July 23

[Zeke]

Yeah, I'm being a little sneaky here. A classic trick of math professors is to leave proving some theorem as an exercise -- thus saving the class time it would take to show the proof. Typically this is done when the proof in question is obvious, tedious, or repetitive of one already shown. But occasionally a prof will forget how a proof is done, and leaving it as an exercise is one way to weasel out of it.

Now, the natural way to read "e of pi" is either e times pi or e over pi. And we know that e and pi are transcendental, but combinations are another story. For example, we don't even know for sure that e+pi and pi^e are irrational, let alone transcendental. (It would be very strange if they were rational, of course.) So, rather than just give him the member title "Irrational" without proof, I decided to acknowledge there was something to prove... while not, of course, proving it myself.

Which is not to say I couldn't, of course. As a matter of fact, I have discovered a truly marvelous proof, which this post is too narrow to contain.