There are two aspects of mathematics. One consists of abstract ideas that people have been drawn to for thousands of years. It is remarkable how many different mathematical concepts people have worked out; the familiar progression from arithmetic through calculus is only a small part. Recent successes include the proof of the Poincare´Conjecture (Grigori Perelman, 2003), the Sphere-Packing Conjecture (Thomas Hales, 1997) and Fermat’s Last Theorem (Andrew Wiles, 1995).

The other aspect of mathematics is its use in other human endeavors, where its impact is equally stunning. Mathematics has always been indispensable in commerce, physics and engineering. In recent years mathematics has driven developments in telecommunications (data compression, encoding); medicine (genome mapping, CAT scans, ultrasound); computers (theory, algorithms); finance (computer trading, options); insurance (setting rates); weather forecasting (seven-day forecasts, climate modeling); car and airplane design (aerodynamics, computer-aided design), and many more.

These developments would have been inconceivable without the strong influence of mathematics to guide their discovery, and yet many can be understood with a well-designed undergraduate background in mathematics.