As for mathematical talks, I’m not sure if that is really the case however. For instance, it’s unclear to me whether Serre ever gave twice the same talk…

]]>There must be SOME way of interpreting the statement that would make it a true fact, and then there should be a corresponding proof of that fact, don’t you think?

I am picturing some planar structure that is initially constructed from random elements of some kind. Then it undergoes a series of transformations and gradually takes on a more ordered structure as a result of the transformations, which would preferably also have random elements or parameters.

]]>The best upper bound for the independence number of the plane comes from this theta number (see e.g. http://arxiv.org/abs/1501.00168) + some extra constraints. A detailed description of the idea can be found in my PhD thesis (see in particular Chapter 4 and Sec. 4.6f):

]]>This line of thinking tells you almost nothing about the degree, though.

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