31. Extremal graph theory started in 1941 when Tur�n proved his result a vital tool in attacking extremal problems. 32. The Rindler spacetime has a horizon, and locally any non-extremal black hole horizon is Rindler. 33. In the area of econophysics, he discovered extremal properties of fixed point profits of elementary merchant tactics. 34. That is to re-iterate the concern about extremal cases not being equivalent in the list immediately above. 35. One difference was that Strominger and Vafa considered only extremal black holes in order to make the calculation tractable. 36. The calculation makes use of the notion of dynamical horizon and is done for non-extremal black holes. 37. Extremal combinatorics owes to him a whole approach, derived in part from the tradition of analytic number theory.38. It has been suggested by Sean Carroll that the entropy of an extremal black hole is equal to zero. 39. Much of extremal combinatorics concerns Sperner's theorem, which gave rise to much of extremal set theory. 40. Much of extremal combinatorics concerns Sperner's theorem, which gave rise to much of extremal set theory.
