Do numbers and the other objects of mathematics enjoy a timeless existence independent of human minds, or are they the products of cerebral invention? Do we discover them, as Plato supposed and many others have believed since, or do we construct them? Does mathematics constitute a universal language that in principle would permit human beings to communicate with extraterrestrial civilizations elsewhere in the universe, or is it merely an earthly language that owes its accidental existence to the peculiar evolution of neuronal networks in our brains? Does the physical world actually obey mathematical laws, or does it seem to conform to them simply because physicists have increasingly been able to make mathematical sense of it? Jean-Pierre Changeux, an internationally renowned neurobiologist, and Alain Connes, one of the most eminent living mathematicians, find themselves deeply divided by these questions.
The problematic status of mathematical objects leads Changeux and Connes to the organization and function of the brain, the ways in which its embryonic and post-natal development influences the unfolding of mathematical reasoning and other kinds of thinking, and whether human intelligence can be simulated, modeled,--or actually reproduced-- by mechanical means. The two men go on to pose ethical questions, inquiring into the natural foundations of morality and the possibility that it may have a neural basis underlying its social manifestations. This vivid record of profound disagreement and, at the same time, sincere search for mutual understanding, follows in the tradition of Poincare, Hadamard, and von Neumann in probing the limits of human experience and intellectual possibility. Why order should exist in the world at all, and why it should be comprehensible to human beings, is the question that lies at the heart of these remarkable dialogues.
Jean-Pierre Changeux is Director of the Molecular Neurobiology Laboratory at the Institut Pasteur in Paris and Professor at the Coll ge de France. Alain Connes, winner of the 1982 Fields Medal, is Professor of Mathematics at the Institut des Hautes tudes Scientifiques in Bures-sur-Yvette and Professor at the Coll ge de France.
Translator's NotePreface to the Original French Edition1Mathematics and the Brain32Plato as Materialist?253Nature Made to Order414The Neuronal Mathematician745Darwin among the Mathematicians1226Thinking Machines1537The Real and the Rational179Epilogue: Ethical Questions210Glossary of Mathematical Terms237Glossary of Neurobiological Terms247Index253