Here are 100 books that Great Circles fans have personally recommended if you like
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Meaningful communications with people through life, books, and films have always given me a certain kind of mental nirvana of being transported to a place of delight. I see fine writing as an informative and entertaining conversation with a stranger I just met on a plane who has interesting things to say about the world. Books of narrative merit in mathematics and science are my strangers eager to be met. For me, the best narratives are those that bring me to places I have never been, to tell me things I have not known, and to keep me reading with the feeling of being alive in a human experience.
This book is a brilliant interweaving of politics, history, and intrigue, with characters living ordinary lives, described in the spirit of a Russian novel. With one story threading into another, the book moves us forwards. We fly over the tall mountains, misty valleys, and green fields of current abstract maths and fundamental physics to witness the true beauties of truth. And in the end, Stewart confesses: “No one could have predicted that a pedantic question about equations could reveal the deep structure of the physical world, but that is exactly what's happened.”
As with many of Stewart’s books, Why Beauty is Truth is a joy to read. It brings us through current material with ease of understanding and out oversimplifying. I love the way Stewart uses tangible examples to describe the fundamental forces of nature as he escorts us with clarity through so many eloquent connections between mathematics and physics.…
At the heart of relativity theory, quantum mechanics, string theory, and much of modern cosmology lies one concept: symmetry. In Why Beauty Is Truth , world-famous mathematician Ian Stewart narrates the history of the emergence of this remarkable area of study. Stewart introduces us to such characters as the Renaissance Italian genius, rogue, scholar, and gambler Girolamo Cardano, who stole the modern method of solving cubic equations and published it in the first important book on algebra, and the young revolutionary Evariste Galois, who refashioned the whole of mathematics and founded the field of group theory only to die in…
It is April 1st, 2038. Day 60 of China's blockade of the rebel island of Taiwan.
The US government has agreed to provide Taiwan with a weapons system so advanced that it can disrupt the balance of power in the region. But what pilot would be crazy enough to run…
Meaningful communications with people through life, books, and films have always given me a certain kind of mental nirvana of being transported to a place of delight. I see fine writing as an informative and entertaining conversation with a stranger I just met on a plane who has interesting things to say about the world. Books of narrative merit in mathematics and science are my strangers eager to be met. For me, the best narratives are those that bring me to places I have never been, to tell me things I have not known, and to keep me reading with the feeling of being alive in a human experience.
For me, this book was an adventure. I felt as if I was on an expedition to Virginia with Harriot teaching me astronomy and navigation. There I was, infatuated with rainbows and imagining myself scrutinizing scientific wonders of elliptical planetary motion, atomic theory of matter, and how cannonballs could be stacked to fill space. I found myself with Harriot back in 1591 searching for a sphere-packing formula, an old problem questioning the most stable way to stack cannonballs on ships. Thomas Harriot is a fast-moving biography packed with the world- and mind-changing curiosities.
Thomas Harriot (1560-1621) was a pioneer in both the figurative and literal sense. Navigational adviser and loyal friend to Sir Walter Ralegh, Harriot took part in the first expedition to colonize Virginia. Not only was he responsible for getting Ralegh's ships safely to harbor in the New World, once there he became the first European to acquire a working knowledge of an indigenous language (he also began a lifelong love of tobacco, which may have been his undoing). Harriot's abilities were seemingly unlimited and nearly awe-inspiring. He was the first to use a telescope to map the moon's craters, and,…
Meaningful communications with people through life, books, and films have always given me a certain kind of mental nirvana of being transported to a place of delight. I see fine writing as an informative and entertaining conversation with a stranger I just met on a plane who has interesting things to say about the world. Books of narrative merit in mathematics and science are my strangers eager to be met. For me, the best narratives are those that bring me to places I have never been, to tell me things I have not known, and to keep me reading with the feeling of being alive in a human experience.
Ekeland’s book is an entwinement of philosophical views of scientists with metaphysics dealing with nature’s directives. It’s an embroidery of lively anecdotes involving illustrious individuals and great historical moments of human decisions. We go through the Peloponnesian Wars, Venetian concessions to the Hapsburg emperor Maximilian, Darwin’s voyage to the Galapagos, and other enriching accounts. His explanations are clear, elegant, fluid, exhilarating, and suspenseful, reminding me of the effortless style of Richard Feynman. While reading, I felt compelled by a force of nature and purpose to learn about the best of all possible worlds.
Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what is the best of all possible worlds? How do we define it? This question has preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer. This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle, Ekeland…
A Duke with rigid opinions, a Lady whose beliefs conflict with his, a long disputed parcel of land, a conniving neighbour, a desperate collaboration, a failure of trust, a love found despite it all.
