/4/2025
So, at last, here is a full draft of Introducing Category Theory. All 49 chapters and 477 pages. I really didn’t set out to go on at such length. Honestly … In this latest version 2.7, Chapters 45–48 are very significantly improved. But the final...
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...
The Aperiodical --- 4/2/2025
Here’s a round-up of some mathematical and maths-related news that happened in March 2025 that we didn’t otherwise cover on the site. The three-dimensional Kakeya set conjecture has been proved. The result is described by Terry Tao as “spectacular...
The Aperiodical --- 4/2/2025
Double Maths First Thing picked the wrong week to give up calculus. Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight of doing mathematical things. It’s nice to finally be in a new month after April 1st was...
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...
Property, recognition, and the temporalities of life. Reading Kopenawa and Albert’s The Falling Sky. Words of a Yanomami Shaman from the perspective of economic philosophy
Crooked Timber --- 3/31/2025
What is it that people desire when they desire riches? It may seem strange that once all basic needs are fulfilled, individuals would continue to strive for ever more, working ever harder, even at the cost of their own health. Why don’t they just...
Crooked Timber --- 3/30/2025
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...
Crooked Timber --- 3/29/2025
One of the things that’s becoming clear is the determination of the Trump administration to divide humans living in the United States into two groups (to whom Wilhoit’s Law applies), citizens and immigrants. Actually it is a bit more complicated...
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.
The Aperiodical --- 3/26/2025
I’m aperiodically working my way through Martin Gardner’s cover images from Scientific American, the so-called Gardner’s Dozen, attempting to recreate these in the LaTeX drawing package TikZ. View the previous attempts. This time I chose January...
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...
The Aperiodical --- 3/26/2025
Double Maths First Thing just doesn’t know any more Hello! My name is Colin and I am a mathematician on a mission to spread delight and joy in doing maths for the sake of it. This week I have mainly been figuring out the mechanics of the Bokeh...
Crooked Timber --- 3/25/2025
Today I’d like to talk about that delightful little companion of field and garden: the shrike. [copyright Rosemary Mosco, 2024, birdandmoon.com] If you know, you know. And if you don’t know… well, let’s talk about shrikes. Shrikes are a group 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...
Crooked Timber --- 3/24/2025
As universities worldwide face major cuts, especially to the humanities, this meme has been doing the rounds. So I thought I’d share my story about Indiana Jones’ last day of work, drawn in part from Indiana Jones and the Dial of Destiny. Indiana...
Crooked Timber --- 3/23/2025
Computational Complexity --- 3/22/2025
BILL: Lance, my wife asked if you dislike Ramsey Theory because you are colorblind.LANCE: (laughs) It's why I don't like Ramsey Theory talks--impossible for me to follow. But I don't actually dislike Ramsey theory. I just don't like it as much as...
Crooked Timber --- 3/22/2025
Yesterday Columbia University gave in to blackmail by President Trump (see here the letter [HT: NYT]) in order to allow to begin negotiations over the recovery of $400 million in research funding. Its unsigned letter (here HT: Leiterreports) leaves...
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...
The Aperiodical --- 3/19/2025
Double Maths First Thing cannot currently take your call. Please leave a message after the beep. Beep. Hello! My name is Colin and I am a mathematician on a mission to spread mathematical joy and delight. This week, I am mainly swearing at Scroggs...
Crooked Timber --- 3/19/2025
It’s been evident since Trump’s inauguration that the US, as we knew it, is over. I’ve been looking at some of the US-centred organisations and economic dependencies that will need to be rebuilt. But I hadn’t given much thought to the university...
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…
Crooked Timber --- 3/17/2025
Here are two groups of Western philosophers. We’ll call them Group A and Group B. Here’s Group A: Plato, Epicurus, Plotinus, Aquinas, Duns Scotus, Francis Bacon, Hobbes, Locke, Spinoza, Newton, Leibniz, David Hume, Herbert Spencer, John Stuart...
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...
Crooked Timber --- 3/16/2025
At the cutting edge of world history and industrial progress back when it was built in 1799, but now Ironbridge and nearby Coalbrookdale are bucolic backwaters where you struggle to get a decent phone signal.
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.
Blog - Logic Matters --- 3/10/2025
The post Schubert, extraordinarily appeared first on Logic Matters.
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...
Blog - Logic Matters --- 3/7/2025
I had written a few paragraphs here sounding off about some published “continental philosophy” style meanderings about the philosophy of mathematics (which, as typical, show no real knowledge of mathematics) when I checked and discovered that the...
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....
Karp recently turned 90 but there was no conference to celebrate that. Which numbers do we use and why?
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...
Blog - Logic Matters --- 2/27/2025
At least Zeno’s arrow got ever-closer to its target. But the newly posted version 2.6 of Introducing Category Theory has two chapters fewer than version 2.5 … I’m not really going backwards. In the last three weeks, there have been distractions,...
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.
Computational Complexity --- 2/26/2025
Just as I was complaining that we haven't seen many surprising breakthroughs in complexity recently, we get an earthquake of a result to start the year, showing that all algorithms can be simulated using considerable less memory than the time of...
The n-Category Café --- 2/26/2025
Who are the applied category theorists working on AI, and what are they doing?
Computational Complexity --- 2/24/2025
Alice is scheduled to teach X in the Spring.Then Alice CAN'T! (illness, death, or some other reason)What is the department to do?1) If it's an undergraduate class then likely there are other people who are QUALIFIED. Perhaps a grad student, perhaps...
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...
