72 3. MATHEMATICAL CULTURES II
Refugee mathematicians. Like the United States and Canada, Australia took in
some prominent European mathematicians who were fleeing persecution during the
Nazi era. Among them were Kurt Mahler (1903-1988), Hans Schwerdtfeger (1902-
1990), George Szekeres (b. 1911), Hanna Neumann (1914-1971), and her husband
Bernhard Neumann (1909-2002). In honor of the mathematical achievements of
these refugees the Australian Mathematical Society sponsors a Mahler Lectureship,
a George Szekeres Medal, and a B.H. Neumann Prize.
Ties provided by the British Commonwealth seem to have facilitated the careers
of many of these people. Rutherford and Schwerdtfeger, for example, both worked
for a time at McGill University in Montreal, besides the time they spent in New
Zealand, Australia, Britain, and elsewhere.
7. The modern era
The advanced work in number theory, geometry, algebra, and calculus that began in
the seventeenth century will be incorporated into the discussion of the mathematics
itself beginning in Chapter 5. There are two reasons for not discussing it here.
First, many of the names from this time on, such as Pascal, Descartes, Leibniz,
Newton, Cauchy, Riemann, Weierstrass are probably already familiar to the reader
from mathematics courses. Second, the increasing unity of the world makes it
less meaningful to talk of "European mathematics" or "Chinese mathematics" or
"Indian mathematics," since in the modern era mathematicians the world over work
on the same types of problems and use the same approaches to them. We shall now
look at some general features of modern mathematics the world over.
Up to the nineteenth century mathematics for the most part grew as a wild
plant. Although the academies of science of some of the European countries nour-
ished mathematical talent once it was exhibited, there were no mathematical so-
cieties dedicated to producing mathematicians and promoting their work. This
situation changed with the French Revolution and the founding of technical and
normal schools to make education systematic. The effects of this change were mo-
mentous. The curriculum shifted its emphasis from classical learning to technology,
and research and teaching became linked.
7.1. Educational institutions. At the time of the French Revolution the old
universities began to be supplemented by a system of specialized institutions of
higher learning. The most famous of these was the Ecole Polytechnique, founded
in 1795. A great deal of the content of modern textbooks of physics and mathe-
matics was first worked out and set down in the lectures given at this institution.
Admission to the Ecole Polytechnique was a great honor, and only a few hundred
of the brightest young scholars in France were accepted each year. This institution
and several others founded during the time of the French Revolution, such as the
Ecole Normale Superieure, produced a large number of brilliant mathematicians
during the nineteenth century. Some of their research was devoted to questions of
practical importance, such as cartography and canal building, but basic research
into theoretical questions also flourished.
In Germany the unification of teaching and research proceeded from the other
direction, as professors at reform-minded universities such as Gottingen (founded
in 1737) began to undertake research along with their teaching. This model of
development was present at the founding of the University of Berlin in 1809. This
