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Sampling actual writings from the history of mathematics, Benjamin Wardhaugh reveals the questions that will unlock the meaning and significance of a given text--Who wrote it, why, and for whom? What was its author's intended meaning? How did it reach its present form? Is it original or a translation? Why is it important today? Wardhaugh teaches readers to think about what the original text might have looked like, to consider where and when it was written, and to formulate questions of their own. Readers pick up new skills with each chapter, and gain the confidence and analytical sophistication needed to tackle virtually any text in the history of mathematics.

Introduces readers to the methods of textual analysis used by historians Uses actual source material as examples Features boxed summaries, discussion questions, and suggestions for further reading Supplements all major sourcebooks in mathematics history Designed for easy reference Ideal for students and teachersThe math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it.

Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?

How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.

Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

Math is boring, says the mathematician and comedian Matt Parker. Part of the problem may be the way the subject is taught, but it's also true that we all, to a greater or lesser extent, find math difficult and counterintuitive. This counterintuitiveness is actually part of the point, argues Parker: the extraordinary thing about math is that it allows us to access logic and ideas beyond what our brains can instinctively do—through its logical tools we are able to reach beyond our innate abilities and grasp more and more abstract concepts.

In the absorbing and exhilarating Things to Make and Do in the Fourth Dimension, Parker sets out to convince his readers to revisit the very math that put them off the subject as fourteen-year-olds. Starting with the foundations of math familiar from school (numbers, geometry, and algebra), he reveals how it is possible to climb all the way up to the topology and to four-dimensional shapes, and from there to infinity—and slightly beyond.

Both playful and sophisticated, Things to Make and Do in the Fourth Dimension is filled with captivating games and puzzles, a buffet of optional hands-on activities that entices us to take pleasure in math that is normally only available to those studying at a university level. Things to Make and Do in the Fourth Dimension invites us to re-learn much of what we missed in school and, this time, to be utterly enthralled by it.

The present volume contains a rich selection of 70 of the best of these brain teasers, in some cases including references to new developments related to the puzzle. Now enthusiasts can challenge their solving skills and rattle their egos with such stimulating mind-benders as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, The Fork in the Road, Bronx vs. Brooklyn, Touching Cigarettes, and 64 other problems involving logic and basic math. Solutions are included.

Throughout history, scientists have come up with theories and ideas that just don't seem to make sense. These we call paradoxes. The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds. For example, how can a cat be both dead and alive at the same time? Why will Achilles never beat a tortoise in a race, no matter how fast he runs? And how can a person be ten years older than his twin?

With elegant explanations that bring the reader inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle. Just as surely as Al-Khalili narrates the enduring fascination of these classic paradoxes, he reveals their underlying logic. In doing so, he brings to life a select group of the most exciting concepts in human knowledge. Paradox is mind-expanding fun.

With coverage spanning the foundations of origami construction and advanced methods using both paper and pencil and custom-built free software, Origami Design Secrets helps readers cultivate the intuition and skills necessary to develop their own designs. It takes them beyond merely following a recipe to crafting a work of art.

Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct—including the revelation that ants can actually count how many steps they’ve taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games.

Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize.

Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. Here’s Looking at Euclid is a rare gem that brings the beauty of math to life.

Part of the reason for the book's success is its marvelously varied assortment of brainteasers ranging from simple "catch" riddles to difficult problems (none, however, requiring advanced mathematics). Many of the puzzles will be new to Western readers, while some familiar problems have been clothed in new forms. Often the puzzles are presented in the form of charming stories that provide non-Russian readers with valuable insights into contemporary Russian life and customs. In addition, Martin Gardner, former editor of the Mathematical Games Department, Scientific American, has clarified and simplified the book to make it as easy as possible for an English-reading public to understand and enjoy. He has been careful, moreover, to retain nearly all the freshness, warmth, and humor of the original.

Lavishly illustrated with over 400 clear diagrams and amusing sketches, this inexpensive edition of the first English translation will offer weeks or even months of stimulating entertainment. It belongs in the library of every puzzlist or lover of recreational mathematics.

