Tutors Study Origins of Modern Math at St. John’s
(Winter 2001-2002 Newsletter)
Dr. Ronald J. Richard
Dr. John Nieto
Two tutors spent eight weeks this summer on the campus of
St. John's College in Santa Fe, New Mexico, studying the causes
of the fundamental shift that occurred from ancient to modern
mathematics. The study, underwritten by a grant from the Andrew
W. Mellon Foundation, is overseen by St. John's, Annapolis,
Dean, Harvey Flaumenhaft, and will extend over eight weeks
next summer as well.
The purpose of the study is to examine the connection between
the mathematical work of French philosopher, Rene Descartes,
and the ancient mathematicians whom Descartes attempted to
supersede. The focus of this summer's study was Apollonius
and his work on Conics. "It's what we do at our program
here, but we did it more deeply and more intensely there,"
said Dr. Ronald Richard, who for a dozen times over the last
25 years, has taught the year-long sophomore mathematics course
that covers this material.
The former Jet Propulsion Labs research engineer, who holds
a doctorate in astrophysics, found great satisfaction in undertaking
the study. "Apollonius does not explain why he does certain
things in some of his mathematical propositions. We spent
time uncovering some of those reasons." Providing a more
thorough understanding of Apollonius, he said, can give us
a better understanding of the radical shift that occurred
in the 17th century, which led to the modern world.
"When the ancients looked at mathematical figures and
particular curves," explains Dr. John Nieto, a former
National Science Foundation Fellow, "they were looking
at their properties and relationships - in other words, as
beings that had a reality apart from man. The moderns, however,
looked at those same figures and curves and saw proportion
and measurement - man then became the measure of things. Under
that perspective, a host of practical applications were introduced,
which helps explain, in part, why the sciences advanced as
they did."
. Both Richard and Nieto enjoyed the camaraderie they found
with the other six conference participants from St. John's.
And they took advantage of the local sights, sounds, and cuisine
of greater Sant Fe. "This was the greatest summer I have
spent since I was a kid," said Richard, whose wife, Carol,
joined him during the stay.
-- Qtrly Newsletter, Winter 2002
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