Are mathematics a high-skill intellectual game in which experts showcase their abilities by tackling invented problems, or do mathematicians engage in acts of discovery as they explore an independent realm of mathematical reality?

What is the reason that this seemingly abstract scientific discipline provides the key that unlocks the deep secrets of the physical universe? The way one answers these questions significantly affects metaphysical reflection about reality.

An interdisciplinary symposium, featuring mathematicians, physicists, and philosophers, sought to discuss these issues in two meetings, in Castel Gandolfo and Cambridge. This volume presents, in edited form, the contributions of each participant to the lively discussions that took place.

Every effort has been made to achieve a balance between the precision of thought required by such an endeavor and the attempt to make its content accessible to the non-specialist reader who intends to put in the necessary effort to engage with these problems.