The Age of Science: What Scientists Learned in the Twentieth Century
by Gerard Piel
The author is the man who practically invented modern science journalism and revived Scientific American in the 1940s.
The book is a highly readable work by one of the most important scientists and journalists of our time. Each chapter is compelling in its own right and can be read by anyone who is curious about the scientific discovery process. Fans of Uncle Tungsten and Tuxedo Park will enjoy this book. It covers physics, biology, earth science, and anthropology, with a strong emphasis on the physical sciences.
As a summary of our learning up to Y2K, it does, however, pretty much exclude the electronics revolution and the computer revolution it spawned.
The Crest of the Peacock: Non-European Roots of Mathematics
by George Gheverghese Joseph
This is a book of scholarship and clarity. Mathematics is viewed as truly global pursuit in which every society has participated. It demolishes all the Eurocentric assumptions which were byproducts of past dominance.
He explains ancient African, American, and Asian methods of counting and manipulating numbers with ease, paying particular attention to the historical development of and interrelationships between cultures.
The revised edition includes a lengthy section, titled "Reflections," that updates and expands on the original material.
Mathematics Elsewhere: An Exploration of Ideas Across Cultures
by Marcia Ascher
This book belongs on the shelves of mathematicians, math students, and math educators, and in the hands of anyone interested in societies other than our own. It is a significant contribution to the recognized but still-emerging field of ethno-mathematics The ideas discussed come from geographically varied cultures: for example - the Borana and Malagasy of Africa, the Tongans and Marshall Islanders of Oceania, the Tamil of South India, the Basques of Western Europe, and the Balinese and Kodi of Indonesia.
Through such examples of how particular societies structure time, reach decisions about the future, make models and maps, systematize relationships, and create intriguing figures, the author demonstrates that traditional cultures have mathematical ideas that are far more substantial and sophisticated than has been generally acknowledged.
For example. Malagasy divination rituals rely on complex algebraic algorithms. And some cultures use calendars far more abstract and elegant than our own. The Basque notion of equivalence, for example, is a dynamic and temporal one not adequately captured by the equal sign. Other ideas taken to be the exclusive province of professionally trained Western mathematicians are, in fact, shared by people in many societies.
Mathematics in Western Culture
by Morris Kline, Richard Courant
This book gives a remarkably fine account of the influences mathematics has had on the development of philosophy, the physical sciences, religion, and the arts in Western life.
The author illustrates the processes by which people think and how those processes have also changed through the ages (i.e., The Age of Reason versus The Renaissance). This book gives some real insights as to the nature and limitations of the current state of mathematics and physics.
Metaphysical Club: A Story of Ideas in America
by Louis Menand
A quadruple biography of Oliver Wendell Holmes, William James, Charles Sanders Pierce, and John Dewey that shows how these four men developed a philosophy of pragmatism following the Civil War, a period Menand likens to post-cold-war times. Together, they formed the Metaphysical Club, a conversational club formed in Cambridge, Massachusetts, in 1872. Dozens of figures receive fascinating thumbnail sketches, from Ralph Waldo Emerson and Charles Darwin to Jane Addams and Eugene Debs. The result is a grand portrait of an age that will appeal to anyone with even a modest interest in the history of philosophy and ideas. Note that "these 4 men were more responsible than any other group for moving American thought into the modern world." Academic freedom and cultural pluralism are just two of their legacies.
The Music of Reason : Experience the Beauty of Mathematics Through Quotations
by Theoni Pappas
Learn what Alice in Wonderland, Albert Einstein, William Shakespeare, Mae West, Plato and others have to say about mathematics. The Music of Reason is a compendium of profound and profane thoughts on mathematics by mathematicians, scientists, authors and artists. This collection of quotes is a mixed bag of the humorous and the philosophical is a thought-provoking sampler on mathematics, dealing with mathematics and the imaginations, the arts, history, nature, numbers, sciences, computers and much...
Number: From Ahmes to Cantor
by Gazale Midhat
History is always relevant. We might take numbers and counting for granted, but we shouldn't. Our number literacy rests upon centuries of human effort, punctuated here and there by strokes of genius. Midhat Gazale takes us on a journey from the ancient worlds of the Egyptians, the Mesopotamians, the Mayas, the Greeks, the Hindus, up to the Arab invasion of Europe and the Renaissance. Our guide introduces us to some of the most fascinating and ingenious characters in mathematical history, from Ahmes the Egyptian scribe (whose efforts helped preserve some of the mathematical secrets of the architects of the pyramids) through the modern era of Georg Cantor (the great nineteenth-century inventor of transfinite numbers). Abundantly illustrated the book is remarkable for its coherency and simplicity. Number will be indispensable for all those who enjoy mathematical recreations and puzzles, and for those who delight in numeracy. It is a sequel to Gnomon.
