Dreaming of mathematical neuroscience for half a century

Theoreticians have been enchanted by the secrets of the brain for many years: how and why does it work so well? There has been a long history of searching for its mechanisms. Theoretical or even mathematical scientists have proposed various models of neural networks which has led to the birth of a new field of research. We can think of the ‘pre-historic’ period of Rashevski and Wiener, and then the period of perceptrons which is the beginning of learning machines, neurodynamics approaches, and further connectionist approaches. Now is currently the period of computational neuroscience. I have been working in this field for nearly half a century, and have experienced its repeated rise and fall. Now having reached very old age, I would like to state my own endeavors on establishing mathematical neuroscience for half a century, from a personal, even biased, point of view. It would be my pleasure if my experiences could encourage young researchers to participate in mathematical neuroscience.