The Prime Number Conspiracy: The Biggest Ideas in Math from Quanta

by Thomas Lin (editor), James Gleick (Foreword)

The Pulitzer Prize–winning magazine’s stories of mathematical explorations show that inspiration strikes haphazardly, revealing surprising solutions and exciting discoveries—with a foreword by James Gleick These stories from Quanta Magazine map the routes of mathematical exploration, showing readers how cutting-edge research is done, while illuminating the productive tension between conjecture and proof, theory and intuition. The stories show that, as James Gleick puts it in the foreword, “inspiration strikes willy-nilly.” One researcher thinks of quantum chaotic systems at a bus stop; another suddenly realizes a path to proving a theorem of number theory while in a friend's backyard; a statistician has a “bathroom sink epiphany” and discovers the key to solving the Gaussian correlation inequality. Readers of The Prime Number Conspiracy, says Quanta editor-in-chief Thomas Lin, are headed on “breathtaking intellectual journeys to the bleeding edge of discovery strapped to the narrative rocket of humanity's never-ending pursuit of knowledge.”Winner of the 2022 Pulitzer Prize for Explanatory Reporting, Quanta is the only popular publication that offers in-depth coverage of the latest breakthroughs in understanding our mathematical universe. It communicates mathematics by taking it seriously, wrestling with difficult concepts and clearly explaining them in a way that speaks to our innate curiosity about our world and ourselves. Readers of this volume will learn that prime numbers have decided preferences about the final digits of the primes that immediately follow them (the “conspiracy” of the title); consider whether math is the universal language of nature (allowing for “a unified theory of randomness”); discover surprising solutions (including a pentagon tiling proof that solves a century-old math problem); ponder the limits of computation; measure infinity; and explore the eternal question “Is mathematics good for you?” Contributors Ariel Bleicher, Robbert Dijkgraaf, Kevin Hartnett, Erica Klarreich, Thomas Lin, John Pavlus, Siobhan Roberts, Natalie Wolchover Copublished with Quanta Magazine

Genres: Mathematics, Science, Nonfiction, Audiobook, Stem, Essays, Popular Science

295 pages, Kindle Edition

Published December 4, 2018

About the author

Thomas Lin is the founding publisher of Quanta Books. From 2012 to 2024, he was the founding editor-in-chief of Quanta Magazine, a Pulitzer Prize-winning publication that reports on developments in science and mathematics, with content syndicated in Wired, The Atlantic, Scientific American and The Washington Post. Lin previously worked at The New York Times, where he edited online features and wrote about science, technology and tennis. He has also written for Quanta, The New Yorker, Tennis, and other publications.

Book ratings: 5 stars = must read; 4 stars = recommended; 3 stars = worth taking a look if you're interested in the topic.

Reviews

[Josh Friedlander · Rating 3 out of 5]

A collection of essays from Quanta magazine. As founding editor Thomas Lin explains in the introduction, the magazine was started intending to produce high-quality, literary science coverage (akin to the pieces Jeremy Bernstein used to write for the New Yorker) that only focused on things with no real-world relevance: maths, and theoretical problems in physics, biology, and computer science. It launched in 2008 - a bad time for media in general - but was funded by the Simons Foundation (billionaire quant and RenTech founder Jim Simons, subject of the recent biography The Man Who Solved the Market). The articles are ambitious and demanding, starting from first principles and going deep. In fact my biggest issue with Quanta and this book is that it would serve readers better if structured as a wiki, instead of a traditional news magazine. Rather than explaining each time from scratch the definition of a twin prime, modular form, multiplicative function or ZFC, the authors could explain it once and then reference that definition in future, rather than cram each article with half a dozen increasingly strained simplifications. Still, the value of the current approach is that readers can enter at any point and have a chance of keeping up; Wikipedia's articles on mathematics are mostly accessible only to people who already have some domain knowledge.

