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National Amateur Press Association
Monthly Bundle Sample, Boxwooder 357, p.3
kind as myself, and their work has been, so far at any rate as I have helped them to it, as useless as my own. . . ."

In the same book Hardy compares the reality of mathematics and physics. Physics, he says, deals with what we consider to be real things. But, says Hardy, a chair is really simply a collection of whirling electrons and really cannot be actually defined. On the other hand he says a prime number (a number that is evenly divisible only by itself and one) such as 317 "is a prime not because we think it so or because our minds our shaped in one way or another, but because it is so, because mathematical reality is built that way." Hardy was of the firm opinion that mathematics exists without reference to humans and that what mathematicians do is "discover" it. There are mathematicians who believe that mathematics is created by mathematicians and not simply discovered. This is a difficult philosophical problem. More later on this.

Mathematicians have been interested in prime numbers for some 2300 years. Euclid about 300 BC proved that there is no largest prime number and therefore that there are an infinite number of prime numbers. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, etc. The distance between primes grows as the numbers get larger and there are many indications that the distance between them is not a random function, but no actual method, given a prime, of determining the next prime is known. Prime numbers are considered by mathematicians to be the building blocks of numbers since every positive whole number can be expressed as the product of prime numbers in only one way. Thus 55=5 x 11; 56=2 x 2 x 2 x 7; 58=2 x 29 and 59=1 x 59, etc. For over 2000 years mathematicians have found larger and larger prime numbers. The largest, as of January 1998, was found by a 19-year-old graduate student, Roland Clarkson,

 

    Last updated: 03/05/2000