History of mathematics Books

Book SynopsisTrade ReviewFull of interesting ideas, insightful and thought-provoking ... A stimulating book that perhaps leaves the reader with more questions than answers. That, in case you are wondering, is intended as praise -- Tony Mann * Times Higher Education *

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Book SynopsisDoes the universe embody beautiful ideas?   Artists as well as scientists throughout human history have pondered this “beautiful question.” With Nobel laureate Frank Wilczek as your guide, embark on a voyage of related discoveries, from Plato and Pythagoras up to the present. Wilczek’s groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. This is the deep logic of the universe—and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring.   Wilczek is hardly alone among great scientists in charting his course using beauty as his compass. As he reveals in A Beautiful Question, this has been the heart of scientific pursuit from Pythagoras and the ancient belief in the music of the spheres to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentieth-century physics. Wilczek brings us right to the edge of knowledge today, where the core insights of even the craziest quantum ideas apply principles we all understand. The equations for atoms and light are almost the same ones that govern musical instruments and sound; the subatomic particles that are responsible for most of our mass are determined by simple geometric symmetries.   Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. It is a dazzling and important work from one of our best thinkers, whose humor and infectious sense of wonder animate every page. Yes: The world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.

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Book SynopsisThis book gives a remarkably fine account of the influences mathematics has exerted on the development of philosophy, the physical sciences, religion, and the arts in Western life.Trade Review"[Kline] is unfalteringly clear in explaining mathematical ideas; he is learned but not pedantic; he has historical discernment, a sympathetic social outlook and a nice sense of fun and irony.... The beauty and fascination and rare excellence of mathematics emerge from his story. It is an exciting, provocative book."--Scientific American "Still the best textbook for the history and philosophy of mathematics for undergraduate liberal arts students. Especially good for the age of the Scientific Revulution."--Janet A. Fitzgerald, Molloy College, NY

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Book SynopsisMolecular biology as a distinct scientific discipline had its origins in chemistry and physical biochemistry, gradually emerging in the period between 1930 and the elucidation of DNA in the mid 1950s. Today this field has risen to a dominant position, and with its focus on deciphering genetic structure, it has endowed scientists with unprecedented power over life. In this fascinating study, however, Lily Kay argues that molecular biology did not evolve in a random fashion but, rather, was the result of systematic efforts by key scientists and their supporting foundations to direct the development of biological research toward a preconceived vision of science and society. The author traces and analyses the conceptual roots of molecular biology and the social matrix in which it was developed, focusing on the role of leading researchers headquartered at Caltech, and on the Rockefeller Foundation''s sponsorship of the new science. The study thus explores a number of vital, sometimes controTrade Reviewthe book has the great merit to give insight in the expectation of young American scientists and in what troubles their minds! * Cellular and Molecular Biology, vol.43, no.5, July 1997 *Table of Contents1. "Social Control:" the Rockefeller Foundation's Agenda in the Human Sciences, 1913-1933 ; 2. The Technological Frontier: Southern California and the Emergence of Life Science at Caltech ; 3. Visions and Realitites: The Biology Division in the Morgan Era ; Interlude 1 - The Protein Paradigm ; 4. From Flies to Molecules: Physiological Genetics in the Morgan Era ; 5. A Convergence of Goals: From Physical Chemistry to Bio-Organic Chemistry ; 6. The Spoils of War: Immunochemistry and Serological Genetics, 1940-1945 ; 7. Microorganisms and Macromanagement: Beadle's Return to Caltech ; 8. The Molecular Empire

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Book SynopsisThis is a charming and insightful contribution to an understanding of the Science Wars between postmodernist humanism and science, driving toward a resolution of the mutual misunderstanding that has driven the controversy. It traces the root of postmodern theory to a debate on the foundations of mathematics, early in the 20th century then compares developments in mathematics to what took place in the arts and humanities, discussing issues as diverse as literary theory, arts, and artificial intelligence. This is a straight forward, easily understood presentation of what can be difficult theoretical concepts and demonstrates that a pattern of misreading mathematics can be seen on both the part of science and on the part of postmodern thinking. This is a humorous, playful yet deeply serious look at the intellectual foundations of mathematics for those in the humanities and is the perfect critical introduction to the bases of modernism and postmodernism for those in the sciences.Trade ReviewThe book makes pleasant and interesting reading. * Mathematical Reviews *Table of Contents1: Introduction 2: Around the Cartesian Circuit 2.1: Imagination 2.2: Intuition 2.3: Counting to One 3: Space Oddity and Linguistic Turn 4: Wound of Language 4.1: Being and Time Continuum 4.2: Language and Will 5: Beyond the Code 5.1: Medium of Free Becoming 5.2: Nonpresence of Identity 6: The Expired Subject 6.1: Empire of Signs 6.2: Mechanical Bride 7: The Vanishing Author 8: Say Hello to the Structure Bubble 8.1: Algebra of Language 8.2: Functionalism Chic 9: Don't Think, Look 9.1: Interpolating the Self 9.2: Language Games 9.3: Thermostats "R" Us 10: Postmodern Enigmas 10.1: Unspeakable Diffd'erance 10.2: Dysfunctionalism Chic Notes Select Bibliography Index

