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Joel David Hamkins

mathematics and philosophy of the infinite

Joel David Hamkins

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Tag Archives: Alternative Fields Medal

Alternative Fields Medal, awarded August 2026

Posted on August 8, 2026 by Joel David Hamkins
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I am very pleased to announce that I have been awarded the Alternative Fields Medal in recognition of “Excellence in exposition of mathematics to a popular audience.” The award cites my various books as well as my participation on MathOverflow, mentioning that I have made nearly 2000 posts there since 2010, reaching 5.8 million viewers.

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Posted in Grants and Awards | Tagged Alternative Fields Medal, mathoverflow | Leave a reply

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Proof and the Art of Mathematics, MIT Press, 2020

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  • BodaciousTattvas on Set-theoretic mereology as a foundation of mathematics? Shandong University, Workshop on Mereology, China, June 2026
  • Joel David Hamkins on Set-theoretic mereology as a foundation of mathematics? Shandong University, Workshop on Mereology, China, June 2026
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  • Comment by Joel David Hamkins on Can hereditarily non-well-orderable sets exist?
    @WillBrian Ah, it seems we had essentially the same idea. Your answer folds in the ZF interpretation of the anti-foundational model. I was trying AFA first, using a tree with no leaves and no infinite branch, but bisimilarities allow things to collapse.
  • Answer by Joel David Hamkins for Can hereditarily non-well-orderable sets exist?
    The answer is yes. This is true in any model of BAFA set theory without AC. Let $A$ be any non-well-ordered set, and define a binary relation $E$ on $A$ by which each element is related to all the other elements, but not itself. This is extensional and set-like, so under BAFA it is isomorphic […]
  • Answer by Joel David Hamkins for Was a computational hardness argument ever used to solve a mathematical conjecture?
    One of the standard elementary proofs of Gödel's incompleteness theorem follows the template you suggest. Namely, consider the theory of Peano arithmetic (PA). This theory is quite remarkable in that one can develop essentially all the classical elementary theory of numbers from these basic principles, and before the incompleteness theorem was known, it must have […]
  • Comment by Joel David Hamkins on Examples of eventual counterexamples
    @Number It's no problem---please don't worry about it. In general, you should feel free to edit posts on MathOverflow, since this is how the system is designed, and it works well. Edits are more likely to be accepted, however, when they are about matters of objective factual accuracy or notational corrections.
  • Comment by Joel David Hamkins on Examples of eventual counterexamples
    @AlekseiKulikov Indeed, since I also did not care for the edit, I have rolled it back to my answer. In my view the essence of the answer here does not require Kolmogorov complexity considerations, since for the phenomenon in question one doesn't need the description to be optimal. Nevertheless, the issue is similar to what […]
  • Comment by Joel David Hamkins on Was a computational hardness argument ever used to solve a mathematical conjecture?
    The argument template strikes me as having an affinity with the kind of argument where you prove existence of a phenomenon, such as a graph of a certain kind, by proving that it has nonzero probability in a suitable probability space.
  • Comment by Joel David Hamkins on Was a computational hardness argument ever used to solve a mathematical conjecture?
    Trivial problems are NP hard if and only if P=NP.
  • Comment by Joel David Hamkins on A question relating to the measurability of cardinals
    Yes, that is the phenomenon of the first type of counterexample. The second type is a different phenomenon.

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