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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
7
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
9
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
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
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Joel David Hamkins
17
4
6
Most Popular
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Zeno's paradox
Jan 7, 2023
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Joel David Hamkins
35
14
10
Mathematicians disagree on the essential structure of the complex numbers
Nov 10, 2024
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Joel David Hamkins
29
4
The surreal numbers
Jan 6, 2024
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Joel David Hamkins
38
6
5
The Book of Numbers
Jan 2, 2023
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Joel David Hamkins
44
12
4
The surreal numbers
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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 surreal line is topologically compact—or is it?
Shocking instances of compactness in the surreal line
Nov 28, 2025
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Joel David Hamkins
12
2
5
The surreal line is topologically disconnected—or is it?
The surreal line is topologically disconnected according to a natural conception of connectedness. Nevertheless, on another conception—attending to…
Nov 15, 2025
•
Joel David Hamkins
12
8
4
The ordinal numbers
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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
7
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
9
3
5
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
Ultrafinitism
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The Book of Infinity
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Infinite Games
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A Panorama of Logic
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Proof and the Art
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Philosophy of Mathematics
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The mathematics and philosophy of the infinite
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Recommendations
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The Deranged Mathematician
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Math and Art
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JDH Links
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My Books
Lectures on the Philosophy of Mathematics, MIT Press 2021
Proof and the Art of Mathematics, MIT Press 2020
Proof and the Art of Mathematics: Examples and Extensions, MIT Press, 2021
A Mathematician's Year in Japan, Kindle KDP, 2015
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