In Search of Infinity

by N.Ya. Vilenkin

The concept of infinity is one of the most important, and at the same time, one of the most mysterious concepts of science. Already in antiquity many philosophers and mathematicians pondered over its contradictory nature. In mathematics, the contradictions connected with infinity intensified after the creation, at the end of the 19th century, of the theory of infinite sets and the subsequent discovery, soon after, of paradoxes in this theory. At the time, many scientists ignored the paradoxes and used set theory extensively in their work, while others subjected set-theoretic methods in mathematics to harsh criticism. The debate intensified when a group of French mathematicians, who wrote under the pseudonym of Nicolas Bourbaki, tried to erect the whole edifice of mathematics on the single notion of a set. Some mathematicians greeted this attempt enthusiastically while others regarded it as an unnecessary formalization, an attempt to tear mathematics away from life-giving practical applications that sustain it. These differences notwithstanding, Bourbaki has had a significant influence on the evolution of mathematics in the twentieth century. In this book we try to tell the reader how the idea of the infinite arose and developed in physics and in mathematics, how the theory of infinite sets was constructed, what paradoxes it has led to, what significant efforts have been made to eliminate the resulting contradictions, and what routes scientists are trying to find that would provide a way out of the many difficulties.

Genres: Mathematics

145 pages, Hardcover

First published November 10, 2013

About the author

Naum Yakovlevich Vilenkin, Russian: Наум Яковлевич Виленкин, was a Soviet mathematician, an expert in combinatorics. He is best known as the author of many books in recreational mathematics aimed at middle and high school students.

Reviews

[Caitee Nigro · Rating 4 out of 5]

Hello. My name is Caitee, and I am a mathaholic. Some may even go as far as labeling me a calculations-connoisseur. But despite my passion for problem-solving, I can always appreciate a down to earth math lesson in simple English. Vilenkin masters just that in "In Search of Infinity." The book explores theories ranging from the thought-provoking paradoxes of Zeno, to the provocative philosophies of Aristotle, without using a language which would surpass the mathematical vocabulary of a seventh-grader.
The book and the stories within it (that's right, math stories) are all engaging and easy to grasp, but do not limit your understanding of more complex ideas. This is the perfect read for those looking to try their hand at something new, or for someone who wanted to explore the world of digits, but never seemed to have any luck on the subject passed the fifth grade.
Personally, I enjoyed the book because it provided me with answers to the infamous question,"What the hell am I ever going to use this for in the real world?" Math is quite applicable, as this book proves (minus the truth-tables - double math pun there, for your literary taste-buds), and it just may surprise you where you can take it.

[Yuki · Rating 3 out of 5]

Interesting book on infinity from a Russian perspective.

[Yofish · Rating 3 out of 5]

All about infinity. Very short. Interesting because it's very much written from the Russian perspective. (For example, most Russian mathematicians are listed as authors of 'outstanding works', while Gauss is merely 'the greatest German mathematician of the 19th century.' Well, yes, but....) Four chapters. The first is on philosophical stuff, and not so interesting. The second is on basic Cantor stuff. The third gets into space-filling curves (and similar); actually, I didn't know much about a lot of this stuff. And then the last was about Godel-type stuff. Good stuff all around, but didn't really grab me much.

Really 3.5

[Bob · Rating 3 out of 5]

This is probably a better book than I am giving it credit for; it was worth going through, but did not really tell me anything new. Probably because infinity is something I do not understand very well. Later, I may go through this book again.