Welcome to Infinitely More, 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.

I shall start out with a series of essays all around infinity, serializing the chapters of my forthcoming book, The Book of Infinity, a series of vignettes on infinity, covering all my favorite elementary topics. These will be comparatively light and accessible—no special mathematical background required. But a strong curiosity about infinity is best. Please enjoy, and feel free to post comments with questions or answers. I plan one or two essays each week, which I am also using in my course this semester for my class, Infinity, aimed at mathematics and philosophically inclined undergraduates at Notre Dame.

In the future, I have plans to serialize my book-in-preparation on Infinite Games, and also material from my introductory book, Topics in Logic. There is so much I want to discuss with you all.

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And please go straight to my first essay:

Infinitely More

The Book of Numbers

A curious order on the natural numbers Consider the natural numbers up to ten, but in the following curious order: 8 5 4 9 1 7 6 3 1 0 2 0 What order is this? Is it random? No, I have placed these numbers in a very definite and logical order, using an underlying order idea with which I am sure that you, gentle reader, are familiar. Can you discover t…

24 days ago · 2 likes · Joel David Hamkins

The Book of Numbers

Infinitely More

Welcome to Infinitely More