Just realized that $3.1415\ldots$, blah blah blah gives bad spacing, but $3.1415\ldots,$ blah blah blah looks alright.

Yep! Thanks to @joeldavidhamkins.bsky.social www.infinitelymore.xyz/p/monkey-mad...

The next essay in my series on ultrafinitism. www.infinitelymore.xyz/p/ultrafinit... #InfinitelyMore

Let it go, this too shall pass. I've been enjoying OK Go, video filmed at Notre Dame, in part with the Notre Dame marching band. Enjoy! youtu.be/UJKythlXAIY?...

Steffen Lempp, with the ASL, is organizing an effort to translate the work of Georg Cantor from German to English, with translation and commentary. (I am shocked at how much has never been translated.) If you are interested in getting involved, please contact Lempp.

Substack is allowing a great holiday special for Infinitely More. 50% off the annual subscription for groups of 2 or more! Subscribe for yourself and give a gift. Or just give gifts to others. Sign up at: www.infinitelymore.xyz/special2026 #InfinitelyMore

Enjoy this first in a series of three critical essays on Ultrafinitism, according to which very large numbers simply do not exist. www.infinitelymore.xyz/p/ultrafinit... #InfinitelyMore

New blog post about the history of my collection of geometric visualisation puzzles Jenga Views. BONUS: I've added even more puzzles! cc @joeldavidhamkins.bsky.social davidkbutler.xyz/2025/12/11/j...

Time for epistemic logic puzzles! www.infinitelymore.xyz/p/epistemic-... #InfinitelyMore #PanoramaOfLogic We are discussing these next week in my Core Seminar in Philosophy, Science, and Mathematics.

Plans underway to expand my essay series on the surreal numbers to a book-length introductory treatment.

In truth, at a talk I'd rather hear a clear account of the ideas rather than a clear account of the credit-attribution and reference history of the ideas.

The surreal line is topologically compact—or is it? Read the latest installment in my series of essays on the surreal numbers. #InfinitelyMore www.infinitelymore.xyz/p/surreal-co...

I was at Benedikt Eastaugh's talk today for the Oxford Phil Math Seminar. Quite enjoyable. The topic (joint with Walter Dean) was: The reverse mathematics of philosophical argument, in which he explored the reverse mathematical strength of philosophical arguments w. mathematical engagement.

One of my graduate students asked a great question today: does Zermelo's proof of the well-order theorem from AC use the replacement axiom?

The surreal line is disconnected—or is it? The answer depends on your conception of what counts as an open class. www.infinitelymore.xyz/p/surreal-li... #InfinitelyMore

What is 6!×7! ?

This week's reading for the Core seminar on Philosophy, Science, and Mathematics. We are moving into the philosophy of computability, including complexity theory, and then AI. Starting with Turing 1936.

Speaking on Surreal Arithmetic (SA) next week at the Notre Dame Logic Seminar jdh.hamkins.org/surreal-arit...

See my series of essays on the concept of interpretability for models and theories in first-order logic. www.infinitelymore.xyz/t/interpreta... #InfinitelyMore #PanoramaOfLogic

Tonight on campus at Notre Dame. I assure you that under that snow, the leaves are the most incredible majestic autumn colors!

Barbara Montero on machine consciousness, appearing in the New York Times today: www.nytimes.com/2025/11/08/o...

Take my midterm exam! This was yesterday's midterm exam for my Core Seminar in Philosophy, Science, and Mathematics, an undergraduate seminar here at Notre Dame. So far, we've read the works in this photo, in truth a fairly demanding load for (half) an undergraduate course.

I answered a question on MathOverflow concerning how we are think about running a Turing machine program inside a nonstandard model of arithmetic. mathoverflow.net/a/503573/1946

Midterm exam tomorrow. Wish my students success!

