{"id":11574,"date":"2022-06-29T03:44:07","date_gmt":"2022-06-29T03:44:07","guid":{"rendered":"https:\/\/www.booksofall.com\/tw\/?post_type=product&p=11574"},"modified":"2022-06-29T03:46:13","modified_gmt":"2022-06-29T03:46:13","slug":"the-essence-of-mathematics-through-elementary-problems","status":"publish","type":"product","link":"https:\/\/www.booksofall.com\/tw\/the-essence-of-mathematics-through-elementary-problems\/","title":{"rendered":"The Essence of Mathematics Through Elementary Problems"},"content":{"rendered":"

Understanding mathematics cannot be transmitted by painless entertainment . . . actual contact with the content of living mathematics is necessary. The present book . . . is not a concession to the dangerous tendency toward dodging all exertion. Richard Courant <\/a>(1888{1972) and Herbert Robbins<\/a> (1915{2001)\u00a0<\/em><\/p>\n

Interested students of mathematics, who seek insight into the essence of the discipline”, and who read more widely with a view to discovering what the subject is really about, may emerge with the justifiable impression of serious mathematics as an austere, but distant mountain range { accessible only to those who devote their lives to its exploration. And they may conclude that the beginner can only appreciate its rough outline through a haze of unbridgeable distance. The best popularisers sometimes manage to convey more than this { including hints of the human story behind recent developments, and the way different branches and results interact in unexpected ways; but the essence of mathematics still tends to remain elusive, and the picture they paint is inevitably a broad brush substitute for the detail of living mathematics.<\/p>\n

This collection takes a different approach. We start out by observing that mathematics is not a fixed entity { as one might unconsciously infer from the metaphor of an \\austere mountain range”. Mathematics is a mental universe, a work-in-progress in our collective imagination, which grows dramatically over time, and whose eventual extent would seem to be unconstrained { without any obvious limits. This boundlessness also works in reverse, when applied to small details: features which we thought we had understood are repeatedly filled in, or reinterpreted, in new ways to reveal ner and finer micro-structures.<\/p>\n

Hence whatever the essence of the discipline may be, it is clearly not something which can only be accessed through the complete exploration of some fixed corpus of knowledge. Rather the essential character of mathematics seems to be related to<\/p>\n