In the collective unconscious of most working mathematicians, there is the lambent vision of a mathematics department in which mathematicians sit quietly in their offices and prove theorems. Occasionally they are interrupted by a duty to go teach, or to serve on a committee. But, for the most part, they think about mathematics. The mathematics department in this vision has a truce with the University administration: all the mathematicians have research grants, are regularly invited to other universities to give colloquia and to consult, and are recognized scholars; as a result, the administration does not press too hard about the quality of teaching, or how well the department serves the needs of students from other departments in science and engineering.

For better or for worse, the mathematics department described in the last paragraph no longer exists. There are several reasons for this change. Forty years ago, when that chimeric mathematics department did exist, it could safely be said that mathematics was an elitist subject. Society's demand for the mathematically fluent was quite small, and those few who survived the mathematics curriculum were more than sufficient to fill the need for teachers, researchers, and mathematical scientists. There was no need for self-examination because what we did seemed to work.

There is now a broad perception that what we do does not work. Society now demands a technologically literate work force, and the elitist teaching methodology developed by earlier generations of mathematicians is no longer adequate to the job. More precisely, it is no longer adequate in view of the broad crosssection of society that we are trying to educate, and in view of the level of technical competence that is demanded of those whom we graduate.