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Book SynopsisThe International Bureau of Weights and Measures (BIPM) is currently implementing the greatest change ever in the world''s system of weights and measures -- it is redefining the kilogram, the final artefact standard, and reorganizing the system of international units. This book tells the inside story of what led to these changes, from the events surrounding the founding of the BIPM in 1875 -- a landmark in the history of international cooperation -- to the present. It traces not only the evolution of the science, but also the story of the key individuals and events. The BIPM was the first international scientific laboratory. Founded in 1875 by the Metre Convention, its original tasks were to conserve the new international standards of the metre and the kilogram, to carry out calibrations for Member States and undertake research to advance measurement science. The book is based on the substantial archive of the BIPM which, from the very beginning, recounts the many discussions and arguments first as to whether and how such an institute should be created and in due course, how over the next one hundred and thirty years it should develop. Despite many national and personal rivalries, the institute actually created was admirably suited to its declared tasks. In the years and decades that followed, the scientific work of the small group of men who made up its first staff was of a very high order. One of the early Directors received the Nobel Prize for physics in 1920 for his discovery of invar. The international governing Board of the institute, the International Committee of Weights and Measures, has guided the institute from one charged with the conservation of the prototype artefacts to one now at the centre of world metrology and preparing for the redefinition of the last remaining artifact, the kilogram, in terms of a fixed value for one of the fundamental constants of physics, the Planck constantTable of ContentsIntroduction ; Chapter 1: The origins of the Metre Convention 1851 to 1869 ; Why? ; The need for international agreement on measurement standards ; The great Exhibition of 1851 in London ; The 1855 Paris Universal Exhibition and Statistical Congress ; The Universal Exhibition Paris 1867; a time of political tension in Europe ; The unit of length for geodesy and the original definition of the metre ; The International Conferences on Geodesy, Berlin 1864 and 1867 ; Reactions from France: the Bureau des Longitudes ; Academy of Science of Saint Petersburg ; Reaction from the Academie des Sciences ; Chapter 2: The creation of the International Metre Commission 1869 ; Creation of the Metre Commission ; The members of the French Section of the Metre Commission ; The first meetings of the French Section ; What should be the origin of the new international metre? ; The first meeting of the Metre Commission, August 1870 ; Chapter 3: The International Metre Commission, meetings of 1872/73 ; The order of things from 1869 to 1875 ; The Committee for Preparatory Research April 1872 ; The International Metre Commission September October 1872 ; Chapter 4: The casting of 1874 and the first steps in the fabrication of the new metric standards ; Great Britain decides not to join ; The problem of melting and casting platinum ; Preparations for the Conservatoire casting ; The casting of 250 kilograms of platinum-iridium on 13 May 1874: the alloy of the Conservatoire ; Approval of the Permanent Committee ; First indications that the alloy of the Conservatoire was contaminated with iron and ruthenium ; To proceed regardless ; Chapter 5: The Diplomatic Conference of the Metre 1875 ; The first sessions of the Conference ; The Special Commission ; First drafts of the Convention ; Attempts at a compromise proposal ; The opinion of the French Government ; The first vote on the proposals ; The 12 and 15 April sessions of the Diplomatic Conference ; The signing of the Metre Convention on 20 May 1875 ; Chapter 6: The creation of the BIPM and the beginning of the construction of the new metric prototypes; problems with the French Section ; The first meeting of the International Committee for Weights and Measures ; The founding members of the International Committee ; Choosing the site for the International Bureau, the Pavillon de Breteuil ; Decisions on the main instruments for the new institute ; Progress between April 1875 and April 1876; design for laboratory building ; Difficult relations between the International Committee and the French Section ; First meeting of the International Committee at the Pavillon de Breteuil; the Committee refuses the 1874 alloy ; A new railway line and improved relations with the French Section ; Chapter 7: 1879 to 1889, the first decade of scientific work at the International Bureau ; Progress with metres and instruments ; Publications, official and scientific and the library ; Elections to the International Committee ; Construction of the new prototypes, the metres ; Construction of the new prototypes, the kilograms ; More on the metres ; Good relations with the French Section ; The measurement of temperature, the 1887 hydrogen scale ; A first unsuccessful step towards electrical standards at the BIPM ; Chapter 8: New Member States and the first General Conference on Weights and Measures, 1889 ; New States join including Great Britain ; Time to call a General Conference? ; Final acts of the French Section ; The first General Conference on Weights and Measures September 1889 ; The formal adoption of the new metric prototypes ; The distribution of national prototypes ; In the end, who was right about the alloy of the Conservatoire? ; Chapter 9: The development of the scientific work at the BIPM, the General Conferences of 1895 and 1901 ; More new scientific work ; Thermometry ; The density of water ; The length of the metre in terms of the wavelength of light ; Calibrations ; Staff health problems and building repairs ; Members of the International Committee ; The toise and the Imperial Standard Yard ; The second General Conference and the BIPM pension scheme and reserve fund ; The third General Conference: the BIPM too small and fragile? ; Chapter 10: The creation of the Grands Laboratoires ; Physikalisch-Technische Reichsanstalt (PTR) ; National Physical Laboratory (NPL) ; The National Bureau of Standards (NBS) ; A French national standards laboratory? ; Chapter 11: The story of invar and the extension of the role of the International Bureau at the 6th General Conference 1921 ; The origins of the discovery of invar ; Thermal and mechanical properties of invar ; Samuel Stratton and Sir David Gill and proposals for changing the Convention ; Scientific staff of the Bureau ; The fifth General Conference and proposals for a new temperature scale ; Legal and practical metrology ; The International Bureau 1914 to 1918 ; The meeting of the International Committee in 1920 and the resignation of Foerster ; Plans to broaden the range of the Bureau's work ; The opening of the sixth General Conference 27 September 1921 ; Objections to the new role for the International Bureau ; Final conclusions of the Conference: a new Convention and broader role for the International Bureau ; Chapter 12: The 7th and 8th General Conferences 1927 and 1933, practical metrology and the Bureau during the Second World War ; The financial situation of the Bureau in the 1920s ; Results of the first verification of national prototypes of the metre presented to 7th General Conference ; What should be the standard temperature for the definition of the metre and for industrial length metrology? ; Quartz reference standards for length and proposals for a new definition of the metre ; Agreement for work on electrical standards at the International Bureau and the creation of the Consultative Committee for Electricity ; The International Temperature Scale of 1927 ; The beginning of electrical work at the International Bureau ; The move to absolute electrical units ; A Consultative Committee for Photometry and the CIE, new definition of the standard of light ; The International Committee takes an important decision related to practical metrology ; Other activities of The International Committee and international Bureau in the 1930s ; The International Bureau during the Second World War ; Scientific work during the War ; Chapter 13: The SI, absolute electrical units, the International Committee and the creation of the ionizing radiation section. ; The call for an International System of Units at the 9th General Conference 1948 ; The substitution of absolute electrical units for the 1908 International Units ; Objections on the part of the PTR ; A date for implementation of the absolute system and interruption caused by the war ; The need to act quickly ; Final decisions of the International Committee ; Final discussions on practical metrology ; New science, new prospects for units ; The International Committee after the war ; The International Bureau and its staff after the war, the Accord de Siege ; The creation of the Ionizing Radiation Section at the Bureau ; Chapter 14: The adoption of the SI, revising the Metre Convention, new definitions of the metre and second at the 11th General Conference 1960 ; The International System of Units SI ; Preparations to revise the Metre Convention ; Discussions at the 11th General Conference ; The change in definition of the Metre: arguments for and against ; Which radiation to choose? ; The new definition of the metre and the International Bureau ; Financial matters and problems of the Cold War ; The definition of the second ; The International Committee decides ; Problems with the new definition of the second ; The second redefined again in 1967 ; The development of the scientific work of the International Bureau up to 1975 ; The influence on the Bureau of national standards laboratories ; The influence of the Consultative Committees ; Laser wavelength standards at the Bureau ; Staff development at the Bureau ; Calibrations: an evolving activity at the Bureau ; The new journal, Metrologia ; Chapter 15: The mole, the speed of light and more about the Metre Convention ; The mole and chemistry ; The first attempt to bring chemistry into the affairs of the Bureau ; The 13th CGPM and its refusal to adopt the dotation ; The Centenary of the Metre Convention in 1975 ; Redefinition of the metre in terms of the speed of light ; New proposals to modify the Metre Convention ; The Direction and supervision of the International Bureau from 1975 to 2003 ; The financial situation of the BIPM from 1975 to 2003 ; The Pavillon du Mail, some difficulties with building permission ; Chapter 16: New science at the BIPM and the Recognition of National measurement Standards ; The BIPM staff in the last quarter of the 20th century ; Developments in photometry and radiometry and a new definition of the candela ; International Atomic Time and Coordinated Universal Time ; Other new science at the Bureau ; The new quantum electrical standards ; The BIPM mechanical workshop ; Chemistry at last comes to the CIPM and BIPM ; Traceability in laboratory medicine ; The International Organization for Legal Metrology ; The CIPM Mutual Recognition Arrangement for National Measurement Standards - early discussions ; First moves towards an MRA ; Regional metrology organizations ; Other pressures on national laboratories and looking to the BIPM ; First meeting of Directors of national metrology institutes and first draft of an MRA ; Quality systems and key comparison reference values ; Final agreement reached ; Chapter 17: The redefinition of the kilogram and the move towards the New SI ; The kilogram from 1889 to the present day ; Advances in science that at last make absolute units possible ; The watt balance ; Determine the mass of an atom by x-ray crystal density of silicon ; Comparing the results from the watt balance and the silicon crystal density experiments ; How and when to proceed to an actual redefinition of the kilogram ; What does it mean to fix the numerical value of a fundamental constant and how do we use it to define a unit? ; The arguments against a new definition ; Redefining the ampere, kelvin and mole ; How to formulate the new definitions ; The CIPM proposes an absolute system of units based on the fundamental constants of physics ; Epilogue: The new SI and the future role of the BIPM ; Appendix English text of the Metre Convention ; Bibliography

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Book SynopsisThe oldest known mathematical table was found in the ancient Sumerian city of Shuruppag in southern Iraq. Since then, tables have been an important feature of mathematical activity; table making and printed tabular matter are important precursors to modern computing and information processing. This book contains a series of articles summarising the technical, institutional and intellectual history of mathematical tables from earliest times until the late twentieth century. It covers mathematical tables (the most important computing aid for several hundred years until the 1960s), data tables (eg. Census tables), professional tables (eg. insurance tables), and spreadsheets - the most recent tabular innovation.The book is presented in a scholarly yet accessible way, making appropriate use of text boxes and illustrations. Each chapter has a frontispiece featuring a table along with a small illustration of the source where the table was first displayed. Most chapters have sidebars telling aTrade ReviewThe book itself is the fruit of a very good idea of the British Society for the History of Mathematics, which was to have a conference and then a book on the theme of mathematical tables, and the editors are to be congratulated on a handsome volume on the social history of mathematics. * Notes and Records of The Royal Society *Table of ContentsIntroduction ; Table and tabular formatting in Sumer, Babylonia and Assyria, 2500 BCE - 50 CE ; The making of logarithm tables ; The computation factory: de Prony's project for making tables in the 1790's ; Difference engines: from Muller to Comrie ; The 'unerring certainty of mechanical agency': machines and table making in the nineteenth century ; Table making in astronomy ; The General Registry Office and the tabulation of data, 1837 - 1939 ; Table making by committee; British table maker 1871 - 1965 ; Table making for the relief of labour ; The making of astronomical tables in H.M. Nautical Almanac Office ; The rise and rise of the spreadsheet ; Biographical Notes

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Book SynopsisThis text contains a translation of the "Nine Chapters". The "Nine Chapters" contains math problems and solutions, which fall into nine categories based on practical needs. There are methods for solving problems in areas such as land measurement, construction, agriculture, commerce, and taxation.Trade Reviewa rich compilation of attractive problems telling wonderful fairy tales full of imaginative and delightful connections * Zentralbaltt Mathematik *Table of ContentsIntroduction ; Liu Hui's Preface to his Running Commentary on the Nine Chapters ; 1. Field measurement ; 2. Millet and rice ; 3. Distribution by proportion ; 4. Short width ; 5. Construction consultations ; 6. Fair levies ; 7. Excess and deficit ; 8. Rectangular arrays ; 9. Right-angled triangles ; Appendix ; References ; Index

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Book SynopsisThis is the story behind the idea of number, from the Pythagoreans, up until the turn of the 20th century, through Greek, Islamic & European mathematics.Trade ReviewCorry has compiled a readable account of the history of mathematics focusing on numbers, although for most of the period in question, arithmetic and geometry are not easily separable. The required level of sophistication of the reader is not great, it is certainly at the level of a first-year undergraduate, or a keen sixth-former who is studying mathematics. Even as an experienced university mathematician, the reviewer learnt many interesting things, and has some misconceptions remedied, on reading Corry's Brief History. * Robin Chapman, LMS Newsletter *This fine book gives what its title promises ... a well-written treatment of the subject. * Underwood Dudley, MAA Reviews *It is a highly recommended and pleasant read, not pedantic, but not casual either ... The book is written with great care ... * Adhemar Bultheel, European Mathematical Society *A Brief History of Numbers is a meticulously researched and carefully crafted look at how mathematicians have explored the concept of number. Corry's prose is clear and engaging, and the mathematical content is uniformly accessible to his audience. ... I highly recommend A Brief History of Numbers to mathematics teachers who wish to know more about how our current edifice of natural, rational, real, complex, and infinite numbers came to be built. * James V. Rauff, Mathematics Teacher *Table of Contents1. The System of Numbers: An Overview ; 2. Writing Numbers: Now and Back Then ; 3. Numbers and Magnitudes in the Greek Mathematical Tradition ; 4. Construction Problems and Numerical Problems in the Greek Mathematical Tradition ; 5. Numbers in the Tradition of Medieval Islam ; 6. Numbers in Europe from the 12th to the 16th Centuries ; 7. Number and Equations at the Beginning of the Scientific Revolution ; 8. Number and Equations in theWorks of Descartes, Newton, and their Contemporaries ; 9. New Definitions of Complex Numbers in the Early 19th Century ; 10. "What are numbers and what should they be?" Understanding Numbers in the Late 19th Century ; 11. Exact Definitions for the Natural Numbers: Dedekind, Peano and Frege ; 12. Numbers, Sets and Infinity. A Conceptual Breakthrough at the Turn of the Twentieth Century ; 13. Epilogue: Numbers in Historical Perspective

