The mysterious beauty, harmony, and consistency of mathematics once caused philosopher Hilary Putnam to term its existence a "miracle." Now, advances in the understanding of physics suggest that the foundations of mathematics are encompassed by the laws of nature, an idea that sheds new light on both mathematics and physics.
The philosophical relationship between mathematics and the natural sciences is the subject of "Converging Realities," the latest work by one of the leading thinkers on the subject. Based on a simple but powerful idea, it shows that the axioms needed for the mathematics used in physics can also generate practically every field of contemporary pure mathematics. It also provides a foundation for current investigations in string theory and other areas of physics.
This approach to the nature of mathematics is not really new, but it became overshadowed by formalism near the end of nineteenth century. The debate turned eventually into an exclusive dialogue between mathematicians and philosophers, as if physics and nature did not exist. This unsatisfactory situation was enforced by the uncertain standing of physical reality in quantum mechanics.
The recent advances in the interpretation of quantum mechanics (as described in "Quantum Philosophy," also by Omnes) have now reconciled the foundations of physics with objectivity and common sense. In Converging Realities, Roland Omnes is among the first scholars to consider the connection of natural laws with mathematics.
"It is refreshing to find a physicist joining today's ongoing public conversation about the nature of mathematics... As a physicist who loves mathematics, in Converging Realities [Roland Omnes] comes forward with a new idea, which he proposes to call 'physism.' ... I hope Omnes's daring proposal is taken seriously by those interested in these matters and receives the analysis and critique it deserves."--Reuben Hersh, American Scientit "Roland Omnes provides a systematic development of mathematics and classical reality and then the quantum world, with specific notes on the associated mathematical structures and historical developments. He argues persuasively, with many examples, how the realm of the possible (mathematics) and the realm of the actual (physics) are converging yet distinct realities."--Choice