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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
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
1
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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
•
Joel David Hamkins
7
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The fundamental theorem of finite games
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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
•
Joel David Hamkins
11
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The penny partition paradox
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The hypergame paradox
A confounding paradox arising in the theory of finite games.
Mar 2
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Joel David Hamkins
6
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The hypergame paradox
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Zeno's paradox
Jan 7, 2023
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Joel David Hamkins
30
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Zeno's paradox
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14
The Book of Numbers
Jan 2, 2023
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Joel David Hamkins
34
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The Book of Numbers
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12
Potential versus actual infinity
Apr 14, 2023
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Joel David Hamkins
22
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Potential versus actual infinity
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20
The surreal numbers
Jan 6, 2024
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Joel David Hamkins
22
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The surreal numbers
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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
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Joel David Hamkins
15
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Take my Infinity final exam!
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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
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Throwing Darts at the Real Line
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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
8
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What is the infinite?
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Infinite Games
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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
•
Joel David Hamkins
3
Share this post
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The Chocolatier's game
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Notes
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5
Buckets of Fish!
Can you take the last fish from the buckets? Or the last coin in the game of Whim?
Mar 31
•
Joel David Hamkins
1
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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
•
Joel David Hamkins
7
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The fundamental theorem of finite games
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2
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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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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