The two-part selection of puzzles and paradoxes begins with examinations of the nature of infinity and some curious systems related to Gödel's theorem. The first three chapters of Part II contain generalized Gödel theorems. Symbolic logic is deferred until the last three chapters, which give explanations and examples of first-order arithmetic, Peano arithmetic, and a complete proof of Gödel's celebrated result involving statements that cannot be proved or disproved. The book also includes a lively look at decision theory, better known as recursion theory, which plays a vital role in computer science.

Sprinkling his discussion of numbers and probabilities with quirky stories and anecdotes, Paulos ranges freely over many aspects of modern life, from contested elections to sports stats, from stock scams and newspaper psychics to diet and medical claims, sex discrimination, insurance, lotteries, and drug testing. Readers of Innumeracy will be rewarded with scores of astonishing facts, a fistful of powerful ideas, and, most important, a clearer, more quantitative way of looking at their world.

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 numbers can do.

Hans Magnus Enzensberger is a true polymath, the kind of superb intellectual who loves thinking and marshals all of his charm and wit to share his passions with the world. In The Number Devil, he brings together the surreal logic of Alice in Wonderland and the existential geometry of Flatland with the kind of math everyone would love, if only they had a number devil to teach it to them.

The Dreams That Stuff Is Made Of compiles the essential works from the scientists who sparked the paradigm shift that changed the face of physics forever, pushing our understanding of the universe on to an entirely new level of comprehension. Gathered in this anthology is the scholarship that shocked and befuddled the scientific world, including works by Niels Bohr, Max Planck, Werner Heisenberg, Max Born, Erwin Schrodinger, J. Robert Oppenheimer, Richard Feynman, as well as an introduction by today's most celebrated scientist, Stephen Hawking.

Trigonometry deals with the relationship between the sides and angles of triangles... mostly right triangles. In practical use, trigonometry is a friend to astronomers who use triangulation to measure the distance between stars. Trig also has applications in fields as broad as financial analysis, music theory, biology, medical imaging, cryptology, game development, and seismology.

From sines and cosines to logarithms, conic sections, and polynomials, this friendly guide takes the torture out of trigonometry, explaining basic concepts in plain English and offering lots of easy-to-grasp example problems. It also explains the "why" of trigonometry, using real-world examples that illustrate the value of trigonometry in a variety of careers.

Tracks to a typical Trigonometry course at the high school or college level Packed with example trig problems From the author of Trigonometry Workbook For DummiesTrigonometry For Dummies is for any student who needs an introduction to, or better understanding of, high-school to college-level trigonometry.

Is it possible that the answer to becoming a more efficient and effective thinker is learning how to forget? Yes! Mike Byster will show you how mastering this extraordinary technique—forgetting unnecessary information, sifting through brain clutter, and focusing on only important nuggets of data—will change the quality of your work and life balance forever.

Using the six tools in The Power of Forgetting, you’ll learn how to be a more agile thinker and productive individual. You will overcome the staggering volume of daily distractions that lead to to brain fog, an inability to concentrate, lack of creativity, stress, anxiety, nervousness, angst, worry, dread, and even depression. By training your brain with Byster’s exclusive quizzes and games, you’ll develop the critical skills to become more successful in all that you do, each and every day.

Get hooked on math as Alex delves deep into humankind’s turbulent relationship with numbers, and reveals how they have shaped the world we live in.

In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem.

Some images inside the book are unavailable due to digital copyright restrictions.

One of Lit Hub’s “The Best Books About Books”

“Enlightening.” —The Wall Street Journal

Data meets literature in this brilliant new look at our favorite authors and their masterpieces: Do literary titans follow their own writing advice (and is it any good)? Do men and women write their characters differently? What are each author’s favorite words and clichés?

