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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
7
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Tactics versus strategies—the case of chess
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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
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Joel David Hamkins
6
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The tactical variation of the fundamental theorem
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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
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Joel David Hamkins
12
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Tactics versus strategies in the theory of games
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6
July 2025
The curvature of space
An excerpt from Lectures on the Philosophy of Mathematics
Jul 27
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Joel David Hamkins
13
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The curvature of space
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Random chess position
How likely is a random arrangement of the chess pieces on the chessboard to be a legal position?
Jul 20
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Joel David Hamkins
9
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Random chess position
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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
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Joel David Hamkins
11
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Infinite Sudoku
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4
Infinitesimals revisited
How infinitesimal calculus became rigorous
Jul 4
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Joel David Hamkins
18
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Infinitesimals revisited
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6
June 2025
Boomerang tilings
Can you tile a convex polygon with boomerangs? Let's find out.
Jun 25
•
Joel David Hamkins
6
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Boomerang tilings
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21
Infinite Connect Four
Shall we play infinite Connect Four on the expansive infinite board? What size winning chains might we aspire to make? What are the winning strategies…
Jun 17
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Joel David Hamkins
7
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Infinite Connect Four
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Abstraction in the function concept
A century ago mathematics witnessed a dramatic enlargement and abstraction of this central concept. Let's explore some of the mind-expanding new…
Jun 9
•
Joel David Hamkins
11
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Abstraction in the function concept
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May 2025
On going first
Would you rather go first or second? In many games, there is a definite advantage one way or the other. How can we redress these imbalances, if we seek…
May 30
•
Joel David Hamkins
5
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On going first
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How we might have viewed the continuum hypothesis as a fundamental axiom necessary for mathematics
By mounting a philosophical historical thought experiment, I argue that our attitude toward the continuum hypothesis could easily have been very…
May 22
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Joel David Hamkins
9
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How we might have viewed the continuum hypothesis as a fundamental axiom necessary for mathematics
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