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The Paradox of Giants: Strange Consequences in High Dimension—Lectures on Infinity (lecture 3)
The paradox of giants, the paradox of Gabriel's horn, the painter's paradox, and further paradoxes of dimension.
Jul 23
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Joel David Hamkins
18
4
5
Supertasks: Doing Infinitely Many Things — Lectures on Infinity (Lecture 2)
Let us explore several paradoxical supertasks—the deal with the Devil, balls in a sack, the Chocolatier's game, and more.
Jul 16
•
Joel David Hamkins
26
6
Zeno's Paradox and Infinite Sums—Lectures on Infinity (lecture 1)
An ancient puzzle leads ultimately to a remarkable observation on the malleable nature of infinite sums.
Jul 10
•
Joel David Hamkins
19
1
4
Lectures on Infinity
A series of lectures on infinity, with all my favorite paradoxes and conundrums.
Jul 9
•
Joel David Hamkins
24
3
6
June 2026
The Natural Field of Ordinals
Which numbers are transcendental over the ordinals? Which are irrational? Let us introduce the natural field of ordinals and consider the status of √2…
Jun 25
•
Joel David Hamkins
9
2
6
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
11
3
5
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
16
3
3
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
13
9
5
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
18
4
6
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
17
2
5
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
8
1
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
10
10
2
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