Mathematics and Faith

Abstract:  In this reflection about mathematics I shall confine myself to arithmetic, the study of the numbers 0, 1, 2, 3, 4,.... Everyone has at least the feeling of familiarity with arithmetic, and the issues that concern the human search for truth in mathematics are already present in arithmetic. Here is an illustration of research in arithmetic. About 2500 years ago, the Pythagoreans defined a number to be perfect in case it is the sum of all its divisors other than itself. Thus 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14 are perfect. The Pythagoreans, or perhaps Euclid himself, proved that if 2 n - 1 is a prime, then (2 n - 1) ? 2 n-1 is perfect. 1 More than 2000 years later, Euler proved that every even perfect number is of this form. This left open the question whether there exists an odd perfect number. The search for an odd perfect number or, alternatively, for a proof that no odd perfect number exists, continues today, several centuries after Euler and in the fourth millennium from Pythagoras.