num_pages: 254
description: Numbers and diagrams may well be older than letter-alphabets as aids to human reasoning. Yet despite this mathematics is often denied the discussion and analysis of first principles which would be fundamental to the study of word-subjects at any level; conversely its value as an academic discipline unrelated to actual practice may have been exaggerated. Numerical theory space relationships the nature of our mathematical reasoning are not generally thought to lie within the layman's grasp - or where they are offered to him it is usually in the guise of curiosities or party tricks. The seven self-contained chapter of Professor Freudenthal's book offer a glimpse into the mathematician's workshop. They hold a good deal of high-level mathematics but nothing that cannot be followed from the clear practical applications taken from daily life which are his starting and finishing points. Thus ideas of space orientation concern the righthandedness of a corkscrew; theories of surveying and topology involve tunnel building attempts on Samos in the sixth century B.C. or how the roundness of the earth can be expressed without reference to astronomical points. Present and ancient systems of numbers and their bases lead to the theory of electronic calculators while an introduction to protein synthesis puts before the reader various factors in the genetic code of life which biochemists are now trying to formulate. At all times particular attention is given to the interaction of mathematics and its logic with aspects of human activity which remain unchanged over the centuries and which arise from man's curiosity and needs. Hans Freudenthal is Professor of Theoretical and Applied Mathematics at the University of Utrecht.
language: English
title: Mathematics Observed
publisher: McGraw-Hill