My latest installment in a series of essays on the surreal numbers. This week, we look at several failures of the analogy between the Omnific integers and the integers—Oz is not so very like ℤ after all. www.infinitelymore.xyz/p/omnific-in... #InfinitelyMore

I am truly honoted to be giving the DePrima lecture at Caltech in a few weeks. This distinguished annual lecture series aims to bring mathematical researchers to Caltech to give a talk for the undergraduate mathematical community.

I realized today that the natural sum and product in the ordinals does not play nicely with the concept of even. The every-other pattern breaks down, and we do not have the Euclidean algorithm, because ω cannot be divided by 2 with remainder 0 or 1.

Here are some images I created for a forthcoming article by Barbara Montero and John Toner on the role of effort in expert action. Victory at all costs--the role of effort in expert action.

A paper of mine figures in this MathOverflow question concerning the topic of...wait for it...a strengthening of the weakly superstrong cardinals. mathoverflow.net/q/421788/1946

I have extended my post on the Omnific integers to discuss how they relate to ⟨Ord⟩, the subring generated in No by the ordinal numbers. After all, ⟨Ord⟩ is a discretely ordered subring of the surreals. Is it an integer part? www.infinitelymore.xyz/p/omnific-in... #InfinitelyMore

This week's reading for my undergrad PhilSciMath core seminar.

I answered a question of Elliot Glazer's on MathOverflow which turned on the set-theoretic analogue of the universal algorithm. mathoverflow.net/a/502069/1946

In contrast to Conway, in my new essay I give a purely order-theoretic account of the omnific integers. Also a sign-sequence account, a gap-diameter account, and more, but prove them all equivalent, including Conway's. www.infinitelymore.xyz/p/omnific-in... #InfinitelyMore

The omnific integers are an integer part of the surreal numbers The latest installment in my series of essays on the surreal numbers. www.infinitelymore.xyz/p/omnific-in... #InfinitelyMore

Hit 8000. Thank you subscribers! www.infinitelymore.xyz #InfinitelyMore Weekly content on the mathematics and philosophy of infinity.

Please enjoy my series of essays on the subtle distinction between the game-theoretic concepts of tactics and strategies. www.infinitelymore.xyz/t/tactic #InfinitelyMore

I edited my answer on MO on the fundamental theorem of finite games. Take a look at mathoverflow.net/a/260471/1946

Take a ride on the transfinite subway. See my recent series of essays on the infinite subway paradox. (Start at the oldest essay, at bottom, and move up.) www.infinitelymore.xyz/t/infinite-s... #InfinitelyMore

This Friday, lunch seminar for the History and Philosophy of Science seminar.

How many unit lengths span the interval [0,ω] in the surreal numbers? Find out at www.infinitelymore.xyz/p/surreal-ch.... #InfinitelyMore

I am scheduled to be offering my course on Infinity next semester, and I have been a little worried that previously the class may have been a bit too hard, too demanding of the students. To correct this, my wife Barbara has suggested that I lecture instead on the half infinite.

This week's reading for my undergrad PhilSciMath core seminar. Looking forward to the discussion.

The surreal ω × ω chessboard is bigger—and stranger—than you think! Enjoy my latest post on #InfinitelyMore. www.infinitelymore.xyz/p/surreal-ch...

Asked my pal from Somerset if he knew anyone capable of taking the square root of -𝑟². "I are!" he said. That's a proof by country diction.

I answered a question on MathOverflow about the fruitfulness of considering the closeness-to-falsity of a given statement in mathematics. mathoverflow.net/a/501465/1946

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.)

I am deeply honored to be invited to give the De Prima lecture at Caltech this fall, a distinguished annual math lecture aimed primarily at undergraduates. Help me decide on a topic! What would you request, drawing from topics on which you've seen me write or speak?

I answered a question on MathOverflow about the Boolean ultrapower, regarding the algebraic approach to the ultrapower versus the names-based approach. mathoverflow.net/a/501257/1946

This week's reading for my undergrad PhilSciMath core seminar. Looking forward to the discussion.