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| did we invent math or discover it: Conceptual Programming with Python Thorsten Altenkirch, Isaac Triguero, 2019 Thorsten and Isaac have written this book based on a programming course we teach for Master's Students at the School of Computer Science of the University of Nottingham. The book is intended for students with little or no background in programming coming from different backgrounds educationally as well as culturally. It is not mainly a Python course but we use Python as a vehicle to teach basic programming concepts. Hence, the words conceptual programming in the title. We cover basic concepts about data structures, imperative programming, recursion and backtracking, object-oriented programming, functional programming, game development and some basics of data science. |
| did we invent math or discover it: Is God a Mathematician? Mario Livio, 2011-02-22 Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them. |
| did we invent math or discover it: Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being George Lakoff, Rafael E. Nunez, 2000-11-02 A study of the cognitive science of mathematical ideas. |
| did we invent math or discover it: Numbers and the Making of Us Caleb Everett, 2017-03-13 “A fascinating book.” —James Ryerson, New York Times Book Review A Smithsonian Best Science Book of the Year Winner of the PROSE Award for Best Book in Language & Linguistics Carved into our past and woven into our present, numbers shape our perceptions of the world far more than we think. In this sweeping account of how the invention of numbers sparked a revolution in human thought and culture, Caleb Everett draws on new discoveries in psychology, anthropology, and linguistics to reveal the many things made possible by numbers, from the concept of time to writing, agriculture, and commerce. Numbers are a tool, like the wheel, developed and refined over millennia. They allow us to grasp quantities precisely, but recent research confirms that they are not innate—and without numbers, we could not fully grasp quantities greater than three. Everett considers the number systems that have developed in different societies as he shares insights from his fascinating work with indigenous Amazonians. “This is bold, heady stuff... The breadth of research Everett covers is impressive, and allows him to develop a narrative that is both global and compelling... Numbers is eye-opening, even eye-popping.” —New Scientist “A powerful and convincing case for Everett’s main thesis: that numbers are neither natural nor innate to humans.” —Wall Street Journal |
| did we invent math or discover it: Pythagoras' Revenge Arturo Sangalli, 2009-04-20 The celebrated mathematician and philosopher Pythagoras left no writings. But what if he had and the manuscript was never found? Where would it be located? And what information would it reveal? These questions are the inspiration for the mathematical mystery novel Pythagoras' Revenge. Suspenseful and instructive, Pythagoras' Revenge weaves fact, fiction, mathematics, computer science, and ancient history into a surprising and sophisticated thriller. The intrigue begins when Jule Davidson, a young American mathematician who trolls the internet for difficult math riddles and stumbles upon a neo-Pythagorean sect searching for the promised reincarnation of Pythagoras. Across the ocean, Elmer Galway, a professor of classical history at Oxford, discovers an Arabic manuscript hinting at the existence of an ancient scroll--possibly left by Pythagoras himself. Unknown to one another, Jule and Elmer each have information that the other requires and, as they race to solve the philosophical and mathematical puzzles set before them, their paths ultimately collide. Set in 1998 with flashbacks to classical Greece, Pythagoras' Revenge investigates the confrontation between opposing views of mathematics and reality, and explores ideas from both early and cutting-edge mathematics. From academic Oxford to suburban Chicago and historic Rome, Pythagoras' Revenge is a sophisticated thriller that will grip readers from beginning to surprising end. |
| did we invent math or discover it: The Nothing that is , 2000 In the tradition of Longitude, a small and engagingly written book on the history and meaning of zero--a tour de force of science history that takes us through the hollow circle that leads to infinity. 32 illustrations. |
| did we invent math or discover it: Making up Numbers: A History of Invention in Mathematics Ekkehard Kopp, 2020-10-23 Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject. |
| did we invent math or discover it: What Is Mathematics, Really? Reuben Hersh, 1997-08-21 Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, 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. |
