62 3. MATHEMATICAL CULTURES IIsquare root of a negative number and to formulate rules for operating with such
numbers.
The work being done in Italy did not escape the notice of French and British
scholars of the time, and important mathematical works were soon being produced
in those two countries.
Francois Viete. A lawyer named Frangois Viete (1540 1603), who worked as tutor
in a wealthy family and later became an advisor to Henri de Navarre (who became
the first Bourbon king, Henri IV, in 1598), found time to study Diophantus and
to introduce his own ideas into algebra. His book Artis analyticae praxis (The
Practice of the Analytic Art) contained some of the notational innovations that
make modern algebra much less difficult than the algebra of the sixteenth century.
Girard Desargues. Albertis ideas on projection were extended by the French ar-
chitect and engineer Girard Desargues (1591 1661), who studied the projections of
figures in general and the conic sections in particular.
John Napier. In the late sixteenth century the problem of simplifying laborious
multiplications, divisions, root extractions, and the like, was attacked by the Scot-
tish laird John Napier, Baron of Murchiston (1550-1617). His work consisted of two
parts, a theoretical part, based on a continuous geometric model, and a computa-
tional part, involving a discrete (tabular) approximation of the continuous model.
The computational part was published in 1614. However, Napier hesitated to pub-
lish his explanation of the theoretical foundation. Only in 1619, two years after his
death, did his son publish an English translation of Napier's theoretical work under
the title Mirifici logarithmorum canonis descriptio (A Description of the Marvelous
Law of Logarithms). This subject, although aimed at a practical end, turned out
to have enormous value in theoretical studies as well.
The European colonies. Wherever Europeans went during their great age of expan-
sion, science and mathematics followed once the new lands were settled and acquired
political stability and a certain level of economic prosperity. Like the mathematics
of Europe proper, the story of this "colonial" mathematics is too large to fit into
the present volume, and so we shall, with regret, omit South America and South
Africa from the story and concentrate on the origins of mathematics in Mexico, the
United States, Canada, Australia, and New Zealand.
5. North America
During the American colonial period and for nearly a century after the founding of
the United States, mathematical research in North America was extremely limited.
Educational institutions were in most cases directed toward history, literature, and
classics, the major exception being the academy at West Point, which became the
United States Military Academy in 1802. Modeling itself consciously on the Ecole
Polytechnique, the Academy taught engineering and applied mathematics.^8 For
most of the period up to 1875 there were no professional journals devoted entirely
to mathematics and no mathematical societies of any size. A period of rapid growth
began in the 1870s, coinciding with the closing of the American frontier. By 1900 a
respectable school of American mathematical researchers existed, although it was
(^8) Rensselaer Polytechnic Institute was founded to teach engineering in 1824, and civil engineering
was taught at the University of Vermont as early as 1829.