# 100 Best Number Theory Books of All Time

We've researched and ranked the best number theory books in the world, based on recommendations from world experts, sales data, and millions of reader ratings. Learn more

Sarah-Jayne BlakemoreThe book is great because Simon Singh has this ability to write about the driest and most complex scientific or mathematical concepts and issues, and somehow make them come alive. (Source)

Kirk BorneNew Perspective on Fermat's Last Theorem: https://t.co/YeaHQ6iadB by @granvilleDSC @DataScienceCtrl #abdsc #Mathematics See the best-selling book "Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem": https://t.co/dqenmvUw0A by @SLSingh https://t.co/deyMhQTQLU (Source)

Steve Jurvetson[Steve Jurvetson recommended this book on the podcast "The Tim Ferriss Show".] (Source)

Seth GodinIn the last week, I discovered that at least two of my smart friends hadn't read Godel, Escher, Bach. They have now. You should too. (Source)

Kevin KellyOver the years, I kept finding myself returning to its insights, and each time I would arrive at them at a deeper level. (Source)

*Zero*follows this number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe and its apotheosis as the mystery of the black hole. Today, zero lies at the heart of one of the biggest scientific controversies of all time, the quest for the theory of everything. Elegant, witty, and enlightening,

*Zero*... more

Alex BellosUnlike Ifrah, Charles Seife is a brilliant popular science writer who has here written the ‘biography’ of zero. And even though he doesn’t talk that much about India, it works well as a handbook to Ifrah’s sections on India. Because Seife talks about how zero is mathematically very close to the idea of infinity, which is another mathematical idea that the Indians thought about differently. Seife... (Source)

Bryan JohnsonChronicles how hard it was for humanity to come up with and hold onto the concept of zero. No zero, no math. No zero, no engineering. No zero, no modern world as we know it... (Source)

In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent... more

Alex BellosPetr Beckmann was a Czech electrical engineer who lived in Czechoslovakia until he was 39 in 1963, when he went to America as a visiting professor and just stayed there. (Source)

**Prime Obsession**is a fascinating and fluent account of an epic... more

Solving the Riemann Hypothesis could change the way we do business, since prime numbers are the lynchpin for security in banking and e-commerce. It would also have a profound impact on the cutting-edge of science, affecting quantum mechanics, chaos theory, and the future of... more

**Don't have time to read the top Number Theory books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

*phi*, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing... more

Kirk BorneSome Fun with Gentle Chaos, the Golden Ratio, and Stochastic Number Theory, with Gaming Applications: https://t.co/oQG0y3vA22 #abdsc by @granvilleDSC @DataScienceCtrl #Mathematics #Statistics ————— Learn all about the Golden Ratio in this fantastic book: https://t.co/9QxN9ECpH7 https://t.co/Mt45UZFFHH (Source)

*Elements*. In keeping with Green Lion's design commitment, diagrams have been placed on every spread for convenient reference while working through the proofs; running heads on every page indicate both Euclid's book number and proposition numbers for that page; and adequate space for notes is allowed between propositions and around diagrams. The all-new index has built into it a glossary of Euclid's Greek terms.

Heath's translation has stood the test of time,... more

Bryan Johnson[Bryan Johnson recommended this book on Twitter.] (Source)

In twelve dreams, Robert, a boy who hates math, meets a Number Devil, who leads him to discover the amazing world of numbers: infinite numbers, prime numbers, Fibonacci numbers, numbers that magically appear in triangles, and numbers that expand without. As we dream with him, we are taken further and further into mathematical theory, where ideas eventually take flight, until everyone - from those who fumble over fractions to those who solve complex equations in their heads - winds up marveling at what... more

**Don't have time to read the top Number Theory books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

Shortly after his arrival on Beta Colony, Miles unexpectedly finds himself the owner of an obsolete freighter and in more debt than he ever thought possible. Propelled by his manic "forward momentum," the ever-inventive Miles creates a new identity for himself as the commander of his own mercenary fleet to obtain a lucrative cargo; a shipment of weapons destined for a dangerous warzone. less

The opening chapters offer sound explanations of the basics of elementary number theory and develop the... more

Paulo Ribenboim is Professor Emeritus at Queen's University in Canada, Fellow of the Royal Society of Canada, and recipient of the George Polya Award of the Mathematical Association of America. He is the author... more

**A highly successful presentation of the fundamental concepts of number theory and computer programming**

Bridging an existing gap between mathematics and programming,

*Elementary Number Theory with Programming*provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced... more

**A wide variety of ready-to-use number talks that help kindergarten through second-grade students learn math concepts in fun and easy ways**

Bringing the exciting teaching method of number talks into your classroom has never been easier. Simply choose from the hundreds of great ideas in this book and get going, with no extra time wasted!

From activities on addition and subtraction to fractions and decimals,

*Classroom-Ready Number Talks for Kindergarten, First and Second Grade Teachers*includes:

**Grade-level specific strategies**

Number talk...more

Number talk...