| did we invent math or discover it: Critical Race Theory Norma M. Riccucci, 2022-03-17 This Element explores Critical Race Theory (CRT) and its potential application to the field of public administration. It proposes specific areas within the field where a CRT framework would help to uncover and rectify structural and institutional racism. This is paramount given the high priority that the field places on social equity, the third pillar of public administration. If there is a desire to achieve social equity and justice, systematic, structural racism needs to be addressed and confronted directly. The Black Lives Matter (BLM) movement is one example of the urgency and significance of applying theories from a variety of disciplines to the study of racism in public administration. |
| did we invent math or discover it: Euler William Dunham, 2022-01-13 Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work. |
| did we invent math or discover it: A Mathematician's Lament Paul Lockhart, 2009-04-01 “One of the best critiques of current K-12 mathematics education I have ever seen, written by a first-class research mathematician who elected to devote his teaching career to K-12 education.” —Keith Devlin, NPR’s “Math Guy” A brilliant research mathematician reveals math to be a creative art form on par with painting, poetry, and sculpture, and rejects the standard anxiety-producing teaching methods used in most schools today. Witty and accessible, Paul Lockhart’s controversial approach will provoke spirited debate among educators and parents alike, altering the way we think about math forever. Paul Lockhart is the author of Arithmetic, Measurement, and A Mathematician’s Lament. He has taught mathematics at Brown University, University of California, Santa Cruz, and to K-12 level students at St. Ann’s School in Brooklyn, New York. |
| did we invent math or discover it: a new arithmetic Abraham Leslie Behr, 1969 |
| did we invent math or discover it: Pi in the Sky John D. Barrow, 1992 Famous cosmologist and prolific author John Barrow explores the origin and nature of mathematics and explains the important implications of the numerous unanswered questions in our search for a theory of everything. He weaves together a history of math that illuminates its far-reaching capabilities and its intrinsic limitations, its proven and unproven theories, and its pervasive impact on the way people think and live. Annotation copyrighted by Book News, Inc., Portland, OR |
| did we invent math or discover it: The Man of Numbers Keith Devlin, 2011-11-07 In 1202, a 32-year old Italian finished one of the most influential books of all time, which introduced modern arithmetic to Western Europe. Devised in India in the seventh and eighth centuries and brought to North Africa by Muslim traders, the Hindu-Arabic system helped transform the West into the dominant force in science, technology, and commerce, leaving behind Muslim cultures which had long known it but had failed to see its potential. The young Italian, Leonardo of Pisa (better known today as Fibonacci), had learned the Hindu number system when he traveled to North Africa with his father, a customs agent. The book he created was Liber abbaci, the 'Book of Calculation', and the revolution that followed its publication was enormous. Arithmetic made it possible for ordinary people to buy and sell goods, convert currencies, and keep accurate records of possessions more readily than ever before. Liber abbaci's publication led directly to large-scale international commerce and the scientific revolution of the Renaissance. Yet despite the ubiquity of his discoveries, Leonardo of Pisa remains an enigma. His name is best known today in association with an exercise in Liber abbaci whose solution gives rise to a sequence of numbers - the Fibonacci sequence - used by some to predict the rise and fall of financial markets, and evident in myriad biological structures. In The Man of Numbers, Keith Devlin recreates the life and enduring legacy of an overlooked genius, and in the process makes clear how central numbers and mathematics are to our daily lives. |
| did we invent math or discover it: Unravelling Complexity Francisco Antônio Doria, Shyam Wuppuluri, 2020 The revolutions that Gregory Chaitin brought within the fields of science are well known. From his discovery of algorithmic information complexity to his work on Gödel's theorem, he has contributed deeply and expansively to such diverse fields. This book attempts to bring together a collection of articles written by his colleagues, collaborators and friends to celebrate his work in a festschrift. It encompasses various aspects of the scientific work that Chaitin has accomplished over the years. Topics range from philosophy to biology, from foundations of mathematics to physics, from logic to computer science, and all other areas Chaitin has worked on. It also includes sketches of his personality with the help of biographical accounts in some unconventional articles that will provide a rare glimpse into the personal life and nature of Chaitin. Compared to the other books that exist along a similar vein, this book stands out primarily due to its highly interdisciplinary nature and its scope that will attract readers into Chaitin's world |
