Skip top navigation and go to page content
National Science Foundation
Computer & Information Science
next page Mathematics Home
next page More Research Overviews
Photo, caption follows:

This beautifully convoluted spiral--the technical name is "translation invariant helicoid"--is an example of what mathematicians call a minimal surface. This means that the surface is as flat and taut as possible, rather like a soap bubble that has formed on a helical wire. Minimal surfaces have many applications in fields such as materials science and nanotechnology, and have become an area of intense study in recent years.
Credit: Matthias Weber

Cover Page Credits: K.S. Matz (shell); Matthias Weber

Mathematics is about numbers, shapes, symmetry, chance, change and more. Much more. Math is not only the most rigorous mental discipline ever invented, it's among the richest, most wide-ranging and most useful. Indeed, mathematics is deeply interwoven into all of modern life.

Mathematics is the natural language of science and engineering, for example, as well as being an essential tool for business and industry. No surprise there: these activities were math's original inspiration. Its historical roots go back to our ancestors' first attempts to keep account of their goods, to measure their fields and to predict events in the heavens, and eventually, the techniques they invented grew into arithmetic, algebra, geometry, calculus and a host of other subdisciplines.

Mathematics is also central to the information revolution. Downloadable music files, DVD movies, digital special effects and secure online credit card transactions, essentially any software application you can think of, owes its existence not just to computers, but to the mathematical algorithms that run on computers.

Then too, mathematics is a thing of fiercely compelling beauty in its own right. A vast conceptual framework that extends from Fermat's last theorem to the quantum mysteries of superstring theory to the fragile intricacies of fractals, and far, far beyond.

And of course, mathematics is a field that is still growing, still evolving, still finding new applications. The National Science Foundation contributes to that effort as the leading supporter of fundamental mathematics research in the United States. Among the major research topics now being explored are:

  row bullet Assembling Information into a Big Picture
  row bullet Managing and Modeling Complexity
  row bullet Deciding on the Best Choice
  row bullet Pattern Hunting and Statistical Learning