Two hydrogen atoms meet in a bar. "I think I lost my electron." "Are you sure?" "Yes, I'm positive." Whew...
Desultory flipping through of Karl Sabbagh's book, The Riemann Hypothesis - The Greatest Unsolved Problem In Mathematics. Like other mathematics books for laypeople (such as Zero - The Biography Of A Dangerous Idea and Fermat's Last Enigma), this one is a judicious mix of history, anecdotes and some relatively accesible mathematics.
The Riemann Hypothesis states (more or less) that
that the nontrivial Riemann zeta function zeros, i.e., the values of s other than -2, -4, -6, ... such that ζ(s)=0 (where ζ is the Riemann zeta function) all lie on the "critical line" σ=R[s]=½ (where R denotes the real part of s).Yes, its really that simple. A child could tackle this.
Why is this important, you ask? Maybe you don't ask. But I tell. In the words of Sabbagh
The Riemann Hypothesis matters because, if it is true, it proves that there is a rule for generating the prime numbers...If Tom, Li Mu Bai, and Thirunavukkarasu start generating prime numbers, one will have to wonder what the implications for cryptography are. This is only the tip of the iceberg. There are other obscure mathematical reasons (which I fully comprehend, mind you, but which will be so much Greek to you folks) why this is such an important result.
Many great mathematicians have been trying to prove or disprove the Riemann Hypothesis. It features as one of the 23 unsolved (at the time) problems of David Hilbert. Hardy and Ramanujan tried it and couldn't. Hardy was quite a character, but this post is too long already.
Interesting mathematics websites include the MacTutor History of Mathematics archive. Wolfram Research's Mathworld is a positive treasure, they also have similar sections on physics, chemistry and other sciences. If you fancy yourself as a mathematician, you might want to check out IBM Research's Ponder This problem of the month.
Grafitti on New York City subway wall:
xn + yn = zn
There is no value of n>2 for which the above is true. I have found a truly remarkable proof of this, but my train is coming and I have to go...