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 19yearold graduate student, Roland
Clarkson,
