Philosopher and math populizer Berlinski (The Devil’s Delusion:
Atheism and Its Scientific Pretensions, 2008, etc.) takes on the
challenge of explaining the logical foundation of the elementary
operations of arithmetic. It’s no easy task. Indeed, it was not
until the late 19th century that mathematicians were inspired to
develop the axioms (unproven assumptions) enabling the
development of theorems to prove the legitimacy of all those
rules of thumb you learned in high school—e.g., that the product
of two negative numbers is positive, or to divide fractions you
invert the divisor and multiply. Along the way, mathematicians
developed set theory, which showed that the operations possible
with numbers could be generalized to define arcane structures
called rings or fields. Why bother, Berlinski writes in the
introduction, noting that most people dislike math. However, he
continues, the reason is because such work has the grandeur of
the absolute, of something deep in the human imagination. So
readers with an ope