We all share the basic elements that comprise mathematical sensibility. Without giving it a second thought we all visualize time as a geometric entity—"far in the future" is a perfectly familiar phrase to us. In addition, we are comfortable when the exchange goes the other way, where distance is measured by time. This roundtable will survey some of the different ways our imagination is exercised when we think about mathematics—guessing the odds, as in the Monty Hall TV quiz game; estimating simple numbers (we aren't very good at this). How is it that the most simple geometric constructions can reveal so much? For example, if one thinks of drawing just the right line, it becomes immediately apparent that any two parallelograms of the same base and height have the same area. What is required for someone to visualize this construction? To be convinced by it? This roundtable will examine our conceptions, and mis-conceptions, about the function of mathematics in imagination and in every day life.

Eva Brann has been a teacher in the integrated program of St. Johns College in Annapolis, Maryland, for half a century. She's the author of a book about visual imagination, called The World of the Imagination: Sum and Substance, in addition to numerous other publications. Brann's long history of academic posts and honors includes fellowships with the NEH and the Woodrow Wilson International Center for Scholars.

Barry Mazur is the Gerhard Gade University Professor of Mathematics at Harvard University. He does research in number theory and geometry, and is the author of Imagining Numbers: (particularly the square root of minus fifteen).

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