How the mind and brain work, and how our brains create our minds are questions one could easily see to be both biological and philosophical. Yet they are also mathematical questions.
In the enclosed article, "Linking Mind to Brain: The Mathematics of Biological Intelligence", Professor Stephen Grossberg of Boston University explains how recent advances in mathematics have helped explain the brain and the mind.
These advances are incorporated into mathematical models of the brain. The mathematical models in question are not the plastic models you might see on a neurosurgeon's desk. Rather, they are collections of equations that represent interacting functions of the brain and the way in which these functions give rise to the mind.
These mathematical models can be used to clarify problems like
1. How our minds synthesize huge amounts of data to decide where to look or to move,
2. Understanding mental disorders such as schizophrenia and attention deficit disorder,
3. Creating high-tech systems that adapt to their environment.
Professor Grossberg explains how Form-And-Color-And-DEpth (FACADE) theory helps to answer the question about the illusory perceived square and how Adaptive Resonance Theory (ART) has helped clarify some questions regarding learning, recognition, and forgetting.
He concludes with a statement that an understanding of circuits within the cortex (whose marvelous architecture is being copied in computer chips) has brought us to the threshold of understanding "the cerebral cortex of the brain, that enchanted loom on which so many of our most meaningful experiences, including our mathematical theorems, are played out through our lives."
Professor Grossberg's article will appear in the December 2000 issue of Notices of the AMS. A PDF file containing the article may be downloaded at http://www.ams.org/notices/200011/fea-grossberg.pdf.
Founded in 1888 to further mathematical research and scholarship, the 30,000-member American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.
