Page xi - Prologue

      universe is to use transcendental function. As Gauss, Abel, Jacobi and Riemann have shown, there is an extended class of transcendental functions, best known today as elliptical functions and abelian functions. The use of the transcendental functions has to be combined with the method of inversion. When Jacobi was asked about how he has made so many discoveries, he said: “Always invert.” Using this method he made most of the work of Lagrange on elliptical integrals obsolete.

5.      Try to understand how the most remarkable results known, relate to your problem and how were them discovered. Try to understand the context and the state of mind of the persons that made those discoveries. It seems obvious to me that knowing as much as possible about Riemann will only help in trying to prove the Riemann Hypothesis. If we can get to the point to re-make or re-discover the hypothesis, probably we are very close to where Riemann was when he stated it in the first place. Also, use the original work to get the original ideas. Copies of an idea most of the time become distorted; they are not conformal maps of the original idea. Go back to the titans and get their ideas and their methods. These are proven to work and will probably take you to the solution.

6.      Start working, be consistent, patient and enjoy what you are doing. Don’t wait until you master the subject. Again, it was Jacobi who said: “Your father would never have married and you wouldn’t be here now, if he had insisted in knowing all the girls in the world before marrying one.”

The order chosen to present the ideas and the finding in this book is a combination of both, chronologic and logic. The initial chapters are mostly presented in a chronological order – this is the way I investigated the problem. The results of the investigation are presented in a logical order: at least in that logic that makes sense in my mind.

“I will not make poems with reference to parts;

But I will make leaves, poems, poemets, songs, says, thoughts, with

reference to ensemble:

And I will not sing with reference to

a day, but with reference to all

days;”

Walt Whitman