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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
11
September 2025
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
•
Joel David Hamkins
8
17
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
•
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
The infinite subway paradox
The first in a series of essays on the infinite subway paradox
Sep 3
•
Joel David Hamkins
9
9
August 2025
The Hilbert program
An excerpt from Lectures on the Philosophy of Mathematics
Aug 25
•
Joel David Hamkins
23
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
•
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
July 2025
The curvature of space
An excerpt from Lectures on the Philosophy of Mathematics
Jul 27
•
Joel David Hamkins
15
Random chess position
How likely is a random arrangement of the chess pieces on the chessboard to be a legal position?
Jul 20
•
Joel David Hamkins
9
3
Infinite Sudoku
Shall we play the Sudoku game? Starting from an empty board, we take turns placing numbers, always conforming with the Sudoku condition. Who wins? And…
Jul 12
•
Joel David Hamkins
11
4
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