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Book SynopsisMartin Folkes (1690-1754): Newtonian, Antiquary, Connoisseur is a cultural and intellectual biography of the only President of both the Royal Society and the Society of Antiquaries.Trade ReviewRoos's book—generously illustrated with over seventy images of portraits, medals, engravings, archival documents and other objects—brings Folkes vividly to life. * LIAM SIMS, Cambridge, UK *[Anna Marie Roos's] depth and breadth of knowledge are awe inspiring . . . This is an all-round, first-class piece of scholarship that not only introduces the reader to the little known but important figure of Martin Folkes, but because of the extensive contextual embedding provides a solid introduction to the social and cultural context in which science was practiced not only in England but throughout Europe in the first half of the eighteenth century. Highly recommended and not just for historians of science * Thony Christie, The Renaissance Mathematicus Blog *Roos is to be commended for writing the initial monograph on an unjustly neglected figure, providing thoughtful accounts of Folkes's contributions to a multitude of disciplines. * William Eisler, The Medal *Table of Contents1: Introduction 2: Nascent Newtonian, 1690-1716 3: Lucretia Bradshaw: Recovering a Wife and a Life 4: Folkes and his Social Networks in 1720s London 5: Taking Newton on Tour 6: Martin Folkes, Antiquarian 7: Martin Folkes and the Royal Society Presidency: biological sciences and vitalism 8: Martin Folkes and the Royal Society Presidency: The Electric Imagination 9: Charting a Personal and Institutional Life

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Book SynopsisThe tremendous growth of the mathematical sciences in the early modern world was reflected contemporaneously in an increasingly sophisticated level of practical mathematics in fields such as merchants'' accounts, instrument making, teaching, navigation, and gauging. In many ways, mathematics shaped the knowledge culture of the age, infiltrating workshops, dockyards, and warehouses, before extending through the factories of the Industrial Revolution to the trading companies and banks of the nineteenth century. While theoretical developments in the history of mathematics have been made the topic of numerous scholarly investigations, in many cases based around the work of key figures such as Descartes, Huygens, Leibniz, or Newton, practical mathematics, especially from the seventeenth century onwards, has been largely neglected. The present volume, comprising fifteen essays by leading authorities in the history of mathematics, seeks to fill this gap by exemplifying the richness, diversityTable of Contents1: Philip Beeley and Christopher Hollings: Introduction Part I - Navigation, Seafaring, Warfare 2: Jim Bennett: 'Mecanicall Practises Drawne from the Artes Mathematick': the Mathematical Identity of the Elizabethan Navigator John Davis 3: Margaret E. Schotte: Navigation Exams in the Early Modern Period 4: Rebekah Higgitt: Mathematical Examiners at Trinity House: Teaching and Examining Mathematics for Navigation in London During the Long Eighteenth Century 5: João Caramalho Domingues: What Mathematics for Portuguese Military Engineers? From the Class of Fortification to the Military Academy of Lisbon Part II - Professions, Societies, and Cultures of Mathematics 6: Sloan Evans Despeaux and Brigitte Stenhouse: Mathematical Men in Humble Life: Philomaths from North-west England as Editors of 'Questions for Answer' Journals 7: Benjamin Wardhaugh: Collection, Use, Dispersal: The Library of Charles Hutton and the Fate of Georgian Mathematics 8: Christopher D. Hollings: Mathematics at the Literary and Philosophical Societies 9: David R. Bellhouse: The Evolution of Actuarial Science to 1848 Part III - Mathematical Practitioners and their Scientific Milieus 10: Stefano Gulizia: Assembling the Scribal Self: Gian Vincenzo Pinelli's Circle and Mathematical Practitioners in the Veneto, c. 1580-1606 11: Philip Beeley: Mathematical Businesses: Seventeenth-Century Practitioners and their Academic Friends 12: Thomas Morel: 'All of This Was Born on Paper': The Mathematics of Tunnelling in Eighteenth-Century Metallic Mines Part IV - The Practice and Teaching of Mathematics 13: Ivo Schneider: Climbing the Social Ladder: Johannes Faulhaber's Path from Schoolmaster to Fortification Engineer 14: Albrecht Heeffer: The Difficult Relation of Surveyors with Algebra: The Hundred Mathematical Questions of Cardinael 15: Boris Jardine: The Life Mathematick: John and Euclid Speidell, and the Centrality of Instruments in Seventeenth-Century Pedagogy 16: Mark McCartney: James Thomson Senior and Mathematics at the Belfast Academical Institution, 1814-1832

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Book Synopsis''A must-read to anyone interested in the digital world.'' - Valérie Schafer, Center for Contemporary and Digital History, University of LuxembourgA concise history of the digital revolution and the lore, rhetoric, and debates that surround it.The Digital Revolution aims to tell a story, one of the most powerful ideologies of recent decades: that digitalization constitutes a revolution, a break with the past, a radical change for the human beings who are living through it. The book aims to investigate the origins of this idea, how it evolved, which other past revolutions consciously or unconsciously inspired it, which great stories it has conveyed over time, which of its key elements have changed and which ones have persisted and have been repeated in different historical periods. All these discussions, large or small, have settled and condensed into a series of media, advertising, corporate, political, and technical sources. Readers will be introduced to new, previously unpublished hiTrade ReviewOffers timely insight into a timeless preoccupation with the digital age. * Benjamin Peters, Hazel Rogers Associate Professor of Media Studies and affiliated faculty Cyber Studies, University of Tulsa *Gabriele Balbi delves into a notion whose history, actors and developments shape our digital imaginaries and practices, as well as our relationship with technology, media and innovation. A must-read to anyone interested in the digital world. * Valérie Schafer, Center for Contemporary and Digital History, University of Luxembourg *This short book is both topical and timely. * Jane Winters, Professor of Digital Humanities, School of Advanced Study, University of London *Table of ContentsIntroduction: Understanding the Digital Revolution as an Ideology 1: Defining the Revolution: Blessed Uncertainty 2: Comparing the Revolution: Past Inheritance, Present Construction 3: Thinking About the Revolution: The Mantras 4: Believing in the Revolution: A Contemporary Quasi-Religion Conclusion: Who Needs the Digital Revolution and Why Does it Keep Going?

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Book SynopsisDoes syllogistic logic have the resources to capture mathematical proof? This volume provides the first unified account of the history of attempts to answer this question, the reasoning behind the different positions taken, and their far-reaching implications. Aristotle had claimed that scientific knowledge, which includes mathematics, is provided by syllogisms of a special sort: ''scientific'' (''demonstrative'') syllogisms. In ancient Greece and in the Middle Ages, the claim that Euclid''s theorems could be recast syllogistically was accepted without further scrutiny. Nevertheless, as early as Galen, the importance of relational reasoning for mathematics had already been recognized. Further critical voices emerged in the Renaissance and the question of whether mathematical proofs could be recast syllogistically attracted more sustained attention over the following three centuries. Supported by more detailed analyses of Euclidean theorems, this led to attempts to extend logical theory to include relational reasoning, and to arguments purporting to reduce relational reasoning to a syllogistic form. Philosophical proposals to the effect that mathematical reasoning is heterogenous with respect to logical proofs were famously defended by Kant, and the implications of the debate about the adequacy of syllogistic logic for mathematics are at the very core of Kant''s account of synthetic a priori judgments. While it is now widely accepted that syllogistic logic is not sufficient to account for the logic of mathematical proof, the history and the analysis of this debate, running from Aristotle to de Morgan and beyond, is a fascinating and crucial insight into the relationship between philosophy and mathematics.Table of ContentsIntroduction 1: Aristotelian Syllogism and Mathematics in Antiquity and the Medieval Period 2: Extensions of the Syllogism in Medieval Logic 3: Syllogistic and Mathematics: The Case of Piccolomini 4: Obliquities and Mathematics in the 17th and 18th Centuries: From Jungius to Wolff 5: The Extent of Syllogistic Reasoning: From Rüdiger to Wolff 6: Lambert and Kant 7: Bernard Bolzano on Non-Syllogistic Reasoning 8: Thomas Reid, William Hamilton and Augustus De Morgan Conclusion

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Book SynopsisThe Life and Work of James Bradley: The New Foundations of 18th Century Astronomy is the first major work on the life and achievements of James Bradley for 190 years. This book offers a new perspective and new interpretations of previously published materials, together with various insights about recently researched sources.This book is a complete account of the life and work of Bradley as discerned from surviving documents of his working archive, as well as other documents and records. In addition, it offers a new interpretation of Bradley''s work as an astronomer, not merely from his observations of Jupiter and Saturn and their satellites and annual aberration and the nutation of the Earth''s axis, but also his corroborative work with pendulums and other horological work with George Graham. It also explores the little amount documented about his private life including a degree of speculation about his personal relationships.This work on 18th century astronomy is intended for studentsTable of ContentsPreface Table of contents Introduction: Contexts and connections 1: The King's observator 2: May it please your Honours 3: An ingenious young man 4: A new discovered motion 5: And yet it moves 6: The laws of nature 7: On the figure of the Earth 8: The triumph of Themistocles 9: If such a man could have enemies... 10: Observations beyond compare 11: Fundamenta Astronomiae Conclusion: The man who moved the world

