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The omnific integers are an integer part of the surreal numbers
Can we find a surreal-numbers analogue of the integers? An integer part of the surreal numbers, a discretely ordered subring, for which every surreal…
Oct 23
•
Joel David Hamkins
12
4
The surreal ω × ω chessboard is bigger—and stranger—than you think
What is the nature of the surreal ω × ω chessboard? How many squares are there? How many chess pieces shall we require to set up the board?
Oct 13
•
Joel David Hamkins
8
13
The uncountable transfinite subway
We explore a more sophisticated version of the infinite subway paradox, with stations all the way to the uncountable ordinals and beyond
Sep 28
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Joel David Hamkins
9
20
The infinite subway paradox—extending into the transfinite
We extend the infinite subway paradox into the countable ordinals. Can you meet the infinite subway challenge?
Sep 19
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Joel David Hamkins
7
9
The infinite subway—a full range of paradox
The second in a series of essays on the infinite subway paradox, in which we explore the full range of paradoxical behavior
Sep 11
•
Joel David Hamkins
9
1
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Zeno's paradox
Jan 7, 2023
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Joel David Hamkins
30
14
The surreal numbers
Jan 6, 2024
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Joel David Hamkins
33
6
The Book of Numbers
Jan 2, 2023
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Joel David Hamkins
37
12
Potential versus actual infinity
Apr 14, 2023
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Joel David Hamkins
25
20
The Book of Infinity
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Take my Infinity final exam!
How well can you answer the questions on the final exam for my Infinity course?
Dec 21, 2024
•
Joel David Hamkins
17
15
Throwing Darts at the Real Line
Mathematical philosophers have proposed various thought experiments suggesting different resolutions of the continuum hypothesis. Can we hope…
Sep 25, 2024
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Joel David Hamkins
8
10
What is the infinite?
What does it mean, exactly, to say that a set is infinite? Can we provide precise mathematical definitions of the finite and the infinite?
Sep 11, 2024
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Joel David Hamkins
12
4
Infinite Games
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Tactics versus strategies—the case of chess
Does chess admit of winning or drawing tactics? Which information exactly do we need to include as part of the board position?
Aug 17
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Joel David Hamkins
9
6
The tactical variation of the fundamental theorem
We prove the tactical variation of the fundamental theorem of finite games—for finite games with sufficiently rich board positions, one of the players…
Aug 10
•
Joel David Hamkins
6
2
Tactics versus strategies in the theory of games
How do tactics differ from strategies? Does the fundamental theorem of finite games hold for tactics? Must every finite game have a winning tactic for…
Aug 3
•
Joel David Hamkins
18
6
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
Benjamin Portheault
Pershmail
Michael Pershan
Science without the gobbledygook
Sabine
Math and Art
Erin Carmody
3Blue1Brown mailing list
Grant Sanderson
JDH Links
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JDH on Twitter
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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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