Alexander Cavendish, Duke of Ravensworth, returned from war to find that his father and brother had…
Meaningful communications with people through life, books, and films have always given me a certain kind of mental nirvana of being transported to a place of delight. I see fine writing as an informative and entertaining conversation with a stranger I just met on a plane who has interesting things to say about the world. Books of narrative merit in mathematics and science are my strangers eager to be met. For me, the best narratives are those that bring me to places I have never been, to tell me things I have not known, and to keep me reading with the feeling of being alive in a human experience.
More than any other, this book influenced me most about wanting to study mathematics. Of course, I was young at the time and strongly partial to Einstein’s remark, “This is beyond doubt the most interesting book on the evolution of mathematics which has ever fallen into my hands.” Many years later, when I exhaustively tried to find the book in any bookstore I passed, it was out of print. So I suggested it to my publisher, who immediately acquired the rights and republished it under my editing guidelines. It is the quintessential lure into mathematics for readers of any age.
"Beyond doubt the most interesting book on the evolution of mathematics which has ever fallen into my hands."—Albert Einstein
Number is an eloquent, accessible tour de force that reveals how the concept of number evolved from prehistoric times through the twentieth century. Renowned professor of mathematics Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the…
Philosophy’s core questions have always obsessed me: What is real? What makes life worth living? Can knowledge be made secure? In graduate school at the University of Virginia I was drawn to mathematically formalized approaches to such questions, especially those of C. S. Peirce and Alain Badiou. More recently, alongside colleagues at Endicott College’s Center for Diagrammatic and Computational Philosophy and GCAS College Dublin I have explored applications of diagrammatic logic, category theory, game theory, and homotopy type theory to such problems as abductive inference and artificial intelligence. Philosophers committed to the perennial questions have much to gain today from studying the new methods and results of contemporary mathematics.
From a strictly philosophical perspective, the emergence of category theory as a unifying paradigm rivaling set theory is probably the most important development in mathematics in the last half-century.
But for philosophers without a lot of mathematical background, learning even its rudiments can be daunting. Among many introductory texts (Lawvere and Schanuel, Awodey, Riehl, Spivak), Cheng’s book stands out as perhaps the friendliest and most accessible.
She does not forego rigor, but she isn’t afraid to put aside precise formalism when necessary for intuition and clearer understanding. Her book takes the reader from mathematical beginnings through category theory’s core constructions to glimpses of higher-order categories (one of Cheng’s areas of expertise).
A mathematically novice philosopher who wants to understand the basics of category theory couldn’t do better.
Mathematician and popular science author Eugenia Cheng is on a mission to show you that mathematics can be flexible, creative, and visual. This joyful journey through the world of abstract mathematics into category theory will demystify mathematical thought processes and help you develop your own thinking, with no formal mathematical background needed. The book brings abstract mathematical ideas down to earth using examples of social justice, current events, and everyday life - from privilege to COVID-19 to driving routes. The journey begins with the ideas and workings of abstract mathematics, after which you will gently climb toward more technical material,…
Having majored in both philosophy and physics as an undergraduate, I specialized in the philosophy of science in graduate school–with a focus on the possibility of a “logic of scientific discovery.” Most philosophers of science have been skeptical about such a sub-discipline, restricting their theories of scientific method to the justification of already-formulated hypotheses. Others (including myself) have held that there is also a logic to the generation of hypotheses.
This is a fascinating analysis of the works of Copernicus, Kepler, Galileo, Descartes, Hobbes, Gilbert, Boyle, and Newton. It not only establishes the reasons for the triumph of the modern perspective but also accounts for certain limitations in this view that continue to characterize contemporary scientific thought.
A criticism as well as a history of the change that made possible the rise of modern science, this volume is also a guide to understanding the methods and accomplishments of the great philosopher-scientists of the sixteenth and seventeenth centuries.
s/t: A Historical & Critical Essay Many books well received when originally published ultimately fail the test of time & seem outdated to future generations. Occasionally, a book seen as a solid effort when written is found later to be the definitive work on the subject. The Metaphysical Foundations of Modern Science by Edwin Arthur Burtt is such. Burtt investigates the origins of the modern scientific worldview, a view that's only a few centuries old. Concepts used to describe the world--mass, velocity, energy, time etc--form the substratum of so many modern ideas that their very ubiquity has made it hard…
The Duke's Christmas Redemption
by
Arietta Richmond,
A Duke who has rejected love, a Lady who dreams of a love match, an arranged marriage, a house full of secrets, a most unneighborly neighbor, a plot to destroy reputations, an unexpected love that redeems it all.
