B. Jack Copeland (ed.)
- Published in print:
- 2005
- Published Online:
- January 2008
- ISBN:
- 9780198565932
- eISBN:
- 9780191714016
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198565932.001.0001
- Subject:
- Mathematics, History of Mathematics
The mathematical genius Alan Turing (1912-1954) was one of the greatest scientists and thinkers of the 20th century. Now well known for his crucial wartime role in breaking the ENIGMA code, he was ...
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The mathematical genius Alan Turing (1912-1954) was one of the greatest scientists and thinkers of the 20th century. Now well known for his crucial wartime role in breaking the ENIGMA code, he was the first to conceive of the fundamental principle of the modern computer — the idea of controlling a computing machine's operations by means of coded instructions, stored in the machine's ‘memory’. In 1945, Turing drew up his revolutionary design for an electronic computing machine — his Automatic Computing Engine (‘ACE’). A pilot model of the ACE ran its first programme in 1950 and the production version, the ‘DEUCE’, went on to become a cornerstone of the fledgling British computer industry. The first ‘personal’ computer was based on Turing's ACE. This book describes Turing's struggle to build the modern computer. It contains first-hand accounts by Turing and by the pioneers of computing who worked with him. The book describes the hardware and software of the ACE and contains chapters describing Turing's path-breaking research in the fields of Artificial Intelligence (AI) and Artificial Life (A-Life).Less
The mathematical genius Alan Turing (1912-1954) was one of the greatest scientists and thinkers of the 20th century. Now well known for his crucial wartime role in breaking the ENIGMA code, he was the first to conceive of the fundamental principle of the modern computer — the idea of controlling a computing machine's operations by means of coded instructions, stored in the machine's ‘memory’. In 1945, Turing drew up his revolutionary design for an electronic computing machine — his Automatic Computing Engine (‘ACE’). A pilot model of the ACE ran its first programme in 1950 and the production version, the ‘DEUCE’, went on to become a cornerstone of the fledgling British computer industry. The first ‘personal’ computer was based on Turing's ACE. This book describes Turing's struggle to build the modern computer. It contains first-hand accounts by Turing and by the pioneers of computing who worked with him. The book describes the hardware and software of the ACE and contains chapters describing Turing's path-breaking research in the fields of Artificial Intelligence (AI) and Artificial Life (A-Life).
Apostolos Doxiadis and Barry Mazur (eds)
- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691149042
- eISBN:
- 9781400842681
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149042.001.0001
- Subject:
- Mathematics, History of Mathematics
This book brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. “Circles disturbed” reflect the last words of ...
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This book brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. “Circles disturbed” reflect the last words of Archimedes before he was slain by a Roman soldier—“Don't disturb my circles”—words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds—stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. This book delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of “myths of origins” in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more.Less
This book brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. “Circles disturbed” reflect the last words of Archimedes before he was slain by a Roman soldier—“Don't disturb my circles”—words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds—stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. This book delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of “myths of origins” in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more.
Robin Wilson and John J. Watkins (eds)
- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199656592
- eISBN:
- 9780191748059
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199656592.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics
The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to ...
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The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: it constitutes the first book-length survey of the history of combinatorics, and it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler’s contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th-century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections.Less
The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: it constitutes the first book-length survey of the history of combinatorics, and it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler’s contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th-century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections.
Benjamin Wardhaugh
- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198805045
- eISBN:
- 9780191843150
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805045.001.0001
- Subject:
- Mathematics, History of Mathematics
This book contains complete transcriptions, with notes, of the 133 surviving letters of Charles Hutton (1737–1823). The letters span the period 1770–1823 and are drawn from nearly thirty different ...
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This book contains complete transcriptions, with notes, of the 133 surviving letters of Charles Hutton (1737–1823). The letters span the period 1770–1823 and are drawn from nearly thirty different archives. Most have not been published before. Hutton was one of the most prominent British mathematicians of his generation. He played roles at the Royal Society, the Royal Military Academy, the Board of Longitude, the ‘philomath’ network, and elsewhere. He worked on the explosive force of gunpowder and the mean density of the earth, winning the Royal Society’s Copley Medal in 1778; he was also at the focus of a celebrated row at the Royal Society in 1784 over the place of mathematics there. He is of particular historical interest because of the variety of roles he played in British mathematics, the dexterity with which he navigated, exploited, and shaped personal and professional networks in mathematics and science, and the length and public profile of his career. Hutton corresponded nationally and internationally, and his correspondence illustrates the overlapping, intersection, and interaction of the different networks in which Hutton moved. It therefore provides new information about how Georgian mathematics was structured socially and how mathematical careers worked in that period. It provides a rare and valuable view of a mathematical culture that would substantially cease to exist when British mathematics embraced continental methods from the early nineteenth century onwards.Less
This book contains complete transcriptions, with notes, of the 133 surviving letters of Charles Hutton (1737–1823). The letters span the period 1770–1823 and are drawn from nearly thirty different archives. Most have not been published before. Hutton was one of the most prominent British mathematicians of his generation. He played roles at the Royal Society, the Royal Military Academy, the Board of Longitude, the ‘philomath’ network, and elsewhere. He worked on the explosive force of gunpowder and the mean density of the earth, winning the Royal Society’s Copley Medal in 1778; he was also at the focus of a celebrated row at the Royal Society in 1784 over the place of mathematics there. He is of particular historical interest because of the variety of roles he played in British mathematics, the dexterity with which he navigated, exploited, and shaped personal and professional networks in mathematics and science, and the length and public profile of his career. Hutton corresponded nationally and internationally, and his correspondence illustrates the overlapping, intersection, and interaction of the different networks in which Hutton moved. It therefore provides new information about how Georgian mathematics was structured socially and how mathematical careers worked in that period. It provides a rare and valuable view of a mathematical culture that would substantially cease to exist when British mathematics embraced continental methods from the early nineteenth century onwards.
