Author(s): Grossberg, S. |
Citation: Notices of the American Mathematical Society, 47, 1361-1372.
Abstract: How our brains give rise to our minds is one of the most intriguing questions in all of science. We are now living in a particularly interesting time to consider this question. This is true because, during the last decade, mathematical models about how the brain works have finally succeeded in quantitatively simulating the experimentally recorded dynamics of individual cells in identified brain circuits and the behaviors that these circuits control. The models that have led to these successes incorporate qualitatively new ideas about how the brain is organized to achieve the remarkable flexibility and power of biological intelligence. These advances represent significant challenges and opportunities for mathematicians for several reasons. One obvious reason is that the models themselves are interesting mathematical objects. These models are typically defined by highdimensional dynamical systems in which several types of nonlinear feedback operate across multiple spatial and temporal scales. They represent systems that are capable of autonomously adapting, or self-organizing, in response to a rapidly changing and unpredictable world.