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Book SynopsisFrom Ancient Greek times, music has been seen as a mathematical art, and this relationship has fascinated generations. This new in paperback edition of diverse, comprehensive and fully-illustrated papers, authored by leading scholars, links the two fields in a lucid manner that is suitable for students of each subject as well as the general reader.Trade ReviewAn attractive volume that covers almost al of the important aspects of the interplay between mathematics and music. * Ehrhard Behrends, The Mathematical Intelligencer, Vol 28, 3 *Table of ContentsPART I: MUSIC AND MATHEMATICS THROUGH HISTORY; PART II: THE MATHEMATICS OF MUSICAL SOUND; PART III: MATHEMATICAL STRUCTURE IN MUSIC; PART IV: THE COMPOSER SPEAKS

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Book SynopsisThis Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practise it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, pTrade ReviewReview from previous edition "wonderful food for thought for any practitioner" * Times Higher Education Supplement *"a splendid, something-for-everybody treasure-trove of interesting, informative, challenging, well written testaments to the variety and vigor of history of mathematics in our time" * Historia Mathematica *"Well written, well edited and well rounded... a healthy contribution to a burgeoning field of newly self-aware research." * British Journal for the History of Science *Table of ContentsINTRODUCTION; GEOGRAPHIES AND CULTURES: GLOBAL; GEOGRAPHIES AND CULTURES: REGIONAL; GEOGRAPHIES AND CULTURES: LOCAL; PEOPLE AND PRACTICES: LIVES; PEOPLE AND PRACTICES: PRACTICES; PEOPLE AND PRACTICES: PRESENTATION; INTERACTIONS AND INTERPRETATIONS: INTELLECTUAL; INTERACTIONS AND INTERPRETATIONS: MATHEMATICAL; INTERACTIONS AND INTERPRETATIONS: HISTORICAL; ABOUT THE CONTRIBUTORS; INDEX

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Book SynopsisThis is the fascinating story of two women who lives were guided by a passion for mathematics and an insatiable curiosity to know and understand the world around them -- the beautiful, outrageous Émilie du Châtelet and the charmingly subversive Mary Somerville. Against great odds, Émilie and Mary taught themselves mathematics, and did it so well that they each became a world authority on Newtonian mathematical physics.Seduced by Logic begins with Émilie du Châtelet, an 18th-century French aristocrat, intellectual, and Voltaire''s lover, whose true ambition was to be a mathematician. She strove not only to further Newton''s ideas in France, but to prove that they had French connections, including to the work of Descartes, whom Newton had read. She translated the great Principia Mathematica into French, in what became the accepted French version of Newton''s work, and was instrumental in bringing Newton''s revolutionary opus to a Continental audience. A century later, in Scotland, Mary STrade Review...timely reminder of how little things have changed since the 19th century and how much women of science can accomplish. * Wall Street Journal *Table of ContentsIntroduction ; 1 Madame Newton du Chatelet ; 2 Creating the theory of gravity: the Newtonian controversy ; 3 Learning mathematics and fighting for freedom ; 4 Emilie and Voltaire's Academy of Free Thought ; 5 Testing Newton: the'New Argonauts' ; 6 The danger in Newton: life, love and politics ; 7 The nature of light: Emilie takes on Newton ; 8 Searching for 'energy': Emilie discovers Leibniz ; 9 Mathematics and free will ; 10 The re-emergence of Madame Newton du Chatelet ; 11 Love letters to Saint-Lambert ; 12 Mourning Emilie ; 13 Mary Fairfax Somerville ; 14 The long road to fame ; 15 Mechanism of the Heavens ; 16 Mary's second book: popular science in the nineteenth century ; 17 Finding light waves: the 'Newtonian Revolution' comes of age ; 18 Mary Somerville: a fortunate life ; Epilogue: Declaring a point of view

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Book SynopsisTracing the impact of optimization and the ways in which it has influenced the study of mathematics, biology, economics, and even politics, this title reveals how the idea has driven some of our greatest intellectual breakthroughs.Trade Review"The deity of Leibniz and Maupertuis can only make action stationary; to us remains the challenge to make the world as good as possible.... We can neither evade such problems nor address them without science. Ekeland's admirable account gives us the tools to consider these important questions in greater depth." - Peter Pesic, Times Literary Supplement "A vivid picture of human history and destiny.... Ekeland moves easily from mathematics to physics, biology, ethics, and philosophy." - Freeman Dyson, New York Review of Books "[Ekeland's] explanations are clear and elegant... and his prose is fluid, exhilarating, and suspenseful. I tried to put this book down after chapter 4 but couldn't. It was as if some compelling force of nature had a purpose, an opposing directive in the best of all possible worlds." - Joseph Mazur, Nature"

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Book SynopsisThrough the prism of gender, this text explores the contrasting cultures and practice of mathematics and science and asks how they impacted on women. Claire Jones assesses nineteenth-century ideas about women's intellect, femininity and masculinity, and assesses how these attitudes shaped women's experiences as students and practitioners.Trade ReviewWinner of the Women's History Network Book Prize 2010 'This excellent, thought-provoking study will deepen the understanding of all interested in gender issues and in the conflicts in science and mathematics in this period.' - Reviews in HistoryTable of ContentsList of Illustrations Acknowledgements Introduction The 'glamour' of a 'wrangler': Women and Mathematics at Girton College, Cambridge Women at the 'Shrine of Pure Thought' Professional or Pedestal?: Hertha Ayrton, a Woman among the Engineers Collaboration, Reputation and the Business of Mathematics The Laboratory: A Suitable Place for a Woman?: Women, Masculinity and Laboratory Culture The Mathematics of Gender: Women, Participation and the Mathematical Community Bodies of Controversy: Women and the Royal Society of London Conclusion Notes Bibliography

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Book SynopsisA FINANCIAL TIMES AND TLS BOOK OF THE YEARAn exhilarating new biography of John von Neumann: the lost genius who invented our world''A sparkling book, with an intoxicating mix of pen-portraits and grand historical narrative. Above all it fizzes with a dizzying mix of deliciously vital ideas. . . A staggering achievement'' Tim HarfordThe smartphones in our pockets and computers like brains. The vagaries of game theory and evolutionary biology. Self-replicating moon bases and nuclear weapons. All bear the fingerprints of one remarkable man: John von Neumann.Born in Budapest at the turn of the century, von Neumann is one of the most influential scientists to have ever lived. His colleagues believed he had the fastest brain on the planet - bar none. He was instrumental in the Manhattan Project and helped formulate the bedrock of Cold War geopolitics and modern economic theory. He created the first ever programmable digital computer. He prophesied the potential of nanotechnology and, from his deathbed, expounded on the limits of brains and computers - and how they might be overcome.Taking us on an astonishing journey, Ananyo Bhattacharya explores how a combination of genius and unique historical circumstance allowed a single man to sweep through so many different fields of science, sparking revolutions wherever he went.Insightful and illuminating, The Man from the Future is a thrilling intellectual biography of the visionary thinker who shaped our century.

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Book SynopsisThe role of gender in making and shaping mathematicians.Trade Review'Mathematicians do their best work in their youth'; 'mathematicians work in complete isolation'; 'mathematics and politics don't mix.'These and other myths are discussed and debunked—in both theoretical and concrete terms—in the particular context of the role of women in mathematics. Henrion studies the nature of the participation of women in mathematical research and surrounding issues of gender and race by weaving her narrative around detailed profiles of nine respected women mathematicians (including two African American women). The individual biographies themselves make for enthralling, often inspiring, reading; combined with Henrion's careful, generally evenhanded, and tightly conceived commentary, this volume should be compelling reading for women mathematics students and professionals. A fine addition to the literature on women in science and, as it is written by a mathematical 'insider,' it is all the more likely to receive attention by the mathematics community. Highly recommended. Undergraduates through faculty. -- S. J. Colley * Choice *

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Book SynopsisMax 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.

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Book SynopsisIn MATH WITH BAD DRAWINGS, Ben Orlin answers math''s three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Eschewing the tired old curriculum that begins in the wading pool of addition and subtraction and progresses to the shark infested waters of calculus (AKA the Great Weed Out Course), Orlin instead shows us how to think like a mathematician by teaching us a new game of Tic-Tac-Toe, how to understand an economic crisis by rolling a pair of dice, and the mathematical reason why you should never buy a second lottery ticket. Every example in the book is illustrated with his trademark bad drawings, which convey both his humor and his message with perfect pitch and clarity. Organized by unconventional but compelling topics such as Statistics: The Fine Art of Honest Lying, Design: The Geometry of Stuff That Works, and Probability: The Mathematics of Maybe, MATH WITH BAD DRAWINGS is a perfect read for fans of illustrated popular science.

