April 25, 2005
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Mathematical Style:
Mac Lane Memorial, Part Trois
(See also Part I and Part II.)
“We have seen that there are many diverse styles that lead to success in
mathematics. Choose one mathematician… from the ones we studied
whose
‘mathematical style’ you find most rewarding for you….
Identify the mathematician and describe his or her
mathematical style.”– Sarah J. Greenwald,
take-home exam from
Introduction to Mathematics
at Appalachian State U.,
Boone, North CarolinaFrom today’s Harvard Crimson:
Ex-Math Prof Mac Lane, 95, Dies
[Saunders] Mac Lane was most famous for the
ground-breaking paper he co-wrote with Samuel Eilenberg of Columbia in
1945 which introduced category theory, a framework to show how
mathematical structures relate to each other. This branch of algebra
has since influenced most mathematical fields and also has functions in
philosophy and linguistics, but was first dismissed by many practical
mathematicians as too abstract to be useful.Gade University
Professor of Mathematics Barry Mazur, a friend of the late Mac Lane,
recalled that the paper had at first been rejected from a lower-caliber
mathematical journal because the editor thought that it was “more
devoid of content” than any other he had read.“Saunders wrote
back and said, ‘That’s the point,’” Mazur said. “And in some ways
that’s the genius of it. It’s the barest, most Beckett-like vocabulary
that incorporates the theory and nothing else.”He likened it
to a sparse grammar of nouns and verbs and a limited vocabulary that is
presented “in such a deft way that it will help you understand any
language you wish to understand and any language will fit into it.”
Also from Appalachian State University
(with illustration by Ingmar Bergman):
“In my hour of weakness,that old enemy
tries to steal my soul.But when he comes
like a flood to surround meMy God will step in
and a standard he’ll raise.”
