Number Theory in Science and Communication

Preface: Number theory has been considered since time immemorial to be the very paradigm of pure (some would say useless) mathematics. In fact, the Chinese characters for mathematics are Number Science. 'Mathematics is the queen of sciences - and number theory is the queen of mathematics,' according to Carl Friedrich Gauss, the lifelong Wunderkind, who himself enjoyed the epithet 'Princeps Mathematicorum.' What could be more beautiful than a deep, satisfying relation between numbers. (One is almost tempted to call them wholesome numbers. ) In fact, it is hard to come up with a more appropriate designation than their learned name: the integers - meaning the 'untouched ones'. How high they rank, in the realms of pure thought and aesthetics, above their lesser brethren: the real and complex numbers - whose first names virtually exude unsavory involvement with the complex realities of everyday life!