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Book SynopsisPulsing with drama and excitement, Infinitesimal celebrates the spirit of discovery, innovation, and intellectual achievement-and it will forever change the way you look at a simple line.On August 10, 1632, five men in flowing black robes convened in a somber Roman palazzo to pass judgment on a deceptively simple proposition: that a continuous line is composed of distinct and infinitely tiny parts. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrin

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Book SynopsisAny reader who aspires to be scientifically literate will find this a good starting place.-Publishers WeeklyTrade Review"More than just a celebration of the great equations…[Crease] shows how an equation not only affects science and math but also transforms the thinking of all people." -- Dick Teresi"Wry, probing, philosophically inclined." -- Charles C. Mann, author of 1491: New Revelations of the Americas Before Columbus

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Book SynopsisThe updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind s relationship with numbers, shapes, and patterns.Trade Review"... the book is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it." (Zentralblatt MATH, 2016) "... an 'engaging' read for the mathematically minded." (Inside OR, June 2011)Table of ContentsForeword by Isaac Asimov xi Preface to the Third Edition xiii Preface to the Second Edition xv Preface to the First Edition xvii 1 Traces 1 Concepts and Relationships 1 Early Number Bases 3 Number Language and Counting 5 Spatial Relationships 6 2 Ancient Egypt 8 The Era and the Sources 8 Numbers and Fractions 10 Arithmetic Operations 12 “Heap” Problems 13 Geometric Problems 14 Slope Problems 18 Arithmetic Pragmatism 19 3 Mesopotamia 21 The Era and the Sources 21 Cuneiform Writing 22 Numbers and Fractions: Sexagesimals 23 Positional Numeration 23 Sexagesimal Fractions 25 Approximations 25 Tables 26 Equations 28 Measurements: Pythagorean Triads 31 Polygonal Areas 35 Geometry as Applied Arithmetic 36 4 Hellenic Traditions 40 The Era and the Sources 40 Thales and Pythagoras 42 Numeration 52 Arithmetic and Logistic 55 Fifth-Century Athens 56 Three Classical Problems 57 Quadrature of Lunes 58 Hippias of Elis 61 Philolaus and Archytas of Tarentum 63 Incommensurability 65 Paradoxes of Zeno 67 Deductive Reasoning 70 Democritus of Abdera 72 Mathematics and the Liberal Arts 74 The Academy 74 Aristotle 88 5 Euclid of Alexandria 90 Alexandria 90 Lost Works 91 Extant Works 91 The Elements 93 6 Archimedes of Syracuse 109 The Siege of Syracuse 109 On the Equilibriums of Planes 110 On Floating Bodies 111 The Sand-Reckoner 112 Measurement of the Circle 113 On Spirals 113 Quadrature of the Parabola 115 On Conoids and Spheroids 116 On the Sphere and Cylinder 118 Book of Lemmas 120 Semiregular Solids and Trigonometry 121 The Method 122 7 Apollonius of Perge 127 Works and Tradition 127 Lost Works 128 Cycles and Epicycles 129 The Conics 130 8 Crosscurrents 142 Changing Trends 142 Eratosthenes 143 Angles and Chords 144 Ptolemy’s Almagest 149 Heron of Alexandria 156 The Decline of Greek Mathematics 159 Nicomachus of Gerasa 159 Diophantus of Alexandria 160 Pappus of Alexandria 164 The End of Alexandrian Dominance 170 Proclus of Alexandria 171 Boethius 171 Athenian Fragments 172 Byzantine Mathematicians 173 9 Ancient and Medieval China 175 The Oldest Known Texts 175 The Nine Chapters 176 Rod Numerals 177 The Abacus and Decimal Fractions 178 Values of Pi 180 Thirteenth-Century Mathematics 182 10 Ancient and Medieval India 186 Early Mathematics in India 186 The Sulbasutras 187 The Siddhantas 188 Aryabhata 189 Numerals 191 Trigonometry 193 Multiplication 194 Long Division 195 Brahmagupta 197 Indeterminate Equations 199 Bhaskara 200 Madhava and the Keralese School 202 11 The Islamic Hegemony 203 Arabic Conquests 203 The House of Wisdom 205 Al-Khwarizmi 206 ‘Abd Al-Hamid ibn-Turk 212 Thabit ibn-Qurra 213 Numerals 214 Trigonometry 216 Tenth- and Eleventh-Century Highlights 216 Omar Khayyam 218 The Parallel Postulate 220 Nasir al-Din al-Tusi 220 Al-Kashi 221 12 The Latin West 223 Introduction 223 Compendia of the Dark Ages 224 Gerbert 224 The Century of Translation 226 Abacists and Algorists 227 Fibonacci 229 Jordanus Nemorarius 232 Campanus of Novara 233 Learning in the Thirteenth Century 235 Archimedes Revived 235 Medieval Kinematics 236 Thomas Bradwardine 236 Nicole Oresme 238 The Latitude of Forms 239 Infinite Series 241 Levi ben Gerson 242 Nicholas of Cusa 243 The Decline of Medieval Learning 243 13 The European Renaissance 245 Overview 245 Regiomontanus 246 Nicolas Chuquet’s Triparty 249 Luca Pacioli’s Summa 251 German Algebras and Arithmetics 253 Cardan’s Ars Magna 255 Rafael Bombelli 260 Robert Recorde 262 Trigonometry 263 Geometry 264 Renaissance Trends 271 François Viète 273 14 Early Modern Problem Solvers 282 Accessibility of Computation 282 Decimal Fractions 283 Notation 285 Logarithms 286 Mathematical Instruments 290 Infinitesimal Methods: Stevin 296 Johannes Kepler 296 15 Analysis, Synthesis, the Infinite, and Numbers 300 Galileo’s Two New Sciences 300 Bonaventura Cavalieri 303 Evangelista Torricelli 306 Mersenne’s Communicants 308 René Descartes 309 Fermat’s Loci 320 Gregory of St. Vincent 325 The Theory of Numbers 326 Gilles Persone de Roberval 329 Girard Desargues and Projective Geometry 330 Blaise Pascal 332 Philippe de Lahire 337 Georg Mohr 338 Pietro Mengoli 338 Frans van Schooten 339 Jan de Witt 340 Johann Hudde 341 René François de Sluse 342 Christiaan Huygens 342 16 British Techniques and Continental Methods 348 John Wallis 348 James Gregory 353 Nicolaus Mercator and William Brouncker 355 Barrow’s Method of Tangents 356 Newton 358 Abraham De Moivre 372 Roger Cotes 375 James Stirling 376 Colin Maclaurin 376 Textbooks 380 Rigor and Progress 381 Leibniz 382 The Bernoulli Family 390 Tschirnhaus Transformations 398 Solid Analytic Geometry 399 Michel Rolle and Pierre Varignon 400 The Clairauts 401 Mathematics in Italy 402 The Parallel Postulate 403 Divergent Series 404 17 Euler 406 The Life of Euler 406 Notation 408 Foundation of Analysis 409 Logarithms and the Euler Identities 413 Differential Equations 414 Probability 416 The Theory of Numbers 417 Textbooks 418 Analytic Geometry 419 The Parallel Postulate: Lambert 420 18 Pre- to Postrevolutionary France 423 Men and Institutions 423 The Committee on Weights and Measures 424 D’Alembert 425 Bézout 427 Condorcet 429 Lagrange 430 Monge 433 Carnot 438 Laplace 443 Legendre 446 Aspects of Abstraction 449 Paris in the 1820s 449 Fourier 450 Cauchy 452 Diffusion 460 19 Gauss 464 Nineteenth-Century Overview 464 Gauss: Early Work 465 Number Theory 466 Reception of the Disquisitiones Arithmeticae 469 Astronomy 470 Gauss’s Middle Years 471 Differential Geometry 472 Gauss’s Later Work 473 Gauss’s Influence 474 20 Geometry 483 The School of Monge 483 Projective Geometry: Poncelet and Chasles 485 Synthetic Metric Geometry: Steiner 487 Synthetic Nonmetric Geometry: von Staudt 489 Analytic Geometry 489 Non-Euclidean Geometry 494 Riemannian Geometry 496 Spaces of Higher Dimensions 498 Felix Klein 499 Post-Riemannian Algebraic Geometry 501 21 Algebra 504 Introduction 504 British Algebra and the Operational Calculus of Functions 505 Boole and the Algebra of Logic 506 Augustus De Morgan 509 William Rowan Hamilton 510 Grassmann and Ausdehnungslehre 512 Cayley and Sylvester 515 Linear Associative Algebras 519 Algebraic Geometry 520 Algebraic and Arithmetic Integers 520 Axioms of Arithmetic 522 22 Analysis 526 Berlin and Göttingen at Midcentury 526 Riemann in Göttingen 527 Mathematical Physics in Germany 528 Mathematical Physics in English-Speaking Countries 529 Weierstrass and Students 531 The Arithmetization of Analysis 533 Dedekind 536 Cantor and Kronecker 538 Analysis in France 543 23 Twentieth-Century Legacies 548 Overview 548 Henri Poincaré 549 David Hilbert 555 Integration and Measure 564 Functional Analysis and General Topology 568 Algebra 570 Differential Geometry and Tensor Analysis 572 Probability 573 Bounds and Approximations 575 The 1930s and World War II 577 Nicolas Bourbaki 578 Homological Algebra and Category Theory 580 Algebraic Geometry 581 Logic and Computing 582 The Fields Medals 584 24 Recent Trends 586 Overview 586 The Four-Color Conjecture 587 Classification of Finite Simple Groups 591 Fermat’s Last Theorem 593 Poincaré’s Query 596 Future Outlook 599 References 601 General Bibliography 633 Index 647

