It is no exaggeration to say that mathematics education may hold the key to America's continued world leadership in science and technology and all that springs from them. If students--even a few students--can be excited by mathematics at an early age, a great resource can be nurtured rather than turned off. For that reason and others, some distinguished mathematicians have become increasingly interested in recent years in how their subject is taught in the elementary and secondary schools. The question is how to excite young students.

William F. Lucas, a mathematician at the Claremont Graduate School, is a long-time scholar of game theory and operations research who now devotes much attention to the mathematics curriculum in the schools. In his view the mathematics taught through high school and into college is all very old, giving the impression that mathematics is a finished subject that has to be learned in order to solve problems. In fact, mathematics is a living subject in which new knowledge is being created every day. What's more, Lucas says, much of this mathematics is at an elementary level, requiring few skills beyond counting and adding.

Last Saturday morning a dozen high-school math teachers attended a workshop with Lucas at Woodrow Wilson High School in East Los Angeles conducted under the auspices of the Los Angeles Urban Math/Science Collaborative. Lucas spent nearly four hours describing the growing importance of discrete mathematics--the mathematics of counting things--and detailing real-world problems in the field that are easy to state but can be devilishly difficult to solve. Earlier last week Henry O. Pollak, a past president of the Mathematics Assn. of America and formerly of Bell Laboratories, gave a talk to math teachers here in which he described how discrete mathematics had been put to use solving a very tricky problem for the telephone company: how to find the shortest network that links a large number of cities.