Abuse of Notation --- 2/20/2025
To kill an art, create a way to perform the utilitarian aspect of it in a way that is formulaic and efficient i.e. artless. (The art is not really dead, it is just understood by a very small amount of people (mostly other creators).) The art of...
Computational Complexity --- 2/19/2025
I recently completed Tomorrow, and Tomorrow, and Tomorrow by Gabrielle Zevin, a book recommended by many including the City of Chicago. The novel covers the decades long journey of two game developers, Sadie and Sam, and how their lives interact...
Computational Complexity --- 2/18/2025
Let ([n]) be the set ({1,\ldots,n}). (This is standard.)Let X be a set of integers. (X) is sum-free if there is NO (x,y,z\in X) such that (x+y=z). (Note that (x=y) is allowed.) Lets try to find a large sum-free set of ([n]). One...
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 (...
Computational Complexity --- 2/12/2025
A student asked me if complexity research was easier when I was a student. Interesting question. Let's compare research now versus the late 80's.The big advantage today is technology. Just a small sampling below.Information: Google, Wikipedia,...
Abuse of Notation --- 2/12/2025
The things you fear would happen are already happening. The only way to make them seize is to stop fearing.
Abuse of Notation --- 2/12/2025
title: The hand cluches layout: microblog category: microblog tags: zen — The hand clutches so hard, that it does not realize it is not holding anything.
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,...
The n-Category Café --- 2/10/2025
There's a universal characterization of standard Borel spaces!
Math ∩ Programming --- 2/10/2025
A colleague of mine recently lent a hand implementing a polynomial approximation routine I could port to our compiler, though it wasn’t the method I was expecting. As I had written about previously, I was studying the Remez algorithm and...
Abuse of Notation --- 2/10/2025
This is a list of varioust arguments, quarrels, disagreements i.e. “beefs” that philosophers have had with one another. Heraclitus vs. Parmenides (5th century BCE) Beef: A clash between Heraclitus’s belief in constant change and Parmenides’s...
Blog - Logic Matters --- 2/9/2025
The La Traviata broadcast from the Royal Opera House last night was wonderful — and Lisette Oropesa as Violetta was simply stunning. You can catch the performance on BBC Radio for a month. Don’t miss the chance. The post Don’t miss a superb La...
Math ∩ Programming --- 2/7/2025
Back in 2020, when I worked in the supply chain side of Google, I had a fun and impactful side project related to human-level explanations of linear programs. A linear program is a mathematical model that defines some number of variables, linear...
Blog - Logic Matters --- 2/3/2025
I have updated Introducing Category Theory to version 2.5: download here. As well as many minor corrections, including an improved proofs of a couple of theorems, there is a restored §18.4 on ‘naming’ arrows, and a new §18.5 touching on Lawvere’s...
The n-Category Café --- 2/2/2025
If you want to help save US federal web pages and databases, here are some things to do.
Computational Complexity --- 2/2/2025
The National Science Foundation is one of the agencies most affected by the various executive orders issued by the Trump administration. As a critical funder of research in theoretical computer science, and science and engineering more broadly, the...
Fractal Kitty --- 2/2/2025
Find balance through symmetry.$$f(x) = f(-x)$$Approximation improves with experience.$$e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots$$ To untangle is to meditate.$$\huge{\bigcirc}$$Be...
Math3ma --- 2/2/2025
It's hard for me to believe, but Math3ma is TEN YEARS old today. My first entry was published on February 1, 2015 and is entitled "A Math Blog? Say What?" As evident from that post, I was very unsure about creating this website. At the time,...
Fractal Kitty --- 1/31/2025
One thing I love about math and art is the conversations and iterations that flow from their patterns and beauty. After posting Walking Ripples, I have enjoyed seeing how the simplicity of shading circles propagates in conversation, art, and...
The n-Category Café --- 1/30/2025
Thinking about the cardinality of limits leads to a new numerical invariant of set-valued functors.
The n-Category Café --- 1/29/2025
Warming up to a dual concept to magnitude, with an aside on a new connection between magnitude and entropy.
Computational Complexity --- 1/29/2025
In writing the drunken theorem post, I realized I never wrote a post on Lautemann's amazing proof that BPP is contained in (\Sigma^p_2), the second level of the polynomial-time hierarchy.Clemens Lautemann, who passed away in 2005 at the too young...
On Skolem’s paradox and the transitive submodel theorem, Rust Belt Workshop in the Philosophy of Logic, Language, and Mathematics, February 2025
Joel David Hamkins --- 1/28/2025
This will be a talk for the Rust Belt Workshop in the Philosophy of Logic, Language, and Mathematics, held at Ohio State University in Columbus, Ohio, February 8-9, 2025, University Hall (230 N Oval Mall, Columbus, OH) Room 386B. Abstract. …...
Good Fibrations --- 1/28/2025
Computational Complexity --- 1/27/2025
4444=1936.4545=2025. This year!46*46= 2116.Since my fake birthday is Oct 1, 1960 (I do not reveal my real birthday to try to prevent ID theft), which is past 1936, and I won't live to 2116 unless Quantum-AI finds a way to put my brain in a a vat,...
Fractal Kitty --- 1/27/2025
Do you ever look at knitted items and liken them to dragon scales? - I do. So when I decided to make generative textured hats it made sense to call them Wyrm Beans.Just as we can have generative pixel colors on a screen, we can have generative...
Blog - Logic Matters --- 1/26/2025
In case you missed the announcement on the categories mailing list: Bill’s family is happy to announce that the Lawvere Archives websiteis launched! Click here: https://lawverearchives.com/ We ask you to explore, send us your ideas, and if possible...