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Book SynopsisStatistics have helped shape every area of science. Without the means to analyze critical data, none of the great disoveries of the past would be possible. This paperback reprint of a Wiley bestseller shows the development of these data analysis tools and the manner in which they aided technological development prior to 1750.Trade Review"...the account goes into great detail...very accessible...useful for teachers..." (Short Book Reviews, Vol 24(1), 2004)Table of Contents1. The Book and Its Relation to Other Works. 2. A Sketch of the Background in Mathematics and Natural Philosophy. 3. Early Concepts of Probability and Chance. 4. Cardano and Liber de Ludo Aleae, c. 1565. 5. The Foundation of Probability Theory by Pascal and Fermat in 1654. 6. Huygens and De Ratiociniis in Ludo Aleae, 1657. 7. John Graunt and the Observations Made upon the Bills of Mortality, 1662. 8. The Probabilistic Interpretation of Graunt's Life Table. 9. The Early History of Life Insurance Mathematics. 10. Mathematical Models and Statistical Methods in Astronomy from Hipparchus to Kepler and Galileo. 11. The Newtonian Revolution in Mathematics and Science. 12. Miscellaneous Contributions Between 1657 and 1708. 13. The Great Leap Forward, 1708 - 1718: A Survey. 14. New Solutions to Old Problems, 1708 - 1718. 15. James Bernoulli and Ars Conjectandi, 1713. 16. Bernoulli's Theorem. 17. Tests of Significance Based on the Sex Ratio at Birth and the Binomial Distribution, 1712 - 1713. 18. Montmort and the Essay d'Analyse sur les Jeux de Hazard, 1708 and 1713. 19. The Problem of Coincidences and the Compound Probability Theorem. 20. The Problems of the Duration of Play, 1708–1718. 21. Nicholas Bernoulli. 22. De Moivre and the Doctrine of Chances, 1718, 1738, and 1756. 23. The Problem of the Duration of Play and the Method of Difference Equations. 24. De Moivre's Normal Approximation to the Binomial Distribution, 1733. 25. The Insurance Mathematics of de Moivre and Simpson, 1725-1756. References. Index.

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Book SynopsisThis original anthology collects 10 of Weyl''s less-technical writings that address the broader scope and implications of mathematics. Most have been long unavailable or not previously published in book form. Subjects include logic, topology, abstract algebra, relativity theory, and reflections on the work of Weyl''s mentor, David Hilbert. 2012 edition.

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Book SynopsisThis book is at once an analytical study of one of the most important mathematical texts of antiquity, the Mathematical Collection of the fourth-century AD mathematician Pappus of Alexandria, and also an examination of the work's wider cultural setting.Trade Review'[Cuomo] takes a refreshing approach to the history of mathematics.' Journal of Roman Studies'… Cuomo does an admirable job in hopefully tempting more students and scholars from different fields to tackle these themes and, even more importantly, to cooperate and cross the lines between disciplines.' De novis libris iudiciaTable of ContentsAcknowledgements; Introduction; 1. The outside world; 2. Bees and philosophers; 3. Inclined planes and architects; 4. Altars and strange curves; 5. The inside story; Bibliography; General index; Index locorum.

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Book SynopsisThis book analyzes the historical transformation of early mathematics, from a Greek practice based on the localized solution to an Islamic practice based on the systematic approach. The transformation is accounted for in terms of changing social practices, thereby offering an alternate interpretation of the historical trajectory of mathematics.Trade Review"For the true mathematics historian, this is a fascinating exploration, perhaps different from one's previous ideas of this time period. Highly recommended." M.D. Sanford, Felician College"...engaging, provocative, and definitely worth reading and thinking about." MAA Reviews, Fernando Q. Gouvea"...recommended reading--for its thought-provoking ideas and lively writing--for those with a serious interest in the mathematics of ancient Greece and medieval Islam." - Mathematical Reviews, J.L. BerggrenTable of ContentsAcknowledgements; Introduction; 1. The problem in the world of Archimedes; 2. From Archimedes to Eutocius; 3. From Archimedes to Khayyam; Conclusion; References; Index.

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Book SynopsisThe main part of the third volume of Dr Whiteside's annotated and critical edition of all the known mathematical papers of Isaac Newton reproduces, from the original autograph, Newton's elaborate tract on infinite series and fluxions (the so-called Methodus Fluxionum), including a formerly unpublished appendix on geometrical fluxions. Ancillary documents include, in Part 1, papers on the integration of algebraic functions and, in Part 2, short texts dealing with geometry and simple harmonic motion in a cycloidal arc. Part 3 reproduces, from both manuscript versions of Newton's Lectiones Opticae and from his Waste Book, mathematical excerpts from his researches into light and the theory of lenses at this period. An appendix summarizes mathematical highlights in his contemporary correspondence.Table of ContentsPart I. Researches into Fluxions and Infinate Series: 1. Preliminary Scheme for a Treatsie on Fluxions; 2. The Tract '[De Methodis Serierum et Fluxionum]'; 3. The Quadrature of Curves Defined by Polynomials; Part II. Miscellaneous Researches: 1. The Second Book of Euclid's 'Elements' Reworked; 2. Research into the Elementary Geometry of Curved Surfaces; 3. Harmonic Motion in a Cyclodial Arc; Part III. Researches in Geometrical Optics: 1. Extracts from Newton's Lectures on Optics; 2. Miscellaneous Researches into Refraction at a Curved Interface

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Book SynopsisThis volume reproduces the texts of a number of important, yet relatively minor papers, many written during a period of Newton's life (1677â84) which has been regarded as mathematically barren except for his Lucasian lectures on algebra (which appear in Volume V). Part 1 concerns itself with his growing mastery of interpolation by finite differences, culminating in his rule for divided differences. Part 2 deals with his contemporary advances in the pure and analytical geometry of curves. Part 3 contains the extant text of two intended treatises on fluxions and infinite series: the Geometria Curvilinea (c. 1680), and his Matheseos Universalis Specimina (1684). A general introduction summarizes the sparse details of Newton's personal life during the period, one â from 1677 onwards â of almost total isolation from his contemporaries. A concluding appendix surveys highlights in his mathematical correspondence during 1674â6 with Collins, Dary, John Smith and above all Leibniz.Table of ContentsPart I. Researches in Algebra, Number Theory and Trigonometry: 1. Approaches to a General Theory of Finite Differences; 2. Problems in Elementary Number Theory; 3. Codifications of Elementary Plane and Spherical Trigonometry; 4. Miscellaneous Notes on Annuities and Algebraic Factorization; Part II. Researches in Pure and Analytical Geometry: 1. Miscellaneous Problems in Elementary Geometry; 2. Researches into the Greek 'Solid Locus'; 3. Miscellaneous Topics in Analytical Geometry; Part III. The 'Geometria Curvilinea' and 'Matheseos Universalis Specimina': 1. The 'Geometry of Curved Lines'; 2. Specimens of a Universal System of Mathematics; Appendix.

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Book SynopsisThe fifth volume of this definitive edition centres around Newton's Lucasian lectures on algebra, purportedly delivered during 1673â83, and subsequently prepared for publication under the title Arithmetica Universalis many years later. Dr Whiteside first reproduces the text of the lectures deposited by Newton in the Cambridge University Library about 1684. In these much reworked, not quite finished, professional lectiones, Newton builds upon his earlier studies of the fundamentals of algebra and its application to the theory and construction of equations, developing new techniques for the factorizing of algebraic quantities and the delimitation of bounds to the number and location of roots, with a wealth of worked arithmetical, geometrical, mechanical and astronomical problems. An historical introduction traces what is known of the background to the parent manuscript and assesses the subsequent impact of the edition prepared by Whiston about 1705 and the revised version published by NeTable of ContentsPart I. The Deposited Lucasian Lectures on Algebra (Winter 1683–1684): Introduction; 1. Preliminary notes and drafts for the 'Arithmetica'; 2. The copy deposited in the Cambridge archives; Part II. The 'Arithmeticæ Universalis Liber Primus' (1684): Introduction; Index of Names

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Book SynopsisWhen Newton left Cambridge in April 1696 to take up, at the age of 53, a new career at the London Mint, he did not entirely 'leave off Mathematicks' as he so often publicly declared. This last volume of his mathematical papers presents the extant record of the investigations which for one reason and another he pursued during the last quarter of his life. In January 1697 Newton was tempted to respond to two challenges issued by Johann Bernoulli to the international community of mathematicians, one the celebrated problem of identifying the brachistochrone; both he resolved within the space of an evening, producing an elegant construction of the cycloid which he identified to be the curve of fall in least time. In the autumn of 1703, the appearance of work on 'inverse fluxions' by George Cheyne similarly provoked him to prepare his own ten-year-old treatise De Quadratura Curvarum for publication, and more importantly to write a long introduction to it where he set down what became his besTable of ContentsPart I. Solutions to Challenge-Problems, Revisions of Earlier Researches, and General Retrospections: 1. The Twin Problems of Bernoulli's 1697 'Programma' solved; 2. The 'De Quadratura Curvarum' Revised for Publication; 3. Miscellaneous Writings on Mathematics; 4. The 'Method of [Finite] Differences'; 5. The 'De Quadratura' Amplified as an 'Analysis per Quantitates Fluentes et Earum Momenta'; 6. Proposition X of the Principa's Second Book Reworked; 7. Response to Bernoulli's Second Problem; 8. Analysis and Synthsis: Newton's Declaration of the Manner of their Application in the 'Principia'; 9. Minor Compliments to the 'Arithemetica Universalis'; Part II. Newton's Varied Efforts to Substantiate His Claims to Calculus Priority: Appendix 1; Appendix 2; Appendix 3; Appendix 4; Appendix 5; Appendix 6; Appendix 7; Appendix 8; Appendix 9; Appendix 10; Index of Names

