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Representing integers as a sum
A quick selection from Proof and the Art of Mathematics
Oct 27
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Joel David Hamkins
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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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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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Potential versus actual infinity
Apr 14, 2023
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Joel David Hamkins
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Potential versus actual infinity
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Structuralism
Apr 4
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Joel David Hamkins
13
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Structuralism
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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…
Sep 25
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Joel David Hamkins
7
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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
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Joel David Hamkins
6
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What is the infinite?
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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?
Aug 28
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Joel David Hamkins
14
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We can predict the future
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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…
Jul 6
7
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Quantifier elimination — Presburger arithmetic
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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…
Jun 29
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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…
Jun 15
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Joel David Hamkins
7
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Quantifier elimination — dense linear orders
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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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JDH Links
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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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