Most recommended! ]]>

For some reason, I am already stuck at the argument after making the convex hull a triangle: “Observation 1: No point of R lies outside the convex hull of P. Such a point r should be incident to two lines supporting the convex hull of P.” Why is that? Why can’t it be only incident to lines defined by points in the interior of the triangle?

Thanks for your help! Stefan

]]>Stable Marriages?

It was mentioned in the AMS notices or the monthly in the past few years. ]]>

This was the talk: https://personal.utdallas.edu/~nxw170830/docs/Presentations/kjw_hawaii_match.MP4. See around the 16 minute mark for where the quote appears.

]]>Ronald Coase (1960) only gave simple numerical examples based on fascinating historical examples. At Chicago, his departmental colleagues found it too counterintuitive to believe, more of a “what is wrong with this reasoning” puzzle Coase had foisted on them, until finally Milton Friedman had an aha! moment and then convinced everyone else.

]]>This involves tradeoffs. Most visibly, we gave up our right to say the RH is true (to pick an example) even though it’s been verified as rigorously as almost any law of physics or result in biology. Less visibly, our statements are always conditional (“if A then B”) — we always need axioms. But we also get benefits: our literature largely doesn’t grow stale: results in our literature have half-lives orders of magnitude greater than in the sciences.

I know that this definition sidelines the Grothendieck school emphasis on definitions as opposed to theorems, but I still think it best captures the spirit of pure mathematics.

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