This book is about mathematics, not the history or philosophy of mathematics.
Still, history and philosophy were prominent among my motives for writing
it, and historical and philosophical issues will be major factors in determining
whether it wins acceptance.
Most mathematicians prefer constructive methods. Given two proofs of
the same statement, one constructive and the other not, most will prefer the
constructive proof. The real philosophical disagreement over the role of constructions
in mathematics is between those—the majority—who believe that
to exclude from mathematics all statements that cannot be proved constructively
would omit far too much, and those of us who believe, on the contrary,
that the most interesting parts of mathematics can be dealt with constructively,
and that the greater rigor and precision of mathematics done in that
way adds immensely to its value.