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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
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Joel David Hamkins
16
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
16
2
4
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
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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
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Joel David Hamkins
10
6
2
The Book of Infinity—pre-orders are open
Order now at your favorite bookseller
Mar 28
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Joel David Hamkins
31
6
3
Most Popular
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Zeno's paradox
Jan 7, 2023
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Joel David Hamkins
35
14
9
The surreal numbers
Jan 6, 2024
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Joel David Hamkins
39
6
5
Mathematicians disagree on the essential structure of the complex numbers
Nov 10, 2024
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Joel David Hamkins
29
4
Potential versus actual infinity
Apr 14, 2023
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Joel David Hamkins
25
20
6
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
•
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 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
16
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
16
2
4
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
6
2
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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Mindcreaser - Benjamin Portheault's substack
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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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