Mathematics under the Microscope by Alexandre V. Borovik (PDF)

Description

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? 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. This is an unusual and unusually fascinating book. Readers who never thought about mathematics after their school years will be amazed to discover how many habits of mind, ideas, and even material objects that are inherently mathematical serve as building blocks of our civilization and everyday life. A professional mathematician, reluctantly breaking the daily routine, or pondering on some resisting problem, will open this book and enjoy a sudden return to his or her young days when mathematics was fresh, exciting, and holding all promises. And do not take the word “microscope” in the title too literally: in fact, the author looks around, in time and space, focusing in turn on a tremendous variety of motives, from mathematical “memes” (genes of culture) to an unusual life of a Hollywood star. –Yuri I. Manin, Max-Planck Institute of Mathematics, Bonn, and Northwestern University

User’s Reviews

Editorial Reviews: Review This is an unusual and unusually fascinating book. Readers who never thought about mathematics after their school years will be amazed to discover how many habits of mind, ideas, and even material objects that are inherently mathematical serve as building blocks of our civilization and everyday life. A professional mathematician, reluctantly breaking the daily routine, or pondering on some resisting problem, will open this book and enjoy a sudden return to his or her young days when mathematics was fresh, exciting, and holding all promises. And do not take the word “microscope” in the title too literally: in fact, the author looks around, in time and space, focusing in turn on a tremendous variety of motives, from mathematical “memes” (genes of culture) to an unusual life of a Hollywood star. —-Yuri I. Manin, Max-Planck Institute of Mathematics, Bonn, and Northwestern University

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book which was a gift arrived in good condition and on time. It is much appreciated by the receiver

⭐I was surprised that there were no reviews of this book as it has become one of my favourites. I admit that after my first reading I was still no nearer to understanding what a Coxeter group is. When I told this to a mathematician colleague he gave me the look of appalled disbelief at my lack of ability that is reserved for mathematicians and fitness instructors. But I found it did not matter because the book is not mainly about the work of the author, as is a book like “Love and Math” but about how mathematicians set about things. And unlike many books, admittedly mainly by reminiscing American professors, that divide up fellow researchers into the top men who they have worked with and all the rest who are no-hopers, it introduces the ideas of many contemporary male and female mathematicians so there is always something new to find. It may be hard work, but it is accessible, engaging and sets one thinking about what is involved in doing mathematics and how best to develop the required skills. I also liked the frank admission by the author towards the end that designing an experiment to further our understanding the specific cognitive skills of mathematicians is not so easy. One other charming but bonkers aspect of the book is that mentions of contemporary mathematicians are often accompanied by a photo of them as a child. Many thanks Professor Borovik.

⭐If you like mathematics, or if mathematics plays an important role in your professional life, then read this book.Alexandre Borovik is famous mathematician and author of dozen professional mathematical books. But “Mathematics under microscope” is aimed not for mathematic professionals, but for people with base mathematical background and with interest to cognitive science and mathematics.This book consists of many questions and only a few answers. These are the exciting questions about structure of mathematical concepts, basis of mathematical intuition and how mathematics reflects itself in mathematical “memes” (genes of culture).This is very “private” book. The author speak about his discussions with stars of mathematics and not prominent professionals, his childhood in little village at Baikal Lake deep in Siberian province to explain his extraordinary theses. Absolutely distinguishing feature of this book is the photos of famous mathematicians of modern time in their young days.This is the book for intellectual reading, for inspiration, for pleasure.

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