Algorithms in Modern Mathematics and Computer Science

The life and work of the ninth century scientist al-Khwarizmi, "the father of algebra and algorithms," is surveyed briefly. Then a random sampling technique is used in an attempt to better understand the kinds of thinking that good mathematicians and computer scientists do and to analyze whether such thinking is significantly "algorithmic" in nature. (This is the text of a talk given at the opening session of a symposium on "Algorithms in Modern Mathamatics and Computer Science" held in Urgench, Khorezm Oblast'', Uzbek S.S.R., during the week of September 16-22, 1979.)