The first section deals with number theory conjectures, mostly related to primes, including the titular "conspiracy" (despite seeming randomly distributed, the primes tend to prefer certain patterns, such as avoiding the same end digit in successive primes). I liked an essay on "universality", the clustering tendency in random matrices, witnessed not just in uranium spectra and the internet but also bus systems in Mexico. Another highlight was a pair of essays on formal methods in programming (such as TLA+) and mathematical proof checkers, which discuss the isomorphism between computation and mathematics, Frege and Russell's attempt to set the foundation of mathematics through set theory axioms, Godel's critique, Church and Turing's alternative proposals for Hilbert's Entscheidungsproblem*, dependent types and category theory, the difficulty of formally verifying an inherently probabilistic domain like machine learning, and even (despite the editorial remit) some real world applications in a government cyber-defence project.

The last section consists of interviews and profiles of working mathematicians, the most notable probably being one with Freeman Dyson where he discusses the famous physicists he knew and his climate skepticism. But the real point of the book is the essays: small windows into cloisters of abstraction, encouraging the reader to struggle, look things up, and share in the joy of studying the entirely pointless.

* There's a wonderful discussion of this topic by the mathematician-philosopher Greg Chaitin here.

[Antti Rasinen · Rating 2 out of 5]

It could be a better book, if they’d had the energy to rewrite the book to be more consistent and less repetitive.

The articles are arranged by topic. Sometimes two subsequent articles need to define a concept, so both of them do it.

Sometimes the articles seem to assume the reader knows math. Sometimes they don’t and they call integral “an infinite sum”.

Terence Tao is overrepresented in the first half of the book.

[Tim Robinson · Rating 3 out of 5]

An attempt to explain a lot of really advanced mathematics to an audience of people with technical training but no specialist knowledge of the area. As such, it tries to do far too much in a very limited space. Each chapter discusses an idea so broad and deep that it needs a whole book of its own. Some of the articles have no illustrations at all: a serious omission. By avoiding the details, this collection leaves the reader with only the vaguest sense of what is going on.

For example, "moonshine" connects The Monster Group with a j-function, by way of String Theory. How many people, even at the best universities, have even a basic understanding of all three concepts? I know a little of the Monster and a little of String Theory, but nothing of j-functions.

[Steve Agland · Rating 4 out of 5]

You have to approach this book for what it is: a collection of loosely related magazine articles and accept the disjointedness and occasional repetition of primers on certain topics.

That aside, this is a wonderful peek into the minds and lives of world-class mathematicians. The topics can be very esoteric and difficult to grasp, but at other times are quite simple, profound and thought-provoking. But it's the biographical side that was surprisingly interesting. For some reason I find mathematicians to be fascinating and sympathetic characters.

[Patrick Kijek · Rating 5 out of 5]

A bunch of essays in current Mathematical fields pulled from Quanta Magazine. I’ve loved reading an essay or two every so often and going about my week. Math is more artistic than people realize, especially at the highest levels. This book can help people love to learn about it and the people who are making up new fields, theories and solutions right now.

[Arthur Ryman · Rating 3 out of 5]

This book is essentially a collection of news reports on recent mathematical advances. As such, it was useful as a way to catch up on the latest developments. I would have given it a higher rating if more of its articles explained the math better. Unfortunately, some of the explanations were very high level and vague, so if you didn't already know something about the subject area, you wouldn't come away with any deeper understanding. I expected a book like this to have more actual math. I don't think the target readership would have been put off by a few more equations. Nevertheless, I did enjoy many of the articles and I'd recommend the book to anyone with an interest in understanding the current math scene.

[Cecil New · Rating 5 out of 5]

Wonderful set of essays/articles on advances in math and the mathematicians themselves.

[Ankush · Rating 4 out of 5]

Stories from the frontiers of mathematics describing in layman language some of the cutting edge work by leading mathematician. Highly recommended.

[Gummih · Rating 3 out of 5]

Disclaimer, I am not a mathematician and the math covered here is delightfully out of my reach. This is the sister volume of Alice and Bob Meet the Wall of Fire: The Biggest Ideas in Science from Quanta and I must say that I enjoyed that one more. I consider myself to have a good mathematical background and enjoy numbers and puzzles, so much of this intrigued me, only that much of the time my understanding of the material was rather vague (to put it generously).

It was enjoyable to read some of the obscure problems that are being solved today and at times their surprising applications in physics and computer science. What this volume also covers is a lot of who's who in today's landscape of advanced mathematics, covering a lot of recent Fields Medalists for example.

Essentially a collection of Quanta articles it is somewhat compartmentalized and not like a seamless journey through mathematics. Still it's a stimulating read and is currently included in Audible's Plus Catalog for free.

