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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…
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Joel David Hamkins
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…
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Joel David Hamkins
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…
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Joel David Hamkins
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…
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Joel David Hamkins
12
Take my Philosophy and Logic of Games final exam!
Can you pass the exam for my games course?
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Joel David Hamkins
10

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?
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Joel David Hamkins
15
Throwing Darts at the Real Line
Mathematical philosophers have proposed various thought experiments suggesting different resolutions of the continuum hypothesis. Can we hope…
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Joel David Hamkins
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?
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Joel David Hamkins
4

Infinite Games

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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…
 • 
Joel David Hamkins
1
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…
 • 
Joel David Hamkins
Take my Philosophy and Logic of Games final exam!
Can you pass the exam for my games course?
 • 
Joel David Hamkins
10

A Panorama of Logic

See all

Proof and the Art

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Philosophy of Mathematics

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Infinitely More
Infinitely More
The mathematics and philosophy of the infinite
Recommendations
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The Nature-Nurture-Nietzsche Newsletter
The Nature-Nurture-Nietzsche Newsletter
Steve Stewart-Williams
User's avatar
Math and Art
Erin Carmody
A Piece of the Pi: mathematics explained
A Piece of the Pi: mathematics explained
Richard Green
3Blue1Brown mailing list
3Blue1Brown mailing list
Grant Sanderson
New Work in Philosophy
New Work in Philosophy
Marcus Arvan
JDH Links
JDH web page
JDH on Twitter
JDH on Notes
JDH on MathOverflow
JDH on YouTube
JDH on Google Scholar
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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