Riemann Hypothesis

Riemann Hypothesis 01

What is the Riemann Hypothesis (RH)?

This description is for those who are curious about what has been the greatest unsolved problem in mathematics for decades, but hate learning new things, especially Analytical Number Theory and Complex Arithmetic. Most pages on the Internet do indeed state what the hypothesis is, but really leave everything about it virtually hidden, or at least require extensive cross-referencing to other sites and/or areas of mathematics.

The absolute best way to learn everything about the hypothesis is to purchase John Derbyshire's excellent book, "Prime Obsession." This book explains everything about the problem and includes much background into the mathematicians over the years that surround this issue. If you are any bit interested in mathematics, much less the hypothesis, you'll love this book.

The description at this site will explain the hypothesis only in terms of how Jeff Cook's proof pertains to it. The mathematics literature is over-flowing with statements like, "if the RH is true, then such and such is also true." This is why the hypothesis is so important. However, because there are so many areas of mathematics hinged on it, there is no point in writing here all the wide aspects it covers. Cook's proof is simple and straightforward and solves the problem from a specific direction. It is that direction and the points of the hypothesis that the proof hinge on that this description will include.

With that said, you will know after reading this description more than enough about the RH to be able to discuss it at dinner parties to hold your own with intellectuals, and you will be able to understand everything about Cook's proof and why it indeed solves the problem. So let's begin.

The Riemann Hypothesis is:

All the non-trivial zeros of the Zeta Function have a Real part equal to one half.

Know that statement and the rest will fall into place. Unfortunately, that statement carries terms that mean absolutely nothing to the lay person. These are:

* Non-Trivial Zeros

* Zeta Function

* Real Part

But describing each of those in that order would not be a good idea. Instead, they will be described more like this:

A) The Zeta Function

B) The Real part of a Complex number

C) The zeros of any function

D) The Trivial Zeros of the Zeta Function

E) The Non-Trivial Zeros of the Zeta Function

And after such is effectively explained, you will be able to understand the proof.

Let's begin with the Zeta Function...