After thinking about this some more, here are some of the mathematical theories/theorems/equations that I think should make the list: 1. Computability. The fact that there exists a reasonably robust theory of computability, and that this is intimately connected with the fact of the incompleteness of number theory (Goedel's Theorem, et al). It turns out that computability is even easier (in some respects) to present than arithmetic (at least if you know Lisp & EVAL). 2. The fact that the theory of real closed fields is decidable. This means that essentially all of high school geometry is decidable. 3. The FFT algorithm and its generalizations. 4. Fourier theory in general -- astoundingly beautiful. 5. Real numbers -- perhaps the single most important creation of human beings, to date. They are quintessentially human -- using finite means to gain an insight into the (divine) infinite. At 11:54 AM 10/8/2004, Simon Plouffe wrote:
Hello,
they made a poll asking what are the most beautiful equations to a group of people.