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The Book of Infinity—pre-orders are open
Order now at your favorite bookseller
Mar 28
•
Joel David Hamkins
27
6
3
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
10
4
4
Counting to Epsilon Naught
Let us aspire to count much higher in the ordinals. How high can you count?
Mar 4
•
Joel David Hamkins
14
4
3
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
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Joel David Hamkins
6
3
1
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
10
8
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
•
Joel David Hamkins
39
6
5
Mathematicians disagree on the essential structure of the complex numbers
Nov 10, 2024
•
Joel David Hamkins
29
4
The Book of Numbers
Jan 2, 2023
•
Joel David Hamkins
44
12
4
The surreal numbers
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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
10
4
4
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
See all
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
10
4
4
Counting to Epsilon Naught
Let us aspire to count much higher in the ordinals. How high can you count?
Mar 4
•
Joel David Hamkins
14
4
3
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
10
8
3
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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Pershmail
Michael Pershan
The Curious Mind
Álvaro Muñiz Brea
The Palindrome
Tivadar Danka
3Blue1Brown mailing list
Grant Sanderson
Math and Art
Erin Carmody
JDH Links
JDH web page
JDH on Twitter
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JDH on MathOverflow
JDH on YouTube
JDH on Google Scholar
JDH at MIT Press
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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