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Book SynopsisThe bringing together, in an annotated and critical edition, of all the known mathematical papers of Isaac Newton marks a step forward in the publication of the works of this great natural philosopher. In all, there are eight volumes in this present edition. Translations of papers in Latin face the original text and notes are printed on the page-openings to which they refer, so far as possible. Each volume contains a short index of names only and an analytical table of contents; a comprehensive index to the complete work is included in Volume VIII. Volume I covers three exceptionally productive years: Newton's final year as an undergraduate at Trinity College, Cambridge, and the two following years, part of which were spent at his home in Lincolnshire on account of the closure of the university during an outbreak of bubonic plague.Table of ContentsPart I. The First Mathematical Annotations 1664–1665: 1. Annotations from Oughtred, Descartes, Schooten and Huygens; 2. Annotations from Viete and Oughtred; 3. Annotations from Wallis; Part II. Researches in Analytical Geometry and Calculus 1664–1666: 1. Early notes on Analytical Geometry; 2. Work on the Cartesian Subnormal; 3. Miscellaneous Problems in Analytical Geometry and Calculus; 4. Normals, Curvature and the Resolution of the General Problem of Tangents; 5. The Calculus Becomes an Algorithm; 6. The General Problems of Tangents, Curvature and Limit-Motion Analysed by the Method of Fluxions; 7. The October 1966 Tract of Fluxions; Part III. Miscellaneous Early Mathematical Researches 1664–1666: 1. Early Scraps in Newton's Waste Book; 2. Early Work in Trigonometry; 3. The Theory and Construction of Equations; 4. Miscellaneous Researches in Arithmetic, Number Theory and Geometry; Appendix

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Book SynopsisProbably the most celebrated controversy in all of the history of science was that between Newton and Leibniz over the invention of the calculus. Philosophers at War reveals how the dispute arose and became embittered, the dispositions of the chief actors, and the shifts in their opinions of each other.Table of ContentsPreface; Chronological outline; 1. Introduction; 2. Beginnings in Cambridge; 3. Newton states his claim: 1685; 4. Leibniz encounters Newton: 1672–1676; 5. The emergence of the calculus: 1677–1699; 6. The outbreak: 1693–1700; 7. Open warfare: 1700–1710; 8. The philosophical debate; 9. Thrust and parry: 1710–1713; 10. The dogs of war: 1713–1715; 11. War beyond death: 1715–1722; Appendix; Notes; Index.

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Book SynopsisHistorical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. First published in 1975, this edition includes an introduction that contextualizes his book in light of developing philosophical trends.Trade Review"A fascinating in-depth study of the philosophical aspects of the concept of probability during its founding days." Andreas Karlsson, Uppsala University"[Hacking's] knowledge of the pertinent literature is considerable and the vigorous style of writing makes for enjoyable reading. Hacking states that his book was not written as history: be that as it may, but anyone who is interested in the history of probability and statistics, either as a philosopher or as a statistician, will find much here to think about." A.I. Dale, Mathematical ReviewsTable of ContentsIntroduction; 1. An absent family of ideas; 2. Duality; 3. Opinion; 4. Evidence; 5. Signs; 6. The first calculations; 7. The Roannez circle; 8. The great decision; 9. The art of thinking; 10. Probability and the law; 11. Expectation; 12. Political arithmetic; 13. Annuities; 14. Equipossibility; 15. Inductive logic; 16. The art of conjecturing; 17. The first limit theorem; 18. Design; 19. Induction.

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Book SynopsisThis book analyzes the historical transformation of early mathematics, from a Greek practice based on the localized solution to an Islamic practice based on the systematic approach. The transformation is accounted for in terms of changing social practices, thereby offering an alternate interpretation of the historical trajectory of mathematics.Trade Review"For the true mathematics historian, this is a fascinating exploration, perhaps different from one's previous ideas of this time period. Highly recommended." M.D. Sanford, Felician College"...engaging, provocative, and definitely worth reading and thinking about." MAA Reviews, Fernando Q. Gouvea"...recommended reading--for its thought-provoking ideas and lively writing--for those with a serious interest in the mathematics of ancient Greece and medieval Islam." - Mathematical Reviews, J.L. BerggrenTable of ContentsAcknowledgements; Introduction; 1. The problem in the world of Archimedes; 2. From Archimedes to Eutocius; 3. From Archimedes to Khayyam; Conclusion; References; Index.

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Book SynopsisHistorical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. First published in 1975, this edition includes an introduction that contextualizes his book in light of developing philosophical trends.Trade Review"A fascinating in-depth study of the philosophical aspects of the concept of probability during its founding days." Andreas Karlsson, Uppsala University"[Hacking's] knowledge of the pertinent literature is considerable and the vigorous style of writing makes for enjoyable reading. Hacking states that his book was not written as history: be that as it may, but anyone who is interested in the history of probability and statistics, either as a philosopher or as a statistician, will find much here to think about." A.I. Dale, Mathematical ReviewsTable of ContentsIntroduction; 1. An absent family of ideas; 2. Duality; 3. Opinion; 4. Evidence; 5. Signs; 6. The first calculations; 7. The Roannez circle; 8. The great decision; 9. The art of thinking; 10. Probability and the law; 11. Expectation; 12. Political arithmetic; 13. Annuities; 14. Equipossibility; 15. Inductive logic; 16. The art of conjecturing; 17. The first limit theorem; 18. Design; 19. Induction.

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Book SynopsisIn these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past century: Brouwer, Hilbert, Bernays, Weyl, Gödel, Russell, Quine, Putnam, Wang, and Tait.Trade ReviewParsons is a much admired and highly respected philosopher of mathematics and logic, well-known for his thoughtful and careful reflections on both the great historical figures and on work of the previous century. He is also an astute commentator on the current literature, engaging the contemporary debates and offering illuminating insights about its content and direction. This volume offers a unique opportunity for those not fortunate enough to have attended classes of Parsons’s to form some idea of what such an experience would be like. -- William Demopoulos, University of Western OntarioThis is a truly superb book. Parsons is quite possibly the most distinguished writer on philosophy of mathematics now working and certainly the most careful and probing. These essays examine a rather wide range of historical opinion on mathematical matters, both with an eye to demanding more careful interpretations and formulations from important writers such as Kant or Gödel while remaining sympathetic to their overall philosophical ambitions. Parsons’s treatments are unsurpassed. -- Mark Wilson, University of Pittsburgh

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Book SynopsisSurveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. This work considers every proposed fix, each with its distinctive philosophical advantages and drawbacks.Trade ReviewCo-Winner of the 2007 Shoenfield Prize, Association for Symbolic Logic "Fixing Frege fills a serious gap in the Frege's literature (always increasing but perhaps with an excessive attention paid to semantics and the philosophy of language) and should remain for a long time a necessary reference for scholars in the field."--Ignacio Angelelli, Review of Modern LogicTable of ContentsAcknowledgments ix CHAPTER 1: Frege, Russell, and After 1 CHAPTER 2: Predicative Theories 86 CHAPTER 3: Impredicative Theories 146 Tables 215 Notes 227 References 241 Index 249