| did we invent math or discover it: Fashion, Faith, and Fantasy in the New Physics of the Universe Roger Penrose, 2024-10-22 Nobel Prize–winning physicist Roger Penrose questions some of the most fashionable ideas in physics today, including string theory What can fashionable ideas, blind faith, or pure fantasy possibly have to do with the scientific quest to understand the universe? Surely, theoretical physicists are immune to mere trends, dogmatic beliefs, or flights of fancy? In fact, acclaimed physicist and bestselling author Roger Penrose argues that researchers working at the extreme frontiers of physics are just as susceptible to these forces as anyone else. In this provocative book, he argues that fashion, faith, and fantasy, while sometimes productive and even essential in physics, may be leading today's researchers astray in three of the field's most important areas—string theory, quantum mechanics, and cosmology. Arguing that string theory has veered away from physical reality by positing six extra hidden dimensions, Penrose cautions that the fashionable nature of a theory can cloud our judgment of its plausibility. In the case of quantum mechanics, its stunning success in explaining the atomic universe has led to an uncritical faith that it must also apply to reasonably massive objects, and Penrose responds by suggesting possible changes in quantum theory. Turning to cosmology, he argues that most of the current fantastical ideas about the origins of the universe cannot be true, but that an even wilder reality may lie behind them. Finally, Penrose describes how fashion, faith, and fantasy have ironically also shaped his own work, from twistor theory, a possible alternative to string theory that is beginning to acquire a fashionable status, to conformal cyclic cosmology, an idea so fantastic that it could be called conformal crazy cosmology. The result is an important critique of some of the most significant developments in physics today from one of its most eminent figures. |
| did we invent math or discover it: The Dimensional Philosopher's Toolkit Nathan Coppedgez, 2013-01-10 ---Not a prolegomena, a foundation.--- More descriptive than a manifesto, and deeply pioneering in its formality, this manual uses a diagrammatic method to express new theories and foundations in thought. In place of circular reasoning, it offers recursive proofs; in place of insolvability, it offers exclusive contexts; in place of linguistic deconstruction, it offers categorical deductions. It includes over three-hundred pages of interrelated methods, arguments, and tools, which promise to assist the philosopher in making logical, ethical, and systematic claims. This first published volume of the dimensional encyclopedia is something more than an encyclopedia. Its a guide to genuine philosophy. |
| did we invent math or discover it: To understand is to invent Jean Piaget, 1980 |
| did we invent math or discover it: Zero Charles Seife, 2019-11-28 A NEW YORK TIMES NOTABLE BOOK The Babylonians invented it, the Greeks banned it, the Hindus worshipped it, and the Christian Church used it to fend off heretics. Today it's a timebomb ticking in the heart of astrophysics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything. Within the concept of zero lies a philosophical and scientific history of humanity. Charles Seife's elegant and witty account takes us from Aristotle to superstring theory by way of Egyptian geometry, Kabbalism, Einstein, the Chandrasekhar limit and Stephen Hawking. Covering centuries of thought, it is a concise tour of a world of ideas, bound up in the simple notion of nothing. |
| did we invent math or discover it: الكتاب المختصر فى حساب الجبر والمقابلة Muḥammad ibn Mūsá Khuwārizmī, 1831 |
| did we invent math or discover it: Plato's Ghost Jeremy Gray, 2008-09-02 Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method—debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics. |
| did we invent math or discover it: Trick or Truth? Anthony Aguirre, Brendan Foster, Zeeya Merali, 2016-02-20 The prize-winning essays in this book address the fascinating but sometimes uncomfortable relationship between physics and mathematics. Is mathematics merely another natural science? Or is it the result of human creativity? Does physics simply wear mathematics like a costume, or is math the lifeblood of physical reality? The nineteen wide-ranging, highly imaginative and often entertaining essays are enhanced versions of the prize-winning entries to the FQXi essay competition “Trick or Truth”, which attracted over 200 submissions. The Foundational Questions Institute, FQXi, catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources. |
| did we invent math or discover it: Reciprocity Laws Franz Lemmermeyer, 2013-03-14 This book covers the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number theory and Galois theory will find detailed discussions of the reciprocity laws for quadratic, cubic, quartic, sextic and octic residues, rational reciprocity laws, and Eisensteins reciprocity law. An extensive bibliography will be of interest to readers interested in the history of reciprocity laws or in the current research in this area. |
| did we invent math or discover it: The Pythagorean Proposition Elisha Scott Loomis, 1927 |
