A short math problem instead of a long philosophical text this time! Here's a problem that was given by one of our math lecturers in the University, and I was quite impressed with its solution at that point.
Suppose f(x) is a good function (say, has n-th derivative for every n) on [0,3], f(0)=f(3)=0. Prove or disprove: int(der(f)^2)>=int(f^2), where int() means integral from 0 to 3, and der(f) is the derivative of f. Can you solve it? [right, right, I'm testing if anyone actually reads this :)]
And as a bonus, here's a random blurry picture from my recent trip to London for Google Code Jam (I've tried to find a good picture that has me on it, but it appears there isn't any). London is exciting!