Few people outside of mathematics are aware of the varieties of
mathematical experience - the degree to which different mathematical subjects have
different and distinctive flavors, often attractive to some mathematicians and
repellant to others.
The particular flavor of the subject of minimal surfaces seems to lie in
a combination of the concreteness of the objects being studied, their origin
and relation to the physical world, and the way they lie at the intersection
of so many different parts of mathematics. In the past fifteen years a new
component has been added: the availability of computer graphics to provide
illustrations that are both mathematically instructive and esthetically
pleasing.
During the course of the twentieth century, two major thrusts have played a
seminal role in the evolution of minimal surface theory. The first is the work on
the Plateau Problem, whose initial phase culminated in the solution for which
Jesse Douglas was awarded one of the first two Fields Medals in 1936. (The
other Fields Medal that year went to Lars V. Ahlfors for his contributions to
complex analysis, including his important new insights in Nevanlinna Theory.)
The second was the innovative approach to partial differential equations by
Serge Bernstein, which led to the celebrated Bernstein's Theorem, stating that
the only solution to the minimal surface equation over the whole plane is the
trivial solution: a linear function.