Infinitely More

Fermat’s last theorem in the natural ring of ordinals

Are there any nontrivial solutions of the famous Fermat equation in the natural ring of ordinals?

Jun 13 • Joel David Hamkins

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Set theory, pluralism, and the multiverse view—About Logic #13

A sweeping conversation on the philosophy of mathematics and set theory, including a few core disagreements, on the About Logic series with Deniz…

Jun 3 • Joel David Hamkins

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May 2026

Regrettable Failures in the Natural Ring of Ordinals

The natural ring of ordinals has unique prime factorization, but other natural features go wrong—the concept of even goes awry, greatest common divisors…

May 24 • Joel David Hamkins

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The Natural Ring of Ordinals Has Prime Factorization

The natural ring of ordinals is a unique factorization domain—every number factors uniquely as a finite product of primes.

May 14 • Joel David Hamkins

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The Natural Ring of Ordinals

The natural ring of ordinals is the discretely ordered ring generated by the ordinals in the natural arithmetic. The ring exhibits many attractive…

May 4 • Joel David Hamkins

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April 2026

The big bang of numbers

On the big bang of numbers, the surreal genesis—an excerpt from my podcast with Lex Fridman, a sweeping conversation on infinity, philosophy, and…

Apr 23 • Joel David Hamkins

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The natural product of ordinals

Five different self-standing but equivalent accounts of the natural product of ordinals, reflecting five different philosophical perspectives on this…

Apr 12 • Joel David Hamkins

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March 2026

The Book of Infinity—pre-orders are open

Order now at your favorite bookseller

Mar 28 • Joel David Hamkins

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Natural Ordinal Addition

Five different self-standing accounts of natural addition in the ordinals, reflecting five different philosophical perspectives on how we should best…

Mar 15 • Joel David Hamkins

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Counting to Epsilon Naught

Let us aspire to count much higher in the ordinals. How high can you count?

Mar 4 • Joel David Hamkins

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February 2026

On the greats and mathematical style

Lex Fridman and I discuss who is the greatest mathematician in history, and what are the different mathematical styles of undertaking mathematical…

Feb 22 • Joel David Hamkins

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Cantor Normal Form

Cantor proved a remarkable fact about ordinals, providing an ordinal notation system in which every ordinal admits a unique canonical representation by…

Feb 12 • Joel David Hamkins

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