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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…
18 hrs ago
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Joel David Hamkins
5
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Infinite Connect Four
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1
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
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Joel David Hamkins
10
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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
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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
8
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How we might have viewed the continuum hypothesis as a fundamental axiom necessary for mathematics
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12
Take my Philosophy and Logic of Games final exam!
Can you pass the exam for my games course?
May 14
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Joel David Hamkins
12
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Take my Philosophy and Logic of Games final exam!
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Pushpast
Can the triangles push past the circles?
May 7
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Joel David Hamkins
1
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Pushpast
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April 2025
Bubble Monsters
Will the children make it safely through the bubble monsters?
Apr 25
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Joel David Hamkins
3
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Bubble Monsters
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Face Up
How long is the longest play of the game? Can you play forever, while avoiding the all-face-up position?
Apr 19
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Joel David Hamkins
5
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Face Up
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The Chocolatier's game
The Chocolatier successively serves up an endless parade of exquisite, delectable morsels, while the Glutton aims to eat them all. Who will win?
Apr 6
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Joel David Hamkins
3
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The Chocolatier's game
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5
March 2025
Buckets of Fish!
Can you take the last fish from the buckets? Or the last coin in the game of Whim?
Mar 31
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Joel David Hamkins
3
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Buckets of Fish!
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2
The fundamental theorem of finite games
In every finite two-player game of perfect information, either one player has a winning strategy or both players have drawing strategies.
Mar 18
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Joel David Hamkins
7
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The fundamental theorem of finite games
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2
The penny partition paradox
The penny partition paradox, a perplexing parable of profit—the penny players parlay perfectly precise provable principles to a peculiarly puzzling…
Mar 10
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Joel David Hamkins
11
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The penny partition paradox
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