Pythagoras' Trousers: God, Physics, and the Gender Wars
by Margaret Wertheim
A social and cultural history of physics, from ancient Greece to the present. From its inception, physics has been a male-dominated field and continues to be so today. The author looks at the religious origins of physics as the source of its gender inequality, and argues that the continuing religious undercurrent in contemporary physics is behind women's under-representation in the field.
The Story of Mathematics
by Richard Mankiewicz
The evolution of science, philosophy, and mathematics, all related, is far more important to the history of humanity than a parade of rulers and a procession of wars. Strong words, but Richard Mankiewicz comes mighty close to backing them up in his fascinating book. Divided into brief chapters, the book traces the development of mathematics from a baboon's fibula with 29 clearly visible notches (from Swaziland, circa 35,000 B.C.) to the Babylonian sexagesimal--or base 60--number system, which survives to this day in our method of timekeeping, to Euclid's Elements, described as "the most important textbook of all time," to fractals and other Mandelbrot sets. Along the way, Mankiewicz pays tribute to the men and women at the forefront of mathematics, though he's not afraid to dispel some myths: the Pythagorean theorem was widely known in antiquity before Pythagoras was even born, and a 14th-century Chinese manuscript clearly depicts what is now known as "Pascal's Triangle," a good three centuries before Pascal was born. Most entertaining are the chapters on practical applications of mathematics: astronomy, codemaking and -breaking, military strategy, modern art, and navigation.
The Two Cultures
by C.P.Snow & Stefan Collini
This classic book talks about and tries to promote cooperation between the "two cultures" those trained in the sciences and those trained in the humanities. Writing about his experience as a person trained in science but pursuing a writing career, Snow precisely identifies the problems of the two cultures miscommunicating with each other. Written in the late 1950s, in Britain, Snow's work has influenced a wide range of contemporary thinkers, and has been in no small part an influence on the "writing across the curriculum" movement in American universities. Whether you are interested in the humanities or the sciences, this book clearly will show you the tensions you may face dealing with the "other culture," and the problems such stereotypes pose.
Universal Computer: The Road from Leibniz to Turing
by Martin Davis
Once again, history! Computers rely on such things as semiconductors, memory chips, and electricity. But they also rely on a hard-won body of scientific knowledge that has enabled the now-ubiquitous devices to perform complex calculations, multitask, and even play a game of solitaire. Martin Davis, a fluent interpreter of mathematics and philosophy, locates the source of this knowledge in the work of the remarkable German thinker G. W. Leibniz, who, among other accomplishments, was a distinguished jurist, mining engineer, and diplomat but found time to invent a contraption called the "Leibniz wheel," a sort of calculator that could carry out the four basic operations of arithmetic. Leibniz subsequently developed a method of calculation called the calculus raciocinator, an innovation his successor George Boole extended by turning logic into algebra. Davis traces the development of this logic, essential to the advent of "thinking machines," through the workshops and studies of such thinkers as Georg Cantor, Kurt Gödel, and Alan Turing, each of whom puzzled out just a little bit more of the workings of the world and made the present possible.
The Universal History of Numbers: From Prehistory to the Invention of the Computer
by Georges Ifrah, David Bellos. E.F.Harding & Sophie Wood
This book is a wonderfully comprehensive overview of numbers and counting spanning all the inhabited continents as far back in time as records will allow. Beyond the ancient Babylonians, Sumerians, and Indians, Ifrah takes us farther south into Africa to examine an early decimal counting system and into ancient Mexico to reconstruct what we can of the Mayan calendar and numerical system. The 27 chapters are chiefly organized by culture, though there are some cross-cultural overviews of topics like letters and numbers. After wandering the world for 10 years, studying and learning; this scholastic pilgrim returned with amazing stories to tell. Rigorously researched facts, make The Universal History of Numbers a uniquely important and fascinating volume.
What is Mathematics Really?
by Reuben Hersh
The author argues that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.
What Just Happened: A Chronicle from the Information Frontier
by James Gleick
This book was written as technologies were emerging. For those who have entered the arena late, the book provides the full name of things that are now only known by their acronyms. For instance, I've never known what ISDN stands for, but now I know that it's 'Integrated Services Digital Network.'
With the benefit of hindsight, we can see that some of Gleick's predictions were very prescient (e.g. the Y2K anti-climax), while others were less accurate or at least premature (e.g. cash becoming obsolete). All in all, the book provides a very enjoyable look through the rearview mirror.