Regrettable failures in the natural ring of ordinals. - long intervals of consecutive odd numbers - intervals of consecutive prime numbers - Collatz conjecture fails - GCDs exist, but Bézout identity fails - Euclidean algorithm fails www.infinitelymore.xyz/p/regrettabl... #InfinitelyMore

Genius! youtube.com/shorts/RC2pF...

I posted an answer on MathOverflow in an open-ended question about how (or why) we are to do mathematics in the era of AI. mathoverflow.net/a/511564/1946 #MathOverflow

Please enjoy this essay I wrote some time ago on logical duality in propositional logic. open.substack.com/pub/joeldavi... #InfinitelyMore

AI has taught us something very important. That for most people, "not actually good, but seemingly good-enough-to-get-by" is most people's goal in life.

A rich, thorough exploration of infinity that combines mathematical precision with playful, accessible coverage of a fascinating variety of paradoxes and conundrums. Joel David Hamkins' "The Book of Infinity" publishes in August! mitpress.mit.edu/978026205401...

I asked an AI for its opinion on the arXiv's new "no AI slop" policy and it said it's a very bad idea and to support its argument it cited a recent paper from the Journal of Completely True Things

I have realized that the Collatz conjecture fails in the natural ring of ordinals...

Never forget:

The natural ring of ordinals has prime factorization. Every number factors uniquely as a product of primes. Please enjoy this week's installment on Infinitely More. www.infinitelymore.xyz/p/natural-ri... #InfinitelyMore

Is anybody playing 3D Go?

Back home.

New publication came out today. It's a short reply to a piece by Jimmy Alfonso Licon from me, @hikemix.bsky.social and James Humphries in Philosophy and Technology. link.springer.com/article/10.1... #PhilTech #LLMs #Bullshit

James Hanson has a dagger out for the hype surrounding the Lawvere fixed-point theorem. mathoverflow.net/a/511183/1946

Kurt Gödel was a visiting professor at the University of Notre Dame in 1939, evidently his first and only paid teaching position. He lectured on the axiomatization of set theory and the axiom of choice—this was just after he had proved the relative consistency.

Years ago, when I was a math graduate student TA, I would grade quizzes or exams, and occasionally I would find a submission consisting of incoherent nonsense. At the time, it seemed unkind to give harsh feedback, and so I would write, "Sorry, I don't understand this."

Woo hoo! #InfinitelyMore

Please enjoy my essay series on the infinite subway paradox... open.substack.com/pub/joeldavi...

My latest essay on Infinitely More. www.infinitelymore.xyz/p/the-natura... #InfinitelyMore

I posted an answer to a question of @gro_tsen on MathOverflow about ultrafinitism about what it would take to convince an ultrafinitist that 2^k exists. mathoverflow.net/a/510940/1946

The slides of my talk are now available. jdh.hamkins.org/a-potentiali...

Finishing up with Year 13 in #Mathstoday, looking at some slightly lesser spotted questions to do with integration and logarithms #Alevelmaths

Speaking today on ultrafinitism. calendar.ohio.edu/event/a-pote...

Speaking in Athens on Thursday this week. calendar.ohio.edu/event/a-pote...

Today's bake. #Todaysbake

My periodic reminder of the adjectival hyphenation rule. 1. A red bike factory is a bike factory that is red. 2. A red-bike factory is a factory that makes red bikes. Iterated adjectives are hyphenated to delimit the scope of applicability, like parentheses.

I'm thinking of creating a calendar with various images and mathematical illustrations from my books, perhaps with a short discussion of the mathematical meaning of the image. Good idea? Or would people rather have T-shirts and water bottles, etc.? Let me know.

Speaking next week at Ohio University. A potentialist perspective on ultrafinitism. jdh.hamkins.org/a-potentiali...

A clip from my conversation with Lex Fridman, in which we discuss the big bang of numbers, the surreal genesis. The surreal numbers are a vast number system unifying all our familiar numbers into one collossal system. www.infinitelymore.xyz/p/the-big-ba... #InfinitelyMore @lexfridman.bsky.social

Today I had my students discuss what makes soup soup. www.youtube.com/watch?v=Y1HV...

Please enjoy my essay on nondefinabilty. #InfinitelyMore #PanoramaOfLogic substack.com/home/post/p-...

Today's topic for my infinity class: Infinite Liars! www.infinitelymore.xyz/p/infinite-l... #InfinitelyMore #BookOfInfinity

Last week's guest lecture in my Infinity class was given by Notre Dame philosophy grad student Jacob Harvey, on the genre of Infinitary Hat Puzzles. www.infinitelymore.xyz/p/infinitary...

I will read that for a while. Pen and paper, no LLM cheating…

Detroit public library.

The slides are now available for my Owens Lecture talk today. We had a great discussion in the Q & A. jdh.hamkins.org/truth-and-pa...

Learned today that Gettier was at Wayne State University when he wrote the famous paper on epistemology.

Giving the Owens Lecture tomorrow at Wayne State University. jdh.hamkins.org/truth-and-pa...

Yay! Tomorrow in my Infinity class: Philosophical Dialogue day. Students have all paired up and will perform philosophical dialogues exhibiting various philosophical points of contention. Potentialism versus actualism; Cantor-Hume principle versus Euclid's principle; etc.

This figure shows how to realize the natural product of two ordinals α⊗β as a linearization of the coordinatewise product order. Sort the blocks arising from the Cantor normal form. Each block in effect is a higher-dimensional rectangular product.

Speaking on Tuesday this week for the Notre Dame Logic Seminar. 2pm 125 Hayes-Healey jdh.hamkins.org/consistency-...

A pile of notes and false starts on the way to my essay on the natural product of ordinals.

The Natural Product of Ordinals. Enjoy this latest installment in my series of essays on ordinal arithmetic, part of a larger series on the surreal numbers. www.infinitelymore.xyz/p/natural-pr... #InfinitelyMore

Glass half full, or glass 7/8 empty?!

Today's topic in my Infinity class: The axiom of choice. www.infinitelymore.xyz/p/axiom-of-c... #BookOfInfinity #InfinitelyMore

Take today's quiz in my Infinity class: Tell the story of the continuum hypothesis. What does it say? What is the logical status? Mention the relevant thinkers and dates. What philosophical positions and controversies arise particularly in connection with it?

One of the publication reviewers of The Book of Infinity had objected that some chapters seem to be about the very large finite numbers, rather than infinity itself. Is that a problem? Let me know... #BookOfInfinity

Coming soon on #InfinitelyMore. Natural product of ordinals.

I shall be speaking April 14 at the Notre Dame Logic Seminar. jdh.hamkins.org/consistency-...