Did you know that we can visually see why sqrt(40)=2sqrt(10)? Let's see how we can visualize rewriting square roots!

Although I happily use an abundance of em dashes in my writing—like this, often to set off a comment midstream—I would like to assure everyone that I am in fact human. I do not use AI in my writing.

To which ordinal station can you reach on the transfinite subway line, with a disembarkment at every station along the way, and with a train capacity of n passengers? www.infinitelymore.xyz/p/infinite-s...

Reading Lockhart's Lament in preparation for seminar next week and finding myself underlining nearly every single sentence. What good is that?

Infinite subway paradox. Suppose the train accommodates 25 passengers at most. To which ordinal can you reach, with some schedule of passenger itineraries, while still having at least one disembarkment at every station along the way? www.infinitelymore.xyz/p/infinite-s... #InfinitelyMore

Surprise ending! youtube.com/shorts/y3VDF...

Recently I've had the pleasure of being interviewed on the blog of the American Philosophical Association. You can read the whole thing here: blog.apaonline.org/2025/09/12/a... You don't have to read the whole thing of course, but please enjoy the two snippets that I'm pretty proud of ;)

A teaser. Surreal chess. Consider the ω×ω chessboard in the surreals. What is the order type of the board? Look for the essay soon on #InfinitelyMore.

New post-doctoral position at Notre Dame Core analytic/logic/phil math. philjobs.org/job/show/29622 2 year position, $75K annual salary plus $15K expense account. Please apply! (I am chairing this search.)

Exciting times on my probability question concerning the iterated alternating St. Petersburg gamble. Have a look! mathoverflow.net/q/500343/1946

Can you help me out with a probability question? mathoverflow.net/q/500343/1946

I have found a natural feature of the countable infinity ω that generalizes to all uncountable singular cardinals, but not to the uncountable regular cardinals.

The infinite subway paradox. In this essay, we explore the full range of paradox, providing a necessary and sufficient criteria on the finite passenger counts to realize a given target count at omega. www.infinitelymore.xyz/p/infinite-s... #InfinitelyMore

Recently at the conference in Japan on the occasion of Jörg Brendle's 60th birthday, at the conference banquet I related my account of the Sannomiya incident, when Jörg first made his big splash in the Japanese art world, when he hit the big stage. jdh.hamkins.org/the-sannomiy...

Are ultrapowers necessary for the hyperreal field? I answered on MathOverflow. mathoverflow.net/a/500155/1946

Postdoc job! I expect to have an opening at Johns Hopkins for a postdoctoral researcher working somewhere in the broad realms of physics, philosophy, and complexity. Apply at Academic Jobs Online: academicjobsonline.org/ajo/jobs/30496

The Fundamental Theorem of Finite Games. My new "short stories" essay in the current issue of the AMS Notices, giving five different proofs of the fundamental theorem of finite games, with explanations of how they generalize to infinite games. www.ams.org/journals/not...

The infinite subway paradox www.infinitelymore.xyz/p/infinite-s... #InfinitelyMore

I happened to notice that my name appears (at least once) in the Palgrave Companion to the Philosophy of Set Theory. How very nice!

For your enjoyment, here is the reading list for my undergraduate core seminar this semester in Philosophy, Science, and Mathematics. We shall focus on topics in the philosophy of mathematics, philosophy of science, and philosophy of computability and AI.

A free excerpt from Lectures on the Philosophy of Mathematics. The Hilbert Program. infinitelymore.xyz/p/hilbert-pr... #InfinitelyMore #PhilMaths

A Mathematica demo I made of wandering around a parameter space of the convex hull of various scalings the vertices of a icosahedron, dodecahedron, and icosidodecahedron. Given the right parameters, we can recover all Platonic and Catalan solids with full icosahedral symmetry.

Join me at the 2026 joint ASL-APA conference in February 2026 at the elegant Palmer House hotel in downtown Chicago. The deadline for contributed abstracts is tomorrow, so make your submissions now.

