Infinitely More

About Infinitely More

Infinitely More is my ongoing collecton of essays on the mathematics and philosophy of the infinite. You’ll find paradox and fun—and all my favorite logic conundrums and puzzles. I like to reveal the quirky side of mathematics and logic, but with a keen eye open for when they happen to engage with philosophically deeper foundational matters.

The Book of Infinity

Throughout Spring 2023 and into the summer I shall be serializing here the chapters of my forthcoming book, The Book of Infinity, a series of vignettes on infinity. I aim to cover a huge collection of topics—Zeno’s paradox, the coastline paradox, fractal dimension, supertasks, the paradox of the largest number contest, Galileo’s Salviati, Hilbert’s Grand Hotel, Cantor’s uncountable cardinals, Goodstein and the Hydra, counting in the ordinals, the infinitary Liar paradoxes, the continuum hypothesis, the axiom of choice, orders of infinity, infinitary utilitarianism, infinitary computability, indescribability, the sand reckoner, paradoxes of high dimension, the outer limits of reason via incompleteness, and more.

This substack is an experiment for me, publishing my book by serializing it this way, rather than in the usual manner. I see several benefits, chiefly the stronger connection with all of you, my readers. Please participate in the comment sections on the posts. I try to read everything there and I shall often respond to posts.

I am using this book as the main text for a new undergraduate course I have designed on infinity, which I am teaching this semester at the University of Notre Dame.

A Panorama of Logic

Beginning Summer 2023 I shall be serializing material from my new book, A Panorama of Logic, providing a survey to a wide selection of topics in logic for mathematicians, philosophers, and computer scientists, at advanced undergraduate/early graduate level.

Infinite Games—Frivolities of the Gods

I shall also soon be serializing the chapters from another new book on infinite games. Regular essays on all my favorite instances—infinite chess, infinite checkers, infinite Hex, infinite Go, infinite Wordle, infinite Mastermind, infinite Sudoku, infinite Wordle, connect Infinity, infinite Nim, and many more. We'll discuss the underlying theory of infinite games, developing the whole theory from the ground up, but with a light touch.

Math for Kids

Beginning next year, I will also be serializing my book on Math for Kids, gathering together all my favorite topics for kids, from Kindergarten up to any age. I have regularly gone into my kid’s schools for many years to provide lessons for math enrichment, to inspire a love of mathematics in the kids. The kids love it, the teachers, and the parents, and so I’d like to share all my Math-for-kids activities with you.

About me

My name is Joel David Hamkins, and I am the O’Hara Professor of Logic at the University of Notre Dame. I just arrived here at Notre Dame from the University of Oxford, where until last year I was Professor of Logic, as well as the Sir Peter Strawson Fellow at University College, Oxford. Before Oxford, I was for many years at the City University of New York, where I was Distinguished Professor, on the graduate faculty at the CUNY Graduate Center in Mathematics, in Philosophy, and in Computer Science, and also in Mathematics at the College of Staten Island.

I am both mathematician and philosopher, conducting research in mathematical and philosophical logic, especially set theory and the philosophy of set theory, and the philosophy of mathematics.

My original training is in mathematics, PhD in mathematics 1994 from University of California at Berkeley, BS California Institute of Technology. Over the years my set-theoretic work became increasing engaged with philosophical issues in the foundations of mathematics and so I have turned myself also into a philosopher, although I suppose I have an identity crises as to whether I am a mathematician or philosopher.

You can find out more about me on my blog, on Twitter @JDHamkins, and my YouTube channel. I am the top-rated user on MathOverflow.

I also have several books published with MIT Press:

Find out about all my books here.

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The mathematics and philosophy of the infinite

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Joel David Hamkins 

Mathematics and Philosophy of the Infinite