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Tag Archives: NATO

NATO Research Grant, 1999 – 2000

Posted on October 1, 1999 by Joel David Hamkins

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I was co-PI on this NATO Collaborative Research grant, organized by Mirna Dzamonja, with Arthur Apter, myself and six others as co-PIs.

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Posted in Grants and Awards | Tagged NATO | Leave a reply

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Comment by Joel David Hamkins on Incentivizing mathematics in an era of AI-accelerated proof abundance
The comment thread seems to have become off-topic. Since Carlson had his entire chess career in the era of strong chess engines, he would seem to make a weak case for the argument that people leave chess because of them. In any case, as I mention above, chess is more popular than ever, at almost […]
Comment by Joel David Hamkins on Incentivizing mathematics in an era of AI-accelerated proof abundance
There are more people working as chess tutors and coaches as there ever have been, even though there are also machine tutors. Similarly, I believe there will always be a place for human mathematicians.
Answer by Joel David Hamkins for Incentivizing mathematics in an era of AI-accelerated proof abundance
Why do we play chess if the machines can play it better? Because it is such a joy to take on the challenge and to figure something out. Why will we study mathematics when the machines can do it as well or better? Because it is a joy to figure something out and to share […]
Comment by Joel David Hamkins on When are two proofs of the same theorem really different proofs
Cantor's proof does construct specific transcendental numbers explicitly. He provides an explicit construction enumerating the algebraic numbers, and then the diagonal construction produces a real number not on that list. And indeed the constructive nature of his proof was important to Cantor in his presentation.
Comment by Joel David Hamkins on Borel homomorphism of equivalence relation
I edited to add the subscript 0 in the second displayed equation, since I think that is what you intended.
Comment by Joel David Hamkins on T=ZFC + Con(ZFC), a flawed reasoning process but why
For a theory to prove that there is a contradiction is not the same as the theory proving a contradiction. This is the content of the second incompleteness theorem.
Comment by Joel David Hamkins on If $|\bigcup S|<|S|$, then there is $R\subseteq S$ so that $|\bigcup R|<|R|$ and there exists $\phi:\bigcup R\hookrightarrow R$ with $r\in\phi(r)$
Clearly, $r\in\bigcup R$, so that $\phi(r)$ makes sense.
Comment by Joel David Hamkins on If $|\bigcup S|<|S|$, then there is $R\subseteq S$ so that $|\bigcup R|<|R|$ and there exists $\phi:\bigcup R\hookrightarrow R$ with $r\in\phi(r)$
It is a very nice problem!

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