Abstract: Understanding human brain is one of the greatest challenges of science, not the least because, almost by definition, it is too complex to be understood by a human brain. The brain accounts for about 2% of our body weight, yet it consumes about 20% of the oxygen we intake, showing how central the energy metabolism must be for signalling. What we know about the functioning of the brain is based on indirect information: brain imaging, cell cultures and animal models. Therefore, to quantitatively integrate the information into a comprehensive picture requires an across-the-scales mathematical model that, at the microscopic end of the scale, addresses the physical and biochemical phenomena occurring in the cells that constitute the brain. One of the big challenges in modeling brain is that models complex enough to be capable of addressing the adaptivity of life need to be robust to perturbations, and allow a multitude of viable solutions, making model reduction very difficult. Moreover, complex models depend on a large number of parameters whose values can be inferred on only in an indirect manner. Therefore, a good model must be able to address also the modeling uncertainty. This talk will give an overview of the mathematical work on brain that I have done with my collaborators and students in the last decade.