70 3. MATHEMATICAL CULTURES IIthe use of history in teaching. He is quoted as saying, "The history of a science
clarifies the origins of its fundamental concepts and exhibits the evolution of its
methods" (Garciadiego, 2002, p. 259).
Four years after the death of Prieto the Department of Mathematics was es-
tablished as part of the Faculty of Sciences of the University, now known as the
Universidad Nacional Autonoma de Mexico. At this point, it could be said that the
University had reached academic maturity. Seminars on current research opened,
including one on scientific and philosophical problems. Foreign scholars came there
to visit, and graduates from the University were able to find admission to first-
rate universities in other countries. Upon his retirement from Princeton University
in 1954, the distinguished topologist Solomon Lefschetz (1884-1972) accepted a
position at the University of Mexico and began sending students to the graduate
program at Princeton.^12 An amusing anecdote revealing the relations between the
uninhibited Lefschetz and the Mexicans was reported by his student Gian-Carlo
Rota (1932-1999). (See Rota's article 1989.)
6. Australia and New Zealand
Because of their proximity to each other, we discuss Australia and New Zealand
together, although they are not twins. Australia was settled by pioneers from Asia
around 70,000 years ago, when the ocean levels were much lower than now. Even
with the lower ocean levels, this settlement involved a long sea journey. When ocean
levels rose after the last ice age, many of the original settlements were offshore and
under water. New Zealand, in contrast, was settled by seafaring people only 1500
years ago. Europeans first arrived in this area in the sixteenth century, but actual
settlement by Europeans did not begin until late in the eighteenth century. As in
the United States, there were conflicts between the aboriginal inhabitants and the
new settlers, very fierce in Australia but surprisingly mild in New Zealand. Britain
proclaimed sovereignty over New Zealand in 1840 by including it in the Australian
colony of New South Wales. This merger lasted only 10 months, at which time New
Zealand became an independent colony. At this time a declaration of equal rights
for settlers and Maoris was made; a constitution followed 12 years later. In 1850
the six Australian states gained self-government by act of Parliament, and in 1901
they united in the Commonwealth of Australia.
Comparatively little has been written about the development of mathematics
in these countries, and the present account is based largely on an article (1988) by
Garry J. Tee, a professor of computer science at the University of Auckland, who
has written a great deal on the history of mathematics in general. Tee says that
the indigenous peoples of this area had a well-developed system of numeration and
makes the point that "the common assertions to the effect that 'Aborigines have
only one, two, many' derive mostly from reports by nineteenth century Christian
missionaries, who commonly understood less mathematics than did the people on
whom they were reporting." At the same time, he notes that these missionaries did
teach Western-style mathematics to indigenous people.
6.1. Colonial mathematics. As in other countries, European colonists were not
long in establishing universities in these new lands. Australia acquired universities
at Sydney (1850), Melbourne (1853), Adelaide (1874), and Hobart (University of
(^12) During the present author's years at Princeton (1963-1966) several of the graduate students in
mathematics were Mexican students of Lefschetz.