The notion of making a map of a portion of the Earth's surface led to one of the most fundamental concepts in all of mathematics - that of a mapping or transformation. Mercator introduced one of the best known maps ever devised, but mathematics had not yet advanced enough in his time to allow his map to be expressed with precise equations. We will trace a number of mathematical developments from the time of Mercator to the year 2000 that are linked in various ways to the ideas behind Mercator's map.
Robert Osserman is Professor Emeritus of Mathematics at Stanford University and Special Projects Director at the Mathematical Sciences Research Institute in Berkeley. His research interests have always had a geometric component, including the theory of minimal surfaces, isoperimetric inequalities, and geometric function theory. He has also written a book for the general reader on geometry and cosmology called "Poetry of the Universe: a Mathematical Exploration of the Cosmos."