The Abstract, the Tangible, and the Hoax

Mathematics and the physical universe stand in a peculiar relation. If mathematics were just an exploration of natural law it would be indistinguishable from physics. But if it were totally independent, there would be no explanation for what Eugene Wigner called the ''unreasonable effectiveness of mathematics in the natural sciences." As Galileo wrote, "the grand book, the universe, ... is written in the language of mathematics." The most abstract of theories connects with atomic explosions; the most ordinary of physical facts suggests daring mathematical abstractions. These are also the playful directions of our logic: deduction, the movement toward the particular, and induction, the movement toward the general. But because mathematical statements seem to participate in an indubitable truth which even the world-dependent physical laws cannot attain, the Platonic view of mathematics has been dominant in philosophical thought: