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Representing integers as a sum
A quick selection from Proof and the Art of Mathematics
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Joel David Hamkins
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Zeno's paradox
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14
The Book of Numbers
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12
Potential versus actual infinity
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20
Structuralism
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2

The Book of Infinity

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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
8
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
We can predict the future
Is there a reliable strategy to predict the current and immediate future values of an arbitrary unknown function on the reals?
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Joel David Hamkins
6

A Panorama of Logic

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Quantifier elimination — Presburger arithmetic
The elementary theory of addition in the natural numbers admits a certain logical triviality—every assertion is equivalent to a simple combination of…
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Quantifier elimination — theory of successor
Every assertion about the structure ⟨ℕ,S,0⟩ of the natural-number successor is trivial, being equivalent to a quantifier-free assertion in this…
Quantifier elimination — dense linear orders
In certain special theories, every assertion is equivalent to a trivial combination of atomic facts. Proving this for a given theory typically both…
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Joel David Hamkins

Proof and the Art

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Philosophy of Mathematics

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The mathematics and philosophy of the infinite
Recommendations
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Math Made Simple
Math Made Simple
Álvaro Muñiz Brea
New Work in Philosophy
New Work in Philosophy
Marcus Arvan
3Blue1Brown mailing list
3Blue1Brown mailing list
Grant Sanderson
Science without the gobbledygook
Science without the gobbledygook
Sabine
The Nature-Nurture-Nietzsche Newsletter
The Nature-Nurture-Nietzsche Newsletter
Steve Stewart-Williams
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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