There’s a famous piece of writing advice—offered by Ernest Hemingway, Stephen King, and myriad writers in between—not to use -ly adverbs like “quickly” or “fitfully.” It sounds like solid advice, but can we actually test it? If we were to count all the -ly adverbs these authors used in their careers, do they follow their own advice compared to other celebrated authors? And do great books in general—the classics and the bestsellers—use fewer adverbs?

In Nabokov’s Favorite Word Is Mauve, statistician and journalist Ben Blatt brings big data to the literary canon, exploring the wealth of fun findings that remain hidden in the works of the world’s greatest writers. He assembles a database of thousands of books and hundreds of millions of words, and starts asking the questions that have intrigued curious word nerds and book lovers for generations: What are our favorite authors’ favorite words? Do men and women write differently? Are bestsellers getting dumber over time? Which bestselling writer uses the most clichés? What makes a great opening sentence? How can we judge a book by its cover? And which writerly advice is worth following or ignoring?

Blatt draws upon existing analysis techniques and invents some of his own. All of his investigations and experiments are original, conducted himself, and no math knowledge is needed to understand the results. Blatt breaks his findings down into lucid, humorous language and clear and compelling visuals. This eye-opening book offers a new appreciation of our favorite authors and a fresh perspective on our own writing, illuminating both the patterns that hold great prose together and the brilliant flourishes that make it unforgettable.

These three-dimensional models are created from a number of small pieces of paper that are easily folded and then cleverly fit together to form a spectacular shape. They range from paper polyhedra to bristling buckyballs that are reminiscent of sea urchins—to ornate flower-like spheres.

Each piece of paper is held by the tension of the other papers—demonstrating the remarkable hidden properties of paper, which is at the same time flexible but also strong!

Author Byriah Loper has been creating modular origami sculptures for just five years, but in that time, he's pushed the upper limits of the art form with some of the largest, most complex geometric paper constructions ever assembled. While many geo-modular origami artists focus on creating dense floral spheres, Byriah has pioneered the open, linear "wire frame" approach, which results in a very complex-looking model that reveals the interior of its form. He exhibits his sculptures annually at the Origami USA convention in New York, and was recently a featured artist at the "Surface to Structure" exhibition at the Cooper Union gallery in the East Village.

A great way to learn origami, the easy-to-follow diagrams and step-by-step instructions in this book show you how to fold the paper components and then assemble them to create 22 incredible models. Each model is a new challenge, and the paper sculptures you create look fantastic on your desk or shelf!

Kick start your neurons at Level 1 with puzzles involving hidden words, math calculations, and logical conundrums. At Level 2, fire up your synapses with cryptograms, scrambled sentences, and visual challenges. And activate your brain at Level 3 with fill-in-the-blanks, search-a-words, magic squares, and much more. If you get stumped, an answer key with complete solutions appears at the end.

Both simple and accessible, Math in Minutes is a visually led introduction to 200 key mathematical concepts. Each concept is described by means of an easy-to-understand illustration and a compact, 200-word explanation. Concepts span all of the key areas of mathematics, including Fundamentals of Mathematics, Sets and Numbers, Geometry, Equations, Limits, Functions and Calculus, Vectors and Algebra, Complex Numbers, Combinatorics, Number Theory, and more.

From the Trade Paperback edition.

THINKING IN NUMBERS is the book that Daniel Tammet, mathematical savant and bestselling author, was born to write. In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives.

Inspired variously by the complexity of snowflakes, Anne Boleyn's eleven fingers, and his many siblings, Tammet explores questions such as why time seems to speed up as we age, whether there is such a thing as an average person, and how we can make sense of those we love. His provocative and inspiring new book will change the way you think about math and fire your imagination to view the world with fresh eyes.

How do you apply game theory to select who should be on your Christmas shopping list? What equations should you use to decorate the Christmas tree? Will calculations show Santa is getting steadily thinner—shimmying up and down chimneys for a whole night—or fatter—as he munches on cookies and milk in billions of houses across the world?