| did we invent math or discover it: The Maths Book DK, 2019-09-05 Learn about the most important mathematical ideas, theorems, and movements in The Maths Book. Part of the fascinating Big Ideas series, this book tackles tricky topics and themes in a simple and easy to follow format. Learn about Maths in this overview guide to the subject, great for novices looking to find out more and experts wishing to refresh their knowledge alike! The Maths Book brings a fresh and vibrant take on the topic through eye-catching graphics and diagrams to immerse yourself in. This captivating book will broaden your understanding of Maths, with: - More than 85 ideas and events key to the development of mathematics - Packed with facts, charts, timelines and graphs to help explain core concepts - A visual approach to big subjects with striking illustrations and graphics throughout - Easy to follow text makes topics accessible for people at any level of understanding The Maths Book is a captivating introduction to the world's most famous theorems, mathematicians and movements, aimed at adults with an interest in the subject and students wanting to gain more of an overview. Charting the development of maths around the world from Babylon to Bletchley Park, this book explains how maths help us understand everything from patterns in nature to artificial intelligence. Your Maths Questions, Simply Explained What is an imaginary number? Can two parallel lines ever meet? How can maths help us predict the future? This engaging overview explores answers to big questions like these and how they contribute to our understanding of maths. If you thought it was difficult to learn about topics like algebra and statistics, The Maths Book presents key information in an easy to follow layout. Learn about the history of maths, from ancient ideas such as magic squares and the abacus to modern cryptography, fractals, and the final proof of Fermat's Last Theorem. The Big Ideas Series With millions of copies sold worldwide, The Maths Book is part of the award-winning Big Ideas series from DK. The series uses striking graphics along with engaging writing, making big topics easy to understand. r to understand. |
| did we invent math or discover it: Mathematics for the Nonmathematician Morris Kline, 2013-04-15 Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems. |
| did we invent math or discover it: Why? Mario Livio, 2017-07-11 Astrophysicist and author Mario Livio investigates perhaps the most human of all our characteristics—curiosity—in this “lively, expert, and definitely not dumbed-down account” (Kirkus Reviews) as he explores our innate desire to know why. Experiments demonstrate that people are more distracted when they overhear a phone conversation—where they can know only one side of the dialogue—than when they overhear two people talking and know both sides. Why does half a conversation make us more curious than a whole conversation? “Have you ever wondered why we wonder why? Mario Livio has, and he takes you on a fascinating quest to understand the origin and mechanisms of our curiosity. I thoroughly recommend it.” (Adam Riess, Nobel Prize Winner in Physics, 2011). Curiosity is not only at the heart of mystery and suspense novels, it is also essential to other creative endeavors, from painting to sculpture to music. It is the principal driver of basic scientific research. Even so, there is still no definitive scientific consensus about why we humans are so curious, or about the mechanisms in our brain that are responsible for curiosity. In the ever-fascinating Why? Livio interviewed scientists in several fields to explore the nature of curiosity. He examined the lives of two of history’s most curious geniuses, Leonardo da Vinci and Richard Feynman. He also talked to people with boundless curiosity: a superstar rock guitarist who is also an astrophysicist; an astronaut with degrees in computer science, biology, literature, and medicine. What drives these people to be curious about so many subjects? An astrophysicist who has written about mathematics, biology, and now psychology and neuroscience, Livio has firsthand knowledge of his subject which he explores in a lucid, entertaining way that will captivate anyone who is curious about curiosity. |
| did we invent math or discover it: Synopsis Palmariorum Matheseos William Jones, 1706 |
| did we invent math or discover it: Our Mathematical Universe Max Tegmark, 2014-01-07 Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians. |
| did we invent math or discover it: Incompleteness Rebecca Goldstein, 2006-01-31 An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever--Provided by publisher. |
| did we invent math or discover it: Fibonacci’s Liber Abaci Laurence Sigler, 2012-12-06 First published in 1202, Fibonacci’s Liber Abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe. This is the first translation into a modern European language, of interest not only to historians of science but also to all mathematicians and mathematics teachers interested in the origins of their methods. |
