He who knows other men is discerning; he who knows himself is intelligent. He who overcomes others is strong; he who overcomes himself is mighty.

Wednesday, October 29, 2008

So you can't think of how you would ever use Math?

How about if it made you a million bucks? Think back on those really long Math problems you worked on. You eventually were able to solve it, right? ("Am I right or am I right?")

well this one will take just a bit longer but there is a huge payoff. So break out your pencils, and don't look in the back of the book for the answer until you have arrived at your own answer.

The Riemann hypothesis, along with suitable generalizations, is considered by many mathematicians to be the most important unresolved problem in pure mathematics. First formulated by Bernhard Riemann in 1859, it has withstood concentrated efforts from many outstanding mathematicians for almost 150 years.

The Riemann hypothesis (RH) is a conjecture about the distribution of the zeros of the Riemann zeta-function ΞΆ(s). The Riemann zeta-function is defined for all complex numbers s ≠ 1. It has zeros at the negative even integers (i.e. at s = −2, s = −4, s = −6, ...). These are called the trivial zeros. The Riemann hypothesis is concerned with the non-trivial zeros, and states that:

The real part of any non-trivial zero of the Riemann zeta function is ½.

Thus the non-trivial zeros should lie on the so-called critical line, ½ + it, where t is a real number and i is the imaginary unit. The Riemann zeta-function along the critical line is sometimes studied in terms of the Z-function, whose real zeros correspond to the zeros of the zeta-function on the critical line.

The Riemann hypothesis implies a large body of other important results. Most mathematicians believe the Riemann hypothesis to be true. A $1,000,000 prize has been offered by the Clay Mathematics Institute for the first correct proof.

P.S. if you solve this, not only do you get the money but you would be awarded a PHD from any university you wanted.


WHITNEY said...

they'll just give you a phd?

Matthew said...

Gladly - it would be an honorary degree, but it would carry with it more clout then one that is normally earned.