• Does infinity exist?
• Where does infinity come from?
• How can we reconcile the finiteness of the human brain with the infinity of ideas it produces?
These recent developments also open up new questions of debate, including:
• What is the role played by randomness?
• Are computers capable of handling the infinite through unconventional media of computation?
• How can one approximate efficiently the finite by the infinite, and conversely the infinite by the finite?
Well-known authors from around the world, many of them architects of the mathematics and computer science for the new century, contribute to this volume. While mathematical in spirit, contributions have many connections with computer science, cognitive science, linguistics, philosophy, physics, biology and semiotics.