| did we invent math or discover it: The Growth of Mathematical Knowledge Emily Grosholz, Herbert Breger, 2013-04-17 Mathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. For Plato, mathematics was evidence of Being in the midst of Becoming, garden variety evidence apparent even to small children and the unphilosophical, and therefore of the highest educational significance. In the great central similes of The Republic it is the touchstone ofintelligibility for discourse, and in the Timaeus it provides in an oddly literal sense the framework of nature, insuring the intelligibility ofthe material world. For Descartes, mathematical ideas had a clarity and distinctness akin to the idea of God, as the fifth of the Meditations makes especially clear. Cartesian mathematicals are constructions as well as objects envisioned by the soul; in the Principles, the work ofthe physicist who provides a quantified account ofthe machines of nature hovers between description and constitution. For Kant, mathematics reveals the possibility of universal and necessary knowledge that is neither the logical unpacking ofconcepts nor the record of perceptual experience. In the Critique ofPure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary lawsofNewtonian mechanics. |
| did we invent math or discover it: Diophantus of Alexandria Thomas L. Heath, 1910 |
| did we invent math or discover it: The Book Of Nothing John D. Barrow, 2011-02-15 How do you begin to understand the concept of nothing? Where does it begin and where does it end? From the zeros of the mathematician to the void of the philosophers, from Shakespeare to the empty set, from the ether to the quantum vacuum, from being and nothingness to creatio ex nihilo, there is much ado about nothing at the heart of things. Recent exciting discoveries in astronomy are shown to shed new light on the nature of the vacuum and its dramatic effect upon the explanation of the Universe. This remarkable book ranges over every nook and cranny of nothingness to reveal how the human mind has had to make something of nothing in every field of human enquiry. |
| did we invent math or discover it: Einstein Denis Brian, 1997-08-21 Seit über 20 Jahren ist dies die erste umfassende Einstein-Biographie. Der anerkannte Autor Denis Brian untersucht die private, öffentliche und wissenschaftliche Seite der legendären Persönlichkeit dieses rätselhaften Mannes. Geschickt beleuchtet Brian Einsteins eigenartig-neugierigen Charakter, die Träume und Ereignisse, die den künftigen Wissenschaftler vorangetrieben haben auf seiner unglaublichen Reise zu den Gipfeln des Erfolges und weltweiter Anerkennung. Einsteins Lebenswerk veränderte schließlich die Sichtweise der Wissenschaft von der Welt, angefangen bei seinem ersten Entwurf der revolutionären Relativitätstheorie 1905 bis hin zur Entwicklung der Atombombe (und seiner umstrittenen Position als Gegner des nachfolgenden nuklearen Wettrüstens). Der Autor erforscht Einsteins überwältigendes Erbe in Gesprächen mit vielen Zeitgenossen. Auch lüftet Brian das Geheimnis der Formeln, Theorien und Experimente, damit wir ihre Bedeutung und Tragweite besser verstehen können. Mit Prägnanz und Liebe zum Detail entführt er uns in die Welt, in der Einstein arbeitete, zurückgezogen oder gemeinsam mit anderen; von seinen Assistenten wurde er verehrt und mit anderen Physikern seiner Zeit pflegte er freundschaftliche Beziehungen. (10/97) |
| did we invent math or discover it: Native American Mathematics Michael P. Closs, 2010-06-28 There is no question that native cultures in the New World exhibit many forms of mathematical development. This Native American mathematics can best be described by considering the nature of the concepts found in a variety of individual New World cultures. Unlike modern mathematics in which numbers and concepts are expressed in a universal mathematical notation, the numbers and concepts found in native cultures occur and are expressed in many distinctive ways. Native American Mathematics, edited by Michael P. Closs, is the first book to focus on mathematical development indigenous to the New World. Spanning time from the prehistoric to the present, the thirteen essays in this volume attest to the variety of mathematical development present in the Americas. The data are drawn from cultures as diverse as the Ojibway, the Inuit (Eskimo), and the Nootka in the north; the Chumash of Southern California; the Aztec and the Maya in Mesoamerica; and the Inca and Jibaro of South America. Among the strengths of this collection are this diversity and the multidisciplinary approaches employed to extract different kinds of information. The distinguished contributors include mathematicians, linguists, psychologists, anthropologists, and archaeologists. |
| did we invent math or discover it: Technology and Mathematics Sven Ove Hansson, 2018-10-24 This volume is the first extensive study of the historical and philosophical connections between technology and mathematics. Coverage includes the use of mathematics in ancient as well as modern technology, devices and machines for computation, cryptology, mathematics in technological education, the epistemology of computer-mediated proofs, and the relationship between technological and mathematical computability. The book also examines the work of such historical figures as Gottfried Wilhelm Leibniz, Charles Babbage, Ada Lovelace, and Alan Turing. |