Lady Charlotte Wyndham, given in an arranged marriage to a man she…
I am Professor of Computer Science at Stony Brook University, and have spent the past thirty years thinking/teaching/writing about algorithms. Algorithms are the really cool thing about computer science, for they form the ideas behind any interesting computer program. And algorithms turn out to be the ideas behind many interesting aspects of life that have nothing to do with computers. I have written six books on algorithms, programming, gambling, and history –including the ranking of the historical significance of all the people in Wikipedia.
Polya was a great mathematician who knew what counted (after all, he made major contributions to combinatorics, the mathematics of counting). He thought hard about what he was doing when working on problems in mathematics, developing a mental process that lead to creative breakthroughs and solutions. Polya’s problem-solving method is broadly applicable to domains other than mathematics, and this book features many nice puzzles to improve your thinking.
Algorithm design is challenging because it often requires flashes of sudden insight which seem to come out of the blue. But there is a way of thinking about problems that make such flashes more likely to happen. I try to teach this thought process in my books, but Polya got there first.
A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.
Philosophy’s core questions have always obsessed me: What is real? What makes life worth living? Can knowledge be made secure? In graduate school at the University of Virginia I was drawn to mathematically formalized approaches to such questions, especially those of C. S. Peirce and Alain Badiou. More recently, alongside colleagues at Endicott College’s Center for Diagrammatic and Computational Philosophy and GCAS College Dublin I have explored applications of diagrammatic logic, category theory, game theory, and homotopy type theory to such problems as abductive inference and artificial intelligence. Philosophers committed to the perennial questions have much to gain today from studying the new methods and results of contemporary mathematics.
Zalamea’s book is the perfect introduction and survey if you want to understand how developments in contemporary mathematics are relevant to current philosophy.
Zalamea’s own approach follows closely in the steps of Peirce, Lautman, and Grothendieck, merging pragmatism, dialectics, and sheaf theory, but he also engages the work of dozens of other key mathematicians and philosophers coming from different points of view, sometimes cursorily, always tantalizingly.
No philosopher can read this book without a quickened heartbeat and eager plans to clear shelf space for some of the many volumes of mathematics and philosophy of mathematics canvassed here by Zalamea.
A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest.
A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics.
The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the…
I have enjoyed mathematics and writing since I’ve been a kid, not only enjoying doing research in mathematics but assisting others to appreciate and enjoy mathematics. Along the way, I’ve gained an interest in the history of mathematics and the mathematicians who created mathematics. Perhaps most important, my primary goal has been to show others how enjoyable mathematics can be. Mathematics has given me the marvelous opportunity to meet and work with other mathematicians who have a similar passion for mathematics.
Have you ever been to a mathematics lecture where the speaker wore a tuxedo and baffled the audience with his mystifying knowledge of numbers? Well, I have and the speaker was Arthur Benjamin, who combined mathematics and magic. He even displayed this knowledge with Stephen Colbert on his earlier show The Colbert Report. It is our good fortune that he describes much of this mathematical wizardry in this fascinating book.
A New York Times Bestseller Arthur Benjamin . . . joyfully shows you how to make nature's numbers dance." ,Bill Nye The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples,from ice-cream scoops and poker hands to measuring mountains and making magic squares,this book revels in key mathematical fields including arithmetic, algebra, geometry, and calculus, plus Fibonacci numbers, infinity, and, of course, mathematical magic tricks. Known throughout the world as the mathemagician," Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand for math…
This book follows the journey of a writer in search of wisdom as he narrates encounters with 12 distinguished American men over 80, including Paul Volcker, the former head of the Federal Reserve, and Denton Cooley, the world’s most famous heart surgeon.
In these and other intimate conversations, the book…
I believe that knowledge is power. Understanding how something works leads to practical applications. In markets, I believe you should develop your own ideas on how to invest rather than being told. After all, how can you profit if you’re doing what everyone else is doing? Markets are efficient enough to give an opportunity to everyone but advantage to no one, unless you do something different than the crowd. My list is designed to give you information to develop investment strategies based on chaos theory, complexity, and fractals. It is not designed to tell you how to invest.
Readers of this list may be surprised that there are no books by Benoit Mandelbrot, the father of fractals. I found his books fascinating but frustrating. Feder’s book, by contrast, was readable and usable.
This book taught me how to do fractal analysis. While Feder’s book has nothing to do with markets, it has everything to do with applications. While I reuse much of Feder’s methodology in my books, readers will find it useful to see other practical applications of fractal analysis.
This lovely little book will take off and fly on its own power, but the author has asked me to write a few words, and one should not say no to a friend. Specific topics in fractal geometry and its applications have already benefited from several excellent surveys of moderate length, and gossip and preliminary drafts tell us that we shall soon see several monographic treatments of broader topics. For the teacher, however, these surveys and monographs are not enough, and an urgent need for more helpful books has been widely recognized. To write such a book is no easy…
