  A major question in philosophy of science involves the unreasonable
effectiveness of mathematics in physics. Why should mathematics, created or
discovered, with nothing empirical in mind be so perfectly suited to describe
the laws of the physical universe? We review the well-known fact that the
symmetries of the laws of physics are their defining properties. We show that
there are similar symmetries of mathematical facts and that these symmetries
are the defining properties of mathematics. By examining the symmetries of
physics and mathematics, we show that the effectiveness is actually quite
reasonable. In essence, we show that the regularities of physics are a subset
of the regularities of mathematics.
