The Ancient Greeks were frightened to think about infinity. So is Al Cooper, a character in A Disappearing Number. Certainly for the layperson, it is confounding to hear that, as Al is told, that “some Infinities are larger than others…” What does that mean? How have mathematicians looked at infinity? How does that compare with the way artists and philosophers understand infinity?
Bjorn Poonen is the Claude Shannon Professor of Mathematics at MIT. His research focuses mainly on number theory and algebraic geometry; in particular, he is interested in the rational number solutions to equations. He is a fellow of the American Academy of Arts and Sciences and of the American Mathematical Society, and he is the recipient of several awards, including most recently the 2014 MIT School of Science Prize in Undergraduate Teaching. Fifteen mathematicians have completed a Ph.D. under his guidance.
William Hugh Woodin is Professor of Mathematics and Philosophy at Harvard University. He has made notable contributions to the theory of inner models and determinacy. A type of large cardinal, the Woodin cardinal, bears his name. Woodin has done work on the theory of generic multiverses and now predicts that there should be a way of constructing an inner model for almost all known large cardinals which he calls the Ultimate L. He has served as chair of the Berkeley mathematics department, and is a Fellow of the American Academy of Arts and Sciences.