Radio technology and the theory of numbers

✍ Scribed by Balth van der Pol

• Publisher: Elsevier Science
• Year: 1953
• Tongue: English
• Weight: 940 KB
• Volume: 255
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(53)90294-4

✦ Synopsis

The subject of my lecture combines two sciences which, at first sight, may perhaps seem utterly unrelated. In fact, I do not know of any literature which suggests a relationship between these two domains.

I refer on the one hand to Radio Technology in its widest sense, a subject about which we have all heard a great deal and with which we are personally acquainted, if only through our use of radio sets at home ; and on the other hand, to the Theory of Numbers, a part of pure mathematics, and perhaps even the purest part of it. Gauss, the great German mathematician, is said to have stated that "if mathematics is the Queen of Sciences, then Number Theory is the Queen of Mathematics." Number Theory is concerned for a large part with the natural numbers 1, 2, 3, ..., etc. These natural numbers have an unexpected wealth of properties, and some of the theorems discovered about them belong to the deepest regions human intellect has been able to penetrate. This led another German mathematician, Kronecker, to say "God created the integers, all the rest is the work of men."

We are, of course, to a certain extent, all acquainted with the natural numbers, for example, when in the morning we pay the milkman in Krone and ~)re. But the natural numbers extend beyond a hundred and beyond a million, and even beyond the greatest numbers we encounter in astronomy. Hence the material at the disposal of those who study the Theory of Numbers extends towards infinity. _And each of these natural numbers is either prime or composite. The primes are not divisible by any other integer apart from unity and the prime itself.