Optimization is everywhere. It is human nature to seek the best option among
all that are available. Nature, too, seems to be guided by optimization—many
laws of nature have a variational character. Among geometric figures in the
plane with a fixed perimeter, the circle has the greatest area. Such isoperimet-
ric problems involving geometric figures date back to ancient Greece. Fermat’s
principle, discovered in 1629, stating that the tangent line is horizontal at a
minimum point, seems to have influenced the development of calculus. The
proofs of Rolle’s theorem and the mean value theorem in calculus use the
Weierstrass theorem on the existence of maximizers and minimizers.