Infinitely More

About Infinitely More

Infinitely More is my ongoing collection 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

Over the past year or so, I have been serializing here the chapters of my forthcoming book, The Book of Infinity, a series of vignettes on infinity. We have covered 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.

The book is appearing with MIT Press.

A Panorama of Logic

I am also 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 am also 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.

The Surreal Numbers

I am also regularly posting in my series of essays on the surreal numbers. These are forming what I plan as a new book on this topic.

About me

My name is Joel David Hamkins, and I am the O’Hara Professor of Logic at the University of Notre Dame. I 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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