Why do I think this theorem is cool?

Well, the earth's surface is certainly something like S2. Take any two real valued functions which vary continously as a function of their position on the surface of the earth (say temperature and atmospheric pressure). The theorem says that there exists antipodal points on the earth's surface where these two quantities have the same values (thus the temperature and atmospheric pressure at both places on the earth agree). Kinda slick, I think.

I mentioned this particular example with temperature and pressure to someone I know who does atmospheric modelling and dynamics. They thought it so ludicrous that their reaction was, "You mathematicians have no idea what you're talking about!" I took this to mean that in their modelling they used discontinuous functions of temperature and pressure ;-)

Andrew D. Lewis (andrew at mast.queensu.ca)