| did we invent math or discover it: A History of Pi Petr Beckmann, 1971 Traces the history of the mathematical constant pi from the stone age through the computer age, discussing the background of the times when pi progressed, and when it did not. |
| did we invent math or discover it: The Sand-Reckoner Archimedes, 2015-09-14 THE CLASSIC WORK OF ARCHIMEDES The Sand-Reckoner Dimensio Circuli of Archimedes Translated by Thomas L. Heath (Original publication: Cambridge University Press, 1897). The Sand Reckoner is a work by Archimedes in which he set out to determine an upper bound for the number of grains of sand that fit into the universe. In order to do this, he had to estimate the size of the universe according to the contemporary model, and invent a way to talk about extremely large numbers. The work, also known in Latin as Archimedis Syracusani Arenarius and Dimensio Circuli, which is about 8 pages long in translation, is addressed to the Syracusan king Gelo II (son of Hiero II), and is probably the most accessible work of Archimedes; in some sense, it is the first research-expository paper. Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere and a cylinder, which Archimedes had requested to be placed on his tomb, representing his mathematical discoveries. Unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the first comprehensive compilation was not made until c. 530 AD by Isidore of Miletus in Byzantine Constantinople, while commentaries on the works of Archimedes written by Eutocius in the sixth century AD opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance, while the discovery in 1906 of previously unknown works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results. |
| did we invent math or discover it: Encyclopaedia Britannica Hugh Chisholm, 1910 This eleventh edition was developed during the encyclopaedia's transition from a British to an American publication. Some of its articles were written by the best-known scholars of the time and it is considered to be a landmark encyclopaedia for scholarship and literary style. |
Dissociative identity disorder - Wikipedia
Dissociative identity disorder (DID), previously known as multiple personality disorder (MPD), is …
Dissociative Identity Disorder (DID): Symptoms & Treatment
DID is a way for you to distance or detach yourself from the trauma. DID symptoms may trigger (happen …
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Dissociative Identity Disorder - StatPearls - NCBI Bookshelf
May 16, 2023 · Dissociative identity disorder (DID) is a disorder associated with severe behavioral health …
Dissociative identity disorder - Wikipedia
Dissociative identity disorder (DID), previously known as multiple personality disorder (MPD), is characterized by the presence of at least two personality states or "alters". The diagnosis is …
Dissociative Identity Disorder (DID): Symptoms & Treatment
DID is a way for you to distance or detach yourself from the trauma. DID symptoms may trigger (happen suddenly) after: Removing yourself from a stressful or traumatic environment (like …
Dissociative Identity Disorder (Multiple Personality Disorder)
Sep 21, 2021 · Dissociative identity disorder (DID) is a rare condition in which two or more distinct identities, or personality states, are present in—and alternately take control of—an individual. …
Dissociative Identity Disorder (DID): Myths vs. Facts
Jan 4, 2022 · Dissociative identity disorder (DID) comes with a lot of stigma and misunderstanding. Let's bust some common myths.
Dissociative Identity Disorder - StatPearls - NCBI Bookshelf
May 16, 2023 · Dissociative identity disorder (DID) is a disorder associated with severe behavioral health symptoms. DID was previously known as Multiple Personality Disorder until 1994. …
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Jul 7, 2023 · Dissociative identity disorder (DID), formerly known as multiple personality disorder, is a condition that involves the presence of two or more distinct identities.
DID: Types, Symptoms, Causes, Diagnosis, Treatment and More - Health
Sep 20, 2023 · Dissociative identity disorder (DID) is a psychiatric condition that occurs when a person has multiple identities that function independently.
Dissociative Identity Disorder (DID): Symptoms, Causes,
Nov 22, 2022 · Dissociative identity disorder (DID) is a rare mental health condition that is characterized by identity and reality disruption. Individuals with DID will exhibit two or more …
Dissociative Identity Disorder: Symptoms and Treatment - Healthline
Jun 29, 2018 · The most recognizable symptom of dissociative identity disorder (DID) is a person’s identity being involuntarily split between at least two distinct identities (personality …
Dissociative Identity Disorder (DID) - PsychDB
Dec 5, 2021 · Dissociative Identity Disorder (DID) (also previously known as multiple personality disorder), is a mental disorder characterized by at least two distinct and relatively enduring …