**Don't have time to read the top Number Theory books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

Marcus du SautoyYes, it really appealed to me when I read it as a kid because I was interested in music, I played the trumpet, I loved doing theatre, and somehow GH Hardy in that book revealed to me how much mathematics is a creative art as much as a useful science. In fact he probably goes further, he really revels in the beauty of the subject and says he’s not particularly interested in the applications. That... (Source)

*n*-gon is constructible just in case phi(

*n*) is a power of 2, the fact that the circle cannot be squared, Dirichlet's theorem on primes in arithmetic progressions, the Prime Number Theorem, and Rademacher's partition theorem.

We have made the... more

**Don't have time to read the top Number Theory books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

From the reviews: .,." The book is carefully written - in particular very much self-contained. As was the intention of the author, it is easily accessible to graduate or even undergraduate students, yet even the advanced mathematician will enjoy reading it. The last... more

*An Illustrated Theory of Numbers*gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history.

Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic... more

**Don't have time to read the top Number Theory books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

**Pure Mathematics for Beginners**

**Pure Mathematics for Beginners**consists of a series of lessons in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra.The 16 lessons in this book cover basic through intermediate material from each of these 8 topics. In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively.Pure Mathematics for Beginners is perfect for

professors teaching an introductory college course in higher... more

*Not Even Wrong*, he shows that what many physicists call superstring "theory" is not a theory at all. It makes no... more

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

*The Mathematical Theory of Communication*, published originally as a paper on communication theory in the

*Bell System Technical Journal*more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this... more

**Don't have time to read the top Number Theory books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

**Computational Number Theory**presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and practitioners of cryptography in industry.

Requiring no prior experience with number theory or sophisticated algebraic tools, the book covers many computational aspects of number theory and highlights important and... more

In answering these questions, Barrow provides a bridge between the usually irreconcilable worlds of mathematics and theology. Along the way, he treats... more

Mathematics is inescapable. Wherever you go, whatever you do, however you live your life, mathematics plays a role. From searching for love to donating a kidney, the mathematics governing our world is fascinating, and far reaching. Using interesting anecdotes, simple analogies, and easy explanations,

*Man vs. Math*will distill the complexities of some of the most absorbing mathematics of modern life.

Along the way we will look at why... more

Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects

Authors are well-known and highly-regarded in the field less

"[This book] can be described as a collection of critical historical essays dealing with a large variety of mathematical disciplines and issues, and intended for a broad audience we know of no book on mathematics and its history that covers half as much nonstandard material. Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer)

more

**Don't have time to read the top Number Theory books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

*Los Angeles Times*

"Absorbing; enlightening; lucid; witty; inventive. An exemplar of science writing at its very best." —

*American Mathematical Monthly*

A substantial revision of Martin Gardner's earlier well-known work on mirror symmetry and asymmetry,

*The New Ambidextrous Universe*takes readers on an extraordinary journey. With... more

*tested*cases — the problem is to prove that the law is

*always*correct. Includes van der Waerden's theorem on arithmetic progressions, the Landau-Schnirelmann hypothesis and Mann's theorem, and a solution to Waring's problem. less

The treatment begins with an examination of a formula of Vieta that extends to the notion of statistical independence. Subsequent... more

**Don't have time to read the top Number Theory books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

*Dr. Euler's Fabulous Formula*shares the fascinating story of this groundbreaking formula--long regarded as the gold standard for mathematical beauty--and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's

*An Imaginary Tale*, this book examines the many applications of complex numbers alongside intriguing stories from the history of... more

*School Science and Math*

This book, written by a prominent mathematician and Sterling Professor of Mathematics at Yale, differs from most other books on number theory in two important ways: first, it presents the principal ideas and methods of number theory within a historical and cultural framework, making the subject more tangible and easily grasped. Second, the material requires substantially less mathematical background than many comparable texts. Technical complications and mathematical requirements have been kept to a... more

*n*> 2--Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with... more

The authors introduce the core principles of modern cryptography, including the modern, computational approach to security that overcomes the limitations of perfect secrecy. An extensive treatment of private-key encryption and message authentication follows. The authors also illustrate... more

**Don't have time to read the top Number Theory books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

The second... more

Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's... more

Tyler CowenFrom this I learned how powerful the individual human mind could be, and also how much school wasn’t teaching me. It began to occur to me that the mainstream doesn’t necessarily have the best or only methods. That said, non-mainstream approaches still have the responsibility of coming up with the right answer. Query: does it these days ever make sense to actually use this stuff? (Source)

**Elliptic Curves: Number Theory and Cryptography, Second Edition**develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of elliptic curves.

**New to the Second Edition**

Chapters on isogenies and hyperelliptic curves A discussion of alternative coordinate systems, such as projective, Jacobian, and Edwards coordinates, along with related computational... more

*Proofs from THE BOOK*features an entirely new chapter on Van der Waerden's permanent conjecture, as well as additional, highly original and delightful proofs in other chapters.

**From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition"**

*"... It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. [...] This book does an invaluable service to...*more

**Don't have time to read the top Number Theory books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.