![]() ![]() ![]() Platonic solids are another good example. Numbers are in the first class-you would agree that although you cannot list all the whole numbers, you have a good sense of what numbers are out there. The entities we study in science fall into two categories: those which can be classified in a way a human can understand, and those which are unclassifiably wild. (If that’s what you’re after, Sormani’s home page links to a variety of expositions, including one in the form of a short story.) Instead, I’ll try to explain why Perelman’s theorem matters without explaining what it is. Indeed, it’s pretty hard to give an elementary account of the statement that Poincaré conjectured and that Perelman seems to have confirmed. That’s zingier than anything the Times will run, but may still leave you without a clear picture of Perelman’s theorem. ![]()
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