Abstract

This book discusses in dialogue form the basic principles of mathematics and its applications including the question: What is mathematics? What does its specific method consist of? What is its relation to the sciences and humanities? What can it offer to specialists in different fields? How can it be applied in practice and in discovering the laws of nature? Dramatized by the dialogue form and shown in the historical movements in which they originated, these questions are discussed in their full complexity, yet are easily comprehended. The first dialogue, whose chief actor is Socrates, leads the reader to the source of modern mathematics in Athens in the 5th Century BC. The second dialogue, featuring Archimedes, takes place during the siege of Syracuse in 212 BC and shows the birth of applied mathematics. The third dialogue occurs in the year 1633 in Rome, its chief character being Galileo Galilei who fully realized the central importance of the mathematical method in discovering the laws of nature. Intended as supplemental reading for philosophy of mathematics courses at the high school or college level it will be of interest to both specialists and non-specialists in mathematics. Alfréd Rényi was born in Budapest Hungary in 1921. He studied mathematics and physics at the University of Budapest and received his Ph. D. from the University of Szaged in 1945. Since 1950 he has been Director of the Mathematical Research Institute of the Hungarian Academy of Sciences and since 1952 a professor at the University of Budapest. Dr. Renyi was a visiting professor at Michigan State University in 1961, at the University of Michigan in 1964 and at Stanford University in 1966. His main fields of research are probability theory, mathematical statistics and information theory, and he has also worked in analytic number theory as well as in various branches of analysis, combinatorial analysis and geometry.