Seeing and revealing hidden patterns are what mathematicians do best. “Ordering the Universe: The Role of Mathematics.” In Renewing U. Mathematics: Critical Resource for the Future, 117–162.
Each major discovery opens new areas rich with potential for further exploration.
Not just computers, but also new applications and new theories have significantly expanded the role of mathematics in science, business, and technology.
Students who will live and work using computers as a routine tool need to learn a different mathematics than their ancestors.
Indeed, because new developments build on fundamental principles, it is plausible, as many observers often suggest, that one should focus first on restoring strength to time-honored fundamentals before embarking on reforms based on changes in the contemporary practice of mathematics. Archimedes' Revenge: The Joys and Perils of Mathematics.
Public support for strong basic curricula reinforces the wisdom of the past—that traditional school mathematics, if carefully taught and well learned, provides sound preparation both for the world of work and for advanced study in mathematically based fields.
In the last century alone, the number of mathematical disciplines has grown at an exponential rate; examples include the ideas of Georg Cantor on transfinite sets, Sonja Kovalevsky on differential equations, Alan Turing on computability, Emmy Noether on abstract algebra, and, most recently, Benoit Mandelbrot on fractals. The Divine Proportion: A Study in Mathematical Beauty.
To the public these new domains of mathematics are terra incognita.