The nine mathematicians whose works are represented in
the following pages are among the most famous in the whole
history of mathematics. Each of them made a significant con￾tribution to the science-a contribution which changed the
succeeding course of the development of mathematics. That
is why we have called this book Breakthroughs in Mathe￾matics. Just as surely as there are technological breakthroughs
which change our way of living, so are there breakthroughs
in the pure sciences which have such an impact that they af￾feet all succeeding thought.