[sabine · Rating 3 out of 5]

finally finished this book after it rotted on my shelf for like two and a half years because i wanted to remind myself why i love math. written for a lay audience and thus much more of a casual than a challenging read -- which was good and what i needed

[Maurizio Codogno · Rating 4 out of 5]

Questo libro, raccolta di articoli sulla matematica pubblicati su Quanta Magazine, non è certo di semplice lettura. Gli estensori degli articoli non ne possono nulla, e anzi a parere mio hanno fatto dei miracoli nella semplificazione dei temi trattati: ma stiamo parlando di matematica di frontiera, e soprattutto di temi che non sono così sexy da arrivare nelle prime pagine dei grandi media e così rimangono sconosciute anche a chi come me in fin dei conti dovrebbe saperne un po' di più. Non aspettatevi di trovare matematica vera e propria, naturalmente: in compenso leggendo il libro scoprirete come la matematica appaia in punti a prima vista totalmente scorrelati - un filo conduttore degli articoli è l'applicazione di tecniche da altri campi della matematica. Altro punto interessante è il trovare le biografie di molti giovani matematici contemporanei: non è facile conoscerli in altro modo. Ah: la cospirazione del titolo si collega al fatto che pare che i numeri primi siano un po' meno casuali di quanto crediamo, o almeno che le coppie di primi successivi non lo siano.

[Omarove · Rating 5 out of 5]

Splendid narratives of mathematical achievement and ideas. More of fairy tales! Although one would not understand the technical part of each story, you get to see things through mathematician's eyes. Really fascinating!

PS: this book was my company for many lunches, one story at a time! It was happy eating and reading!

[Stefan · Rating 4 out of 5]

This book provides an overview of the latest developments and breakthroughs in maths. What makes it enjoyable is the attention to the creative process and personality of the people behind these breakthroughs. Enjoyed it as an audio book narrated by Bob Souer.

[Steve Gross · Rating 2 out of 5]

A compilation of magazine articles and it shows. Most of the concepts are either not explained well or too complicated to explain.

[Brandon · Rating 5 out of 5]

This is a collection of articles from the online science magazine "Quanta." Science journalism at its very best. A must read.

[Kit]

In an awkward gray area between rigorous and frivolous. Better to read something heavier, like a textbook, or something lighter, like a youtube video. The middle ground is dry and sandy.

[Alexandra · Rating 4 out of 5]

It was very interesting to read about what's going on in today mathematics. But I wish this book had... more math. Seriously, why did they try to explain everything with words? There are very little equations, graphs, or diagrams even when they would simplify the things. Come on, people who picked up this book won't faint at the sight of an integral or a matrix and can survive introductions to more esoteric math notations too.

I loved the prime numbers sections and the idea of prime number conspiracy. Packing spheres in mutli dimensional spaces was also fun. But my favorite was probably a part about infinity and all the problems it solves and brings at the same time.

[Robert Schmidt · Rating 3 out of 5]

I want to read about mathematics to learn or understand something. If I'm amazed in the process, all the better. This book is thoroughly failing me. I was bored. I found the articles tedious, the mathematics unrelatable, and the people described within uninteresting. I'll probably never finish it.

[Norman Howe · Rating 3 out of 5]

This book told me WAY more about math than I wanted to know.

Not only did I fail to understand many of the concepts discussed, but I failed to recognize the WORDS mentioned in many of the articles.

This was Speculative Fiction, without the fiction. Not that I could tell the difference.

[Vincent V · Rating 5 out of 5]

This book got me more interested in mathematics.

[Kalvin · Rating 4 out of 5]

You get exactly what you came for.

[Person · Rating 4 out of 5]

Very interesting though heavy to get through.

[William E. Ferreira · Rating 5 out of 5]

For thinking people

Learning how really smart people think and grow intellectually and emotionally was the plus for me. Very glad I read this book.

[AttackGirl · Rating 3 out of 5]

If love the language of math, if you feel 8, if you always consider 3 this will be a book you enjoy.

[Tikri /Letitia · Rating 4 out of 5]

#GoodreadsGiveaway
Selected articles from Quanta for advanced Mathematicians. Found it interesting, but over my head.