Closing the Gap: The Quest to Understand Prime Numbers

by Vicky Neale

Overview

In 2013, a little known mathematician in his late 50s stunned the mathematical community with a breakthrough on an age-old problem about prime numbers. Since then, there has been further dramatic progress on the problem, thanks to the efforts of a large-scale online collaborative effort of a type that would have been unthinkable in mathematics a couple of decades ago, and the insight and creativity of a young mathematician at the start of his career.

Prime numbers have intrigued, inspired and infuriated mathematicians for millennia. Every school student studies prime numbers and can appreciate their beauty, and yet mathematicians' difficulty with answering some seemingly simple questions about them reveals the depth and subtlety of prime numbers.

Vicky Neale charts the recent progress towards proving the famous Twin Primes Conjecture, and the very different ways in which the breakthroughs have been made: a solo mathematician working in isolation and obscurity, and a large collaboration that is more public than any previous collaborative effort in mathematics and that reveals much about how mathematicians go about their work. Interleaved with this story are highlights from a significantly older tale, going back two thousand years and more, of mathematicians' efforts to comprehend the beauty and unlock the mysteries of the prime numbers.

Product Details

ISBN-13:	9780198788287
Publisher:	Oxford University Press
Publication date:	12/12/2017
Pages:	172
Product dimensions:	6.10(w) x 9.30(h) x 0.80(d)

About the Author

Vicky Neale, Whitehead Lecturer, Oxford University

Vicky Neale is the Whitehead Lecturer at the Mathematical Institute and Balliol College, University of Oxford. A substantial part of her remit is public communication of mathematics. She has wide experience of working with students of all ages (school children to adults, via undergraduates), and of giving public lectures, and does various media work.

Table of Contents

1. Introduction2. What is a prime? 3. May 20134. It's easy to ask hard questions5. May 20136. Making hard problems easier7. June 20138. How many primes are there? 9. July 201310. What's so mathematical about my mathematical pencil? 11. August 201312. If primes are hard, let's try something else13. November 201314 Generalise . . .15. April 201416. Where next?

Editorial Reviews

"The way [Closing the Gap] explores mathematics and at the same time describes the work mathematicians do, is very interesting and it keeps the reader invested in the book. It is easy to read and precise. The book could be definitely recommended to mathematics students and teachers but also to younger people with an interest in higher-level mathematics." — Panayiotis Vlamos , University of Athens, MAA

"The book features a creative structure that lends itself well to the subject matter. A curious undergraduate mathematics major should enjoy this book and learn a great deal. For mathematicians who do not specialize in number theory but who are curious about the flurry of recent activity in the field, this book provides an excellent entry point." — Stephan Ramon Garcia, Notices of the American Mathematics Society

"If you are looking for an introduction to the world of Polymath; if you are looking for the story of the Twin Primes Conjecture; if you are looking to show you friends and family what your life as a mathematician is; if you would like a bit of asymptotic mathematics explained to you plainly; if you would like a summary of Waring's problem; or if you just have a couple of hours and are looking for a nice diversion, then you have found it." — Deborah Chun, London Mathematical Society

"The book is clearly and enthusiastically written and beautifully presented." — Owen Toller, The Mathematical Gazette

"For myself, I learned a lot, even about subjects I thought I knew before... it is clear from every page in the book that Neale is superb teacher. In sum, I recommend this book highly to anyone interested in mathematics, young people and teachers but also to researchers." — Mathematical Thinking and Learning

"Written in an engaging and inclusive way, it makes a perfect read for beginners but it also picks up the pace fairly quickly, so even enthusiasts like myself are bound to enjoy it. Neale manages to take the readers on a journey to cutting edge research mathematics." — Chalkdust Magazine

"Neale writes in an inviting style that draws readers into this challenging subject, convincing them that, with a little effort, they too can follow along. An enjoyable book and journey, complemented by a helpful reading list and index... Recommended." — CHOICE

"Closing the Gapis an excellent exposition of the study of prime numbers. Not only do we learn about the history of this area since the Greeks, but the book is the first aimed at a lay readership that provides insight into recent breakthroughs. Vicky Neale's passion in the subject is contagious and I enjoyed how she weaves together the mathematics with background on how mathematicians now work, as well as her reflections on what it is like to be a mathematician. This book would be ideal for a curious sixth former wanting to peek ahead at what might lie around the corner if they are considering studying mathematics at a higher level." — Alex Bellos, author of Alex's Adventures in Numberland and Alex Through the Looking-Glass

"Her prose is clear but not patronizing, precise but accessible. The result is a very enjoyable book that can be read with profit not only by laypeople but also by mathematics students and the people who teach them." — MAA Reviews

"Closing The Gap has gone straight into my top ten books to give to interested students... The book's introduction starts with an extended analogy comparing mathematics to climbing [and] Neale sets herself up as this guide, and succeeds brilliantly." — The Aperiodical

"Closing the Gap is among the clearest popular accounts of maths I've read in a while. It's about prime numbers, as the title suggests, but it's also a master piece in the art of weaving. Apart from exploring the mathematics, the book gives an intimate description of the process of doing maths as experienced by those who do it every day, and an account of a particularly exciting, and recent, period when prime number theory made some great leaps forward. And it's a look at a completely new way of doing mathematics: in large online collaborations that anyone can join." — PLUS

From the Publisher