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Closing the Gap: The Quest to Understand Prime Numbers de Vicky Neale

Closing the Gap: The Quest to Understand Prime Numbers

Autor Vicky Neale
en Limba Engleză Hardback – 12 oct 2017

Evoluția cercetării matematice contemporane a marcat o trecere spectaculoasă de la geniul solitar la inteligența colectivă, un fenomen pe care Closing the Gap îl analizează cu o precizie remarcabilă. Apreciem modul în care Vicky Neale reușește să explice cum un domeniu vechi de două milenii a fost revitalizat în 2013 prin descoperirea unui matematician aflat la finalul carierei, urmată de o colaborare globală online fără precedent. Credem că această lucrare depășește granițele unui simplu tratat, oferind o perspectivă rară asupra mecanismelor de gândire care stau în spatele demonstrațiilor matematice.

Structura narativă este una hibridă: capitolele despre progresele recente privind „distanțele mărginite” dintre numerele prime sunt intercalate cu episoade istorice, oferind contextul necesar pentru a înțelege de ce aceste numere au fascinat mințile umane încă din antichitate. Recomandăm această carte ca o alternativă la Bounded Gaps Between Primes de Kevin Broughan pentru cursurile de teoria numerelor, având avantajul unei abordări narative accesibile care pune accent pe procesul descoperirii, nu doar pe rigoarea demonstrațiilor și a programelor de calcul.

În contextul operei sale, dacă în Why Study Mathematics? autoarea oferea un ghid practic despre utilitatea disciplinei, în Closing the Gap ea demonstrează frumusețea intrinsecă a cercetării fundamentale. Stilul este direct, evitând metaforele excesive în favoarea unei clarități care permite cititorului să urmărească firul logic al uneia dintre cele mai mari realizări matematice ale secolului XXI.

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Specificații

ISBN-13: 9780198788287
ISBN-10: 0198788282
Pagini: 172
Dimensiuni: 167 x 241 x 16 mm
Greutate: 0.45 kg
Editura: OUP OXFORD
Colecția OUP Oxford
Locul publicării:Oxford, United Kingdom

De ce să citești această carte

Recomandăm această carte oricărui pasionat de matematică sau istoria științei care dorește să înțeleagă cum se nasc marile idei. Cititorul câștigă o perspectivă unică asupra colaborării moderne (proiectul Polymath) și a modului în care o problemă veche de milenii, precum numerele prime gemene, este abordată astăzi prin tehnologie și creativitate colectivă.

Despre autor

Vicky Neale este o figură proeminentă în comunitatea matematică academică, fiind recunoscută pentru capacitatea sa de a comunica concepte complexe unui public larg. În calitate de docent la Universitatea din Oxford și membru al Balliol College, activitatea sa se concentrează pe teoria numerelor și pe promovarea educației matematice. Lucrările sale, precum Why Study Mathematics?, reflectă angajamentul său de a ghida studenții și profesorii prin peisajul academic modern. În Closing the Gap, Neale își folosește expertiza pentru a documenta tranziția disciplinei către modele de cercetare colaborativă, rămânând fidelă rigoarei științifice specifice Oxford.

Descriere

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.

Recenzii

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.
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.
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.
The book is clearly and enthusiastically written and beautifully presented.
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.
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.
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.
Closing the Gap is 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.
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.
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.
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.

Notă biografică

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.