One of the most cited books in mathematics, John Milnor's exposition of
Morse theory has been the most important book on the subject for more
than forty years. Morse theory was developed in the 1920s by
mathematician Marston Morse. (Morse was on the faculty of the Institute
for Advanced Study, and Princeton published his Topological Methods in
the Theory of Functions of a Complex Variable in the Annals of
Mathematics Studies series in 1947.) One classical application of Morse
theory includes the attempt to understand, with only limited
information, the large-scale structure of an object. This kind of
problem occurs in mathematical physics, dynamic systems, and mechanical
engineering. Morse theory has received much attention in the last two
decades as a result of a famous paper in which theoretical physicist
Edward Witten relates Morse theory to quantum field theory.
Milnor was awarded the Fields Medal (the mathematical equivalent of a
Nobel Prize) in 1962 for his work in differential topology. He has since
received the National Medal of Science (1967) and the Steele Prize from
the American Mathematical Society twice (1982 and 2004) in recognition
of his explanations of mathematical concepts across a wide range of
scienti.c disciplines. The citation reads, "The phrase sublime elegance
is rarely associated with mathematical exposition, but it applies to all
of Milnor's writings. Reading his books, one is struck with the ease
with which the subject is unfolding and it only becomes apparent after
re.ection that this ease is the mark of a master.?
Milnor has published five books with Princeton University Press.