Introducing the elementary theory of surreal arithmetic, a first-order theory of the surreals that is bi-interpretable with set theory. jdh.hamkins.org/theory-of-su...

Advice for academics: please use a recognizable photo of yourself on your department web page. The purpose of these photos is to help your colleagues learn who you are. Some of us are terrible with names, and we need to look you up. When there is only a joke photo or no photo, we are forever unsure.

AI is taking over the world.....except in math evidently. I often find AI overviews on mathematical topics to be wrong. This one contradicts itself.

I'll be speaking about Alan Turing's impactful 1936 paper for the History and Philosophy of Science Colloquium at Notre Dame in October. The question is: Did Turing prove the undecidability of the halting problem? jdh.hamkins.org/did-turing-e...

Tactics versus strategies—the case of chess. Does one player have a winning tactic or both players have drawing tactics? #InfinitelyMore #FrivolitiesOfTheGods www.infinitelymore.xyz/p/tactics-ve...

Very thankful for the appreciation. www.reddit.com/r/math/comme...

The tactical variation of the fundamental theorem of finite games www.infinitelymore.xyz/p/fundamenta... #InfinitelyMore #FrivolitiesOfTheGods

Rear Window

Do you know a basis for P(omega) as a vector space over Z_2 under the operation of symmetric difference? Or P(kappa) or the set-theoretic universe V, for that matter.

Tactics versus strategies in the theory of games This week's post on Infinitely More www.infinitelymore.xyz/p/tactics-ve... #InfinitelyMore #FrivolitiesOfTheGods

Finished my China trip for this summer! 10 lectures at Peking University 1 conference talk at PKU 7 lectures at Fudan University, Shanghai, 1 mini-conference talk at Fudan 1 conference talk in Changchun 1 conference talk in Lanzhou photos.app.goo.gl/tVLoQnzVEoeJ...

Tic Tac is a first-player win. Same goes for Tic.

The curvature of Space A free excerpt from Lectures on the Philosophy of Mathematics #InfinitelyMore #PhilMaths www.infinitelymore.xyz/p/curvature-...

Different ways of drawing the exact same thing….just a plain 32x32 square grid ☺️

Here is the list of challenge questions I asked the audience (mostly graduate students) at my talk yesterday on the surreal numbers. Can you answer? Post your solutions in response to each question separately.

Cast the chess pieces randomly on the board. What are the chances you get a legal position? This week's installment on #InfinitelyMore. www.infinitelymore.xyz/p/random-che... #FrivolotiesOfTheGods

"Are you really going to Changchun?" the student asked, having seen my blog post. "That's my home town!" Yes, we leave tonight from Shanghai. What should we eat there?

Upcoming talks in China in the next few weeks.

In today's lecture on Proof we discussed the syntax/semantics dichotomy and in particular the use/mention distinction. I had a chance to mention my all-time favorite example, using pants as trousers.

I am seeing that Common Knowledge is in the air again. See my essay on epistemic logic puzzles and the problem of common knowledge. www.infinitelymore.xyz/p/epistemic-... #InfinitelyMore #TheBookOfInfinity

A follow up question seeking a chess position with a certain game-theoretic feature regarding castling. chess.stackexchange.com/q/47185/3454 Can you help?

Infinite Sudoku! Care for a game on the integer-by-integer grid of integer-by-integer grids? How about the (ℝ×ℝ)×(ℝ×ℝ) Sudoku board? Or higher cardinals? Perhaps just on a finite board. This week's post on Infinitely More. #InfinitelyMore #FrivolitiesOfTheGodsis

Nice logic argument on Reddit. 1. If God doesn't exist, then it is false that "God responds whenever you pray." 2. You never pray. 3. Therefore, God exists.

I asked a question on chess-stackexchange about a certain kind of chess position example. Can you help? chess.stackexchange.com/q/47174/3454

Shanghai dining. Thought I was ordering wine; turns out to be "wine". No regrets.