My work in the superior mathematics

This book represents a sequence of the book Five Major Breakthroughs in Superior Mathematics. This happened after all nowadays challenges, when Mathematics is so far behind all other Sciences, life Informatics and Genetics, which are evolving with huge steps every day.

There are a lot of entire Mathematical domains that have remained unchanged since the year of 1900.

As a Mathematician, with the burning desire to developing also Mathematics Sciences, I have been trying over the years, using daring and original ideas, to give another impulse to this science.

In 2007, I have managed to make another three huge and extraordinary theoretical breakthroughs which brought up to the light some extremely difficult domains like: The Algebraic Theory of Numbers and The Algebraic Geometry.

I would like to pay special regards this way to my dear professor Eugen Campu from the Mathematical Faculty of Bucharest, to whom I have collaborated over the hard times I have been through trying to solve Riemann Hypothesis. He has helped me solve it after a terrible and tremendous battle I had with all the obstacles I have been through in my way to solve this Hypothesis. I have to mention also that professor Eugen Campu has also been a great moral support for me during all this time.

I would also like to thank to the prestigious Mathematician and professor Daniel Bump from Stanford University who was so willing to read and to comment my work, the one that contained Riemann Hypothesis.

When it comes to the mathematical section, some intricacies may be found in the rationations.

If the ones who will read the book will find these intricacies, the author will be receptive at a civilized and constructive criticism and will apply himself to correct them in a later edition.

The book "5 Major Theoretical Breakthroughs in the Superior Mathematics" is organized and divided in 5 (five) small chapters which contain the 5 theoretical breakthroughs.

What is to be mentioned is the fact that the Internet related bibliography for every chapter is really massive, over 100.000 pages for every single chapter, and the reason why it is not my recommendation for someone else to assume this super-human task.

The book is addressed to the very best students, high-school teachers, researchers, university professors around the country and all around the world. It has the great advantage that with the concomitant use of Internet services, each of the 5 chapters can be developed into separate, individual 200-300 pages books, the author showing no interest in the developing the 5 chapters with the help of the Internet, because he can not engage into a task that is beyond his powers.

It is important to mention that at this moment there is no Romanian mathematician alive to have 5 (five) valid theoretical breakthroughs of such a value, world-wide. There were some efforts to reduce the number of pages in every chapter, because it is well known that nowadays the Internet has complete power over the books and the one who will read the book may continue for a lifetime his study with the help of the Internet for every chapter.

When it comes to the mathematical section, some intricacies may be found in the rationations.

If the ones who will read the book will find these intricacies, the author will be receptive at a civilized and constructive criticism and will apply himself to correct them in a later edition.

After 2000, my areas of interest shifted a little bit from the analytical theory of numbers towards the classical problems of functional analysis and the theory of partial differential equations.

In this regard, in 2005, at the age of 39, I succeed in obtaining a powerful result which makes the connection between the theory of fix point, the spectral theory and the theory of the invariant subspaces.

In the same very year of 2005 I also manage to make a huge theoretical brake in what concerns the Stokes-Navier equations, observing that the formula of integral representation of self-adjoints operators, coming from a domain which is a bit different from the one of differential equations of evolution, has an regulating effect on the equation, the regularization has a solution and then it goes on to the limit on Cauchy sequence and the initial equation's solution is obtained, as well as its uniqueness.