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Book SynopsisConcentrates on thirty highlights of pure and applied mathematics. This book opens by discussing the four main philosophical foundations of mathematics of the nineteenth century and ends by describing the four important open mathematical problems of the twenty-first century.Trade Review"Odifreddi's overview is of course a personal one, but it is hard to argue with either his choices or his organization. This is a perfect handle on an otherwise bewildering proliferation of ideas."--Ben Longstaff, New Scientist "Odifreddi clearly and concisely describes important 20th-century developments in pure and applied mathematics... Unlike similar volumes, this book keeps descriptions general and contains a short section on the philosophical foundations of mathematics to help non-mathematicians easily navigate the material."--Library Journal "This is an astonishingly readable, succinct, and wonderful account of twentieth-century mathematics! It is a great book for mathematics majors, students in liberal-arts courses in mathematics, and the general public. I am amazed at how easily the author has set out the achievements in a broad array of mathematical fields. The writing appears effortless."--Paul Campbell, Mathematics Magazine "Piergiogio Odifreddi's book successfully portrays the major developments in 20th century mathematics by an examination of the mathematical problems that have gained prominence during the past 100 years... [T]he literary style is such that the contents are made accessible to a very wide readership, but with no hint of oversimplification."--P.N. Ruane, MathDL "Odifreddi ... has an engaging and effective style and a knack for compact but comprehensible summaries, making his presentation seem effortless. The Mathematical Century can be dabbled in, read through, or perhaps even used as a quick reference."--Danny Yee, Danny ReviewsTable of ContentsForeword xi Acknowledgments xvii Introduction 1 CHAPTER 1: THE FOUNDATIONS 8 1.1. The 1920s: Sets 10 1.2. The 1940s: Structures 14 1.3. The 1960s: Categories 17 1.4. The 1980s: Functions 21 CHAPTER TWO: PURE MATHEMATICS 25 2.1. Mathematical Analysis: Lebesgue Measure (1902) 29 2.2. Algebra: Steinitz Classification of Fields (1910) 33 2.3. Topology: Brouwer's Fixed-Point Theorem (1910) 37 2.4. Number Theory: Gelfand Transcendental Numbers (1929) 39 2.5. Logic: Godel's Incompleteness Theorem (1931) 43 2.6. The Calculus of Variations: Douglas's Minimal Surfaces (1931) 47 2.7. Mathematical Analysis: Schwartz's Theory of Distributions (1945) 52 2.8. Differential Topology: Milnor's Exotic Structures (1956) 56 2.9. Model Theory: Robinson's Hyperreal Numbers (1961) 59 2.10. Set Theory: Cohen's Independence Theorem (1963) 63 2.11. Singularity Theory: Thom's Classification of Catastrophes (1964) 66 2.12. Algebra: Gorenstein's Classification of Finite Groups (1972) 71 2.13. Topology: Thurston's Classification of 3-Dimensional Surfaces (1982) 78 2.14. Number Theory: Wiles's Proof of Fermat's Last Theorem (1995) 82 2.15. Discrete Geometry: Hales's Solution of Kepler's Problem (1998) 87 CHAPTER THREE: APPLIED MATHEMATICS 92 3.1. Crystallography: Bieberbach's Symmetry Groups (1910) 98 3.2. Tensor Calculus: Einstein's General Theory of Relativity (1915) 104 3.3. Game Theory: Von Neumann's Minimax Theorem (1928) 108 3.4. Functional Analysis: Von Neumann's Axiomatization of Quantum Mechanics (1932) 112 3.5. Probability Theory: Kolmogorov's Axiomatization (1933) 116 3.6. Optimization Theory: Dantzig's Simplex Method (1947) 120 3.7. General Equilibrium Theory: The Arrow-Debreu Existence Theorem (1954) 122 3.8. The Theory of Formal Languages: Chomsky's Classification (1957) 125 3.9. Dynamical Systems Theory: The KAM Theorem (1962) 128 3.10. Knot Theory: Jones Invariants (1984) 132 CHAPTER FOUR: MATHEMATICS AND THE COMPUTER 139 4.1. The Theory of Algorithms: Turing's Characterization (1936) 145 4.2. Artificial Intelligence: Shannon's Analysis of the Game of Chess (1950) 148 4.3. Chaos Theory: Lorenz's Strange Attractor (1963) 151 4.4. Computer-Assisted Proofs: The Four-Color Theorem of Appel and Haken (1976) 154 4.5. Fractals: The Mandelbrot Set (1980) 159 CHAPTER FIVE: OPEN PROBLEMS 165 5.1. Arithmetic: The Perfect Numbers Problem (300 BC) 166 5.2. Complex Analysis: The Riemann Hypothesis (1859) 168 5.3. Algebraic Topology: The Poincare Conjecture (1904) 172 5.4. Complexity Theory: The P=NP Problem (1972) 176 Conclusion 181 References and Further Reading 187 Index 189

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Book SynopsisA student in class asks the math teacher: "Shouldn't minus times minus make minus?" Teachers soon convince most students that it does not. Yet the innocent question brings with it a germ of mathematical creativity. What happens if we encourage that thought, odd and ungrounded though it may seem? Few books in the field of mathematics encourage suchTrade Review"Alberto A. Martinez ... shows that the concept of negative numbers has perplexed not just young students but also quite a few notable mathematicians... The rule that minus times minus makes plus is not in fact grounded in some deep and immutable law of nature. Martinez shows that it's possible to construct a fully consistent system of arithmetic in which minus times minus makes minus. It's a wonderful vindication for the obstinate smart-aleck kid in the back of the class."--Greg Ross, American Scientist "Alberto Martinez ... has written an entire book about the fact that the product of two negative numbers is considered positive. He begins by reminding his readers that it need not be so... The book is written in a relaxed, conversational manner... It can be recommended to anyone with an interest in the way algebra was developed behind the scenes, at a time when calculus and analytic geometry were the main focus of mathematical interest."--James Case, SIAM News "[Negative Math] is very readable and the style is entertaining. Much is done through examples rather than formal proofs. The writer avoids formal mathematical logic and the more esoteric abstract algebras such as group theory."--Mathematics MagazineTable of ContentsFigures ix Chapter 1: Introduction 1 Chapter 2: The Problem 10 Chapter 3: History: Much Ado About Less than Nothing 18 The Search for Evident Meaning 36 Chapter 4: History: Meaningful and Meaningless Expressions 43 Impossible Numbers? 66 Chapter 5: History: Making Radically New Mathematics 80 From Hindsight to Creativity 104 Chapter 6: Math Is Rather Flexible 110 Sometimes -1 Is Greater than Zero 112 Traditional Complications 115 Can Minus Times Minus Be Minus? 131 Unity in Mathematics 166 Chapter 7: Making a Meaningful Math 174 Finding Meaning 175 Designing Numbers and Operations 186 Physical Mathematics? 220 Notes 235 Further Reading 249 Acknowledgments 259 Index 261

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Book SynopsisBy any measure, the Pythagorean theorem is the most famous statement in all of mathematics. In this book, the author reveals the full story of this ubiquitous geometric theorem. It shows that the theorem, although attributed to Pythagoras, was known to the Babylonians more than a thousand years earlier.Trade ReviewHonorable Mention for the 2007 Best Professional/Scholarly Book in Mathematics, Association of American Publishers "This excellent biography of the theorem is like a history of thought written in lines and circles, moving from ancient clay tablets to Einstein's blackboards... There is something intoxicating about seeing one truth revealed in so many ways. It all makes for hours of glorious mathematical distraction."--Ben Longstaff, New Scientist "[The Pythagorean Theorem] is aimed at the reader with an interest in the history of mathematics. It should also appeal to most well-educated people...It is a story based on a theme and guided by a timeline...As a popular account of important ideas and their development, the book should be read by anyone with a good education. It deserves to succeed."--Peter M. Neumann, Times Higher Education Supplement "Based on this recent book, Maor just keeps getting better. Already recognized for his excellent books on infinity, the number e, and trigonometry, Maor offers this new work as a comprehensive overview of the Pythagorean Theorem...If one has never read a book by Eli Maor, this book is a great place to start."--J. Johnson, Choice "Maor expertly tells the story of how this simple theorem known to schoolchildren is part and parcel of much of mathematics itself... Even mathematically savvy readers will gain insights into the inner workings and beauty of mathematics."--Amy Shell-Gellasch, MAA Reviews "Maor's book is a concise history of the Pythagorean theorem, including the mathematicians, cultures, and people influenced by it. The work is well written and supported by several proofs and exampled from Chinese, Arabic, and European sources the document how these unique cultures came to understand and apply the Pythagorean theorem. [The book] provides thoughtful commentary on the historical connections this fascinating theorem has to many cultures and people."--Michael C. Fish, Mathematics Teacher "This book will make for good supplementary reading for high school students, high school teachers, and those with a general interest in mathematics... The author's enthusiasm for his subject is evident throughout the book."--James J. Tattersull, Mathematical Reviews "This book goes beyond the theorem and its proofs to set it beautifully in the context of its time and subsequent history."--Eric S. Rosenthal, Mathematics Magazine "This is an excellent book on the history of the Pythagorean Theorem... This book is suitable to any student who has basic knowledge of calculus but the layperson will also find it interesting... Maor has an exceptional method of writing very technical mathematics in a seamlessly way."--Kuldeep, Mathematics and My Diary "All in all, this affordable book, as with Maor's previous titles, is rollicking good fun and highly recommended to anyone with even the slightest interest in the history of mathematics."--Francis A, Grabowski, European Legacy "The Pythagorean Theorem is rich in information, careful in its presentation, and at times personal in its approach... The variety of its topics and the engaging way they are presented make The Pythagorean Theorem a pleasure to read."--Cecil Rousseau, College Math JournalTable of ContentsList of Color Plates ix Preface xi Prologue: Cambridge, England, 1993 1 Chapter 1: Mesopotamia, 1800 bce 4 Sidebar 1: Did the Egyptians Know It? 13 Chapter 2: Pythagoras 17 Chapter 3: Euclid's Elements 32 Sidebar 2: The Pythagorean Theorem in Art, Poetry, and Prose 45 Chapter 4: Archimedes 50 Chapter 5: Translators and Commentators, 500-1500 ce 57 Chapter 6: Francois Viete Makes History 76 Chapter 7: From the Infinite to the Infinitesimal 82 Sidebar 3: A Remarkable Formula by Euler 94 Chapter 8: 371 Proofs, and Then Some 98 Sidebar 4: The Folding Bag 115 Sidebar 5: Einstein Meets Pythagoras 117 Sidebar 6: A Most Unusual Proof 119 Chapter 9: A Theme and Variations 123 Sidebar 7: A Pythagorean Curiosity 140 Sidebar 8: A Case of Overuse 142 Chapter 10: Strange Coordinates 145 Chapter 11: Notation, Notation, Notation 158 Chapter 12: From Flat Space to Curved Spacetime 168 Sidebar 9: A Case of Misuse 177 Chapter 13: Prelude to Relativity 181 Chapter 14: From Bern to Berlin, 1905-1915 188 Sidebar 10: Four Pythagorean Brainteasers 197 Chapter 15: But Is It Universal? 201 Chapter 16: Afterthoughts 208 Epilogue: Samos, 2005 213 Appendixes A. How did the Babylonians Approximate? 219 B. Pythagorean Triples 221 C. Sums of Two Squares 223 D. A Proof that is Irrational 227 E. Archimedes' Formula for Circumscribing Polygons 229 F. Proof of some Formulas from Chapter 7 231 G. Deriving the Equation x2/3 ??y2/3 ??1 235 H. Solutions to Brainteasers 237 Chronology 241 Bibliography 247 Illustrations Credits 251 Index 253

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