From the theoretical discussions, transdisciplinarity starts to have practical consequences in the development of programs that include consortia of universities, bringing together a large variety of professionnals who set ambitious goals, such as the Human Genome Project in the past decade, and also the Human Brain Project for this decade. We intend to present an approach in the spirit of the new paradigms of knowledge in the Human Brain Project generous program started earlier this year in Europe. A possible transdisciplinary approach on brain functions and structure is to bring a valuable, significant and innovative, unconventional contribution to the theory of multi-scale topics of the HBP project. More precisely, we intend to develop the subproject Mathematical and Theoretical Foundations of Brain Research within the HBP project. Our approach aims at exploring brain function from the perspective of the theories which influenced the last decade researches in Physics and Mathematics, such as the fractal theory, chaos and the dynamics of the nonlinear systems, in order to formulate new theories regarding brain mechanisms. We bring together models and new theories based on a principled approach to nonlinear reality. We wish to develop a new paradigm for assessing brain function, the theory of complex systems, which requires a revolutionary attitude, by rethinking how brain works and it is biologically structured. By this approach, we intend to study not only the corpuscular, but also the wave part of the matter.