In The Indisputable Existence of Santa Claus, distinguished mathematicians Hannah Fry and Thomas Oléron Evans demonstrate, with eminently readable clarity, how applied mathematics are so thoroughly interwoven throughout our everyday lives by explaining mathematical concepts through one very merry motif: Christmas.

In their quest to provide mathematical proof for the existence of Santa, the authors take readers on a festive journey through a traditional holiday season, wherein every activity, from wrapping presents to playing board games to cooking the perfect turkey, is painstakingly and hilariously analyzed. Because who hasn’t always wondered how to set up a mathematically perfect Secret Santa?

Lighthearted and diverting with Christmasy diagrams, sketches and graphs, equations, Markov chains, and matrices, The Indisputable Existence of Santa Claus brightens up the bleak midwinter with stockingsful of mathematical marvels.

A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how calculus, among its other uses, helps trace the path of falling bombs.

Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting." — Saturday Review of Literature.

Drawing on game theory, geometry, linear algebra, target-tracking algorithms, and much more, Nahin also offers an array of challenging puzzles with their historical background and broader applications. Chases and Escapes includes solutions to all problems and provides computer programs that readers can use for their own cutting-edge analysis.

Now with a gripping new preface on how the Enola Gay escaped the shock wave from the atomic bomb dropped on Hiroshima, this book will appeal to anyone interested in the mathematics that underlie pursuit and evasion.

Some images inside the book are unavailable due to digital copyright restrictions.

Illustrated by Karl H. Hofmann

Each main topic is treated in depth from its historical conception through to its status today. Many beautiful solutions have emerged for basic chessboard problems since mathematicians first began working on them in earnest over three centuries ago, but such problems, including those involving polyominoes, have now been extended to three-dimensional chessboards and even chessboards on unusual surfaces such as toruses (the equivalent of playing chess on a doughnut) and cylinders. Using the highly visual language of graph theory, Watkins gently guides the reader to the forefront of current research in mathematics. By solving some of the many exercises sprinkled throughout, the reader can share fully in the excitement of discovery.

Showing that chess puzzles are the starting point for important mathematical ideas that have resonated for centuries, Across the Board will captivate students and instructors, mathematicians, chess enthusiasts, and puzzle devotees.

In Calculating the Cosmos, Ian Stewart presents an exhilarating guide to the cosmos, from our solar system to the entire universe. He describes the architecture of space and time, dark matter and dark energy, how galaxies form, why stars implode, how everything began, and how it's all going to end. He considers parallel universes, the fine-tuning of the cosmos for life, what forms extraterrestrial life might take, and the likelihood of life on Earth being snuffed out by an asteroid.

Beginning with the Babylonian integration of mathematics into the study of astronomy and cosmology, Stewart traces the evolution of our understanding of the cosmos: How Kepler's laws of planetary motion led Newton to formulate his theory of gravity. How, two centuries later, tiny irregularities in the motion of Mars inspired Einstein to devise his general theory of relativity. How, eighty years ago, the discovery that the universe is expanding led to the development of the Big Bang theory of its origins. How single-point origin and expansion led cosmologists to theorize new components of the universe, such as inflation, dark matter, and dark energy. But does inflation explain the structure of today's universe? Does dark matter actually exist? Could a scientific revolution that will challenge the long-held scientific orthodoxy and once again transform our understanding of the universe be on the way? In an exciting and engaging style, Calculating the Cosmos is a mathematical quest through the intricate realms of astronomy and cosmology.

Six Simple Twists: The Pleat Pattern Approach to Origami Tessellation Design explains the process of designing an origami pattern. It answers the questions "how is a tessellation folded" and "what are the further possibilities."

The author introduces an innovative pleat pattern technique of origami design that is easily accessible to anyone who enjoys the geometry of paper. The book begins with basic forms and systematically builds upon them to teach a limitless number of patterns. It then describes a process of design for the building blocks themselves. At the end, what emerges is a fascinating art form that will enrich folders for many years.

Unlike standard, project-based origami books, Six Simple Twists focuses on how to design rather than construct. This leads to a better understanding of more complicated tessellations at the advanced level.

Transforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process—not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and improve their ability to apply mathematics more efficiently and effectively to practical problems in their own work.

Using parts of speech to identify variables and functions in a mathematical model is a new approach, as is the insight that examining aspects of grammar is highly useful when formulating a corresponding mathematical model. This book identifies the basic elements of the language of mathematics, such as values, variables, and functions, while presenting the grammatical rules for combining them into expressions and other structures. The author describes and defines different notational forms for expressions, and also identifies the relationships between parts of speech and other grammatical elements in English and components of expressions in the language of mathematics. Extensive examples are used throughout that cover a wide range of real-world problems and feature diagrams and tables to facilitate understanding.

The Language of Mathematics is a thought-provoking book of interest for readers who would like to learn more about the linguistic nature and aspects of mathematical notation. The book also serves as a valuable supplement for engineers, technicians, managers, and consultants who would like to improve their ability to apply mathematics effectively, systematically, and efficiently to practical problems.

"What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?" So wrote the American mathematician and educator David Eugene Smith. In a similar vein, the German mathematician Karl Weierstrass declared, "A mathematician who is not at the same time something of a poet will never be a full mathematician." Most mathematicians will know what they meant. But what do professional poets think of mathematics?

In this delightful collection, the editors present the view of the same terrain—the connections between mathematics and poetry—from the other side of the equation: the poets. Now is your chance to see if the equation balances.

—Keith Devlin, mathematician, Stanford University, and author of The Math Gene, The Math Instinct, and The Language of Mathematics

logic—the one indispensable tool in man’s quest to understand the world. Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.

Give your mind a playful workout with this collection of more than 100 inventive puzzles. Finding the solutions requires only minimal mathematical knowledge and will test your imagination as well as your brainpower. The motley collection ranges from conundrums and mathematical stunts to practical situations involving counting and measuring. Chess problems, magic squares, and a host of other intriguing scenarios will amuse and challenge puzzle enthusiasts and fans of recreational mathematics. Answers appear at the end of each chapter.

These puzzles are the inventions of a gifted Soviet mathematician, Yakov Perelman, whose popular science books on astronomy, physics, and mathematics inspired generations of readers. Perelman's distinctive style, abounding in wit and ingenuity, adds a special flair to his timeless riddles and brainteasers.

In A Cultural History of Physics, Hungarian scientist and educator Károly Simonyi succeeds in bridging this chasm by describing the experimental methods and theoretical interpretations that created scientific knowledge, from ancient times to the present day, within the cultural environment in which it was formed. Unlike any other work of its kind, Simonyi’s seminal opus explores the interplay of science and the humanities to convey the wonder and excitement of scientific development throughout the ages.

These pages contain an abundance of excerpts from original resources, a wide array of clear and straightforward explanations, and an astonishing wealth of insight, revealing the historical progress of science and inviting readers into a dialogue with the great scientific minds that shaped our current understanding of physics.

Beautifully illustrated, accurate in its scientific content and broad in its historical and cultural perspective, this book will be a valuable reference for scholars and an inspiration to aspiring scientists and humanists who believe that science is an integral part of our culture.

Students and puzzle enthusiasts will find plenty of thought-provoking enjoyment mixed with a bit of painless mathematical instruction among these twenty-eight conundrums. Some of them involve counting, some deal with infinity, and others draw on principles of geometry and arithmetic. None requires an extensive background in higher mathematics. Challenges include The Curve That Shook the World, a variation on the famous Monty Hall Problem, Space Travel in a Wineglass, Through Cantor's Looking Glass, and other fun-to-ponder paradoxes.

The author of more than twenty books, mathematician Raymond Smullyan is also a magician and musician with decades of experience in keeping audiences entertained. Many of his stories are rooted in classic puzzles, but his innovative approaches offer even the most mathematically knowledgeable readers novel ways of thinking about traditional logic problems. Fifteen chapters abound in riddles and other playful devices, and the creative solutions are as much fun as the puzzles!

Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics.

From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.