Mathematics Under The Microscope
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Mathematics under the Microscope
Author: Alexandre Borovik
language: en
Publisher: American Mathematical Soc.
Release Date: 2010
Discusses, from a working mathematician's point of view, the mystery of mathematical intuition: Why are certain mathematical concepts more intuitive than others? And to what extent does the 'small scale' structure of mathematical concepts and algorithms reflect the workings of the human brain?
Mathematics Under the Microscope
"This book will be interesting--perhaps for different reasons--to school teachers of mathematics, to math majors at universities, to graduate students in mathematics and computer science, to research mathematicians and computer scientists, to philosophers and historians of mathematics, and to psychologists and neurophysiologists. The author's goal is to start a dialogue between mathematicians and cognitive scientists. He discusses, from a working mathematician's point of view, the mystery of mathematical intuition: why are certain mathematical concepts more intuitive than others? To what extent does the "small scale" structure of mathematical concepts and algorithms reflect the workings of the human brain? What are the "elementary particles" of mathematics that build up the mathematical universe? One of the principal points of the book is the essential vertical unity of mathematics, the natural integration of its simplest objects and concepts into the complex hierarchy of mathematics as a whole. The same ideas and patterns of thinking can be found in elementary school arithmetic and in cutting-edge mathematical theories. There are no boundaries between "recreational", "elementary", "undergraduate", and "research" mathematics; the book freely moves throughout the whole range. Nevertheless, the author takes great care in keeping the book as non-technical as possible. The book is saturated with amusing examples from a wide range of disciplines--from turbulence to error-correcting codes to logic--as well as with just puzzles and brainteasers. Despite the very serious subject matter, the author's approach is lighthearted and entertaining."--Publisher's website.
The Mathematics of Life
Biologists have long dismissed mathematics as being unable to meaningfully contribute to our understanding of living beings. Within the past ten years, however, mathematicians have proven that they hold the key to unlocking the mysteries of our world -- and ourselves. In The Mathematics of Life, Ian Stewart provides a fascinating overview of the vital but little-recognized role mathematics has played in pulling back the curtain on the hidden complexities of the natural world -- and how its contribution will be even more vital in the years ahead. In his characteristically clear and entertaining fashion, Stewart explains how mathematicians and biologists have come to work together on some of the most difficult scientific problems that the human race has ever tackled, including the nature and origin of life itself.