Philip Beeley and Christoph J. Scriba
- Published in print:
- 2003
- Published Online:
- September 2008
- ISBN:
- 9780198510666
- eISBN:
- 9780191705892
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198510666.001.0001
- Subject:
- Mathematics, History of Mathematics
This book is the first of a six volume edition of the complete correspondence of John Wallis (1616-1703). It begins with his earliest known letters written shortly before the outbreak of the first ...
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This book is the first of a six volume edition of the complete correspondence of John Wallis (1616-1703). It begins with his earliest known letters written shortly before the outbreak of the first Civil War while he was serving as a private chaplain, and ends on the eve of the restoration of the monarchy in 1660, by which time he was already an established figure within the Republic of Letters. The period covered is thus a momentous one in Wallis's life. It witnesses his election to Savilian professor of geometry at the University of Oxford in 1649 and his subsequent rise to become one of the leading mathematicians of his day, particularly through his introduction of new arithmetical approaches to Cavalieri's method of quadratures. The correspondence reflects the full breadth of his professional activities in theology and mathematics, and provides insights not only into religious debates taking place during the revolutionary years but also into the various questions with which the mathematically-orientated scientific community was concerned. Many of the previously unpublished letters also throw light on University affairs. After his controversial election to the post of Keeper of the Archives in 1658, Wallis fought vigorously to uphold the rights of the University of Oxford whenever necessary, and to prevent as far as possible outside interference from political and religious quarters.Less
This book is the first of a six volume edition of the complete correspondence of John Wallis (1616-1703). It begins with his earliest known letters written shortly before the outbreak of the first Civil War while he was serving as a private chaplain, and ends on the eve of the restoration of the monarchy in 1660, by which time he was already an established figure within the Republic of Letters. The period covered is thus a momentous one in Wallis's life. It witnesses his election to Savilian professor of geometry at the University of Oxford in 1649 and his subsequent rise to become one of the leading mathematicians of his day, particularly through his introduction of new arithmetical approaches to Cavalieri's method of quadratures. The correspondence reflects the full breadth of his professional activities in theology and mathematics, and provides insights not only into religious debates taking place during the revolutionary years but also into the various questions with which the mathematically-orientated scientific community was concerned. Many of the previously unpublished letters also throw light on University affairs. After his controversial election to the post of Keeper of the Archives in 1658, Wallis fought vigorously to uphold the rights of the University of Oxford whenever necessary, and to prevent as far as possible outside interference from political and religious quarters.
Philip Beeley and Christoph Scriba
- Published in print:
- 2005
- Published Online:
- September 2008
- ISBN:
- 9780198566014
- eISBN:
- 9780191713996
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566014.001.0001
- Subject:
- Mathematics, History of Mathematics
This is the second book of a six volume edition of the complete correspondence of one of the leading figures in the scientific revolution of the 17th century, the Oxford mathematician and theologian ...
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This is the second book of a six volume edition of the complete correspondence of one of the leading figures in the scientific revolution of the 17th century, the Oxford mathematician and theologian John Wallis (1616–1703). It covers the period 1660 to September 1668 and thus some of the most decisive years of political and scientific reorganization in England during that century. The volume begins shortly before the restoration of the monarchy in 1660 and witnesses the emergence of the Royal Society from scientific circles, which had existed earlier in London and Oxford. Wallis's involvement in the Royal Society stretches back to its beginnings. After its official establishment, he became one of its most active members, corresponding regularly with its secretary Henry Oldenburg and attending meetings whenever he was in London. Wallis contributed extensively to contemporary scientific debate both in England and on the continent, and many of his letters to Oldenburg on mathematical and physical topics were edited and published in the journal Philosophical Transactions to this purpose. The correspondence contained in the volume, much of which is previously unpublished, throws new light on the background to the scientific revolution and on university politics during this time. As Keeper of the Archives, Wallis was often called upon to prepare papers aimed at defending the University of Oxford's ancient rights and privileges, and was also required to spend a considerable amount of his time in London. To this extent, at least his university commitments and scientific interests were able to go hand-in-hand.Less
This is the second book of a six volume edition of the complete correspondence of one of the leading figures in the scientific revolution of the 17th century, the Oxford mathematician and theologian John Wallis (1616–1703). It covers the period 1660 to September 1668 and thus some of the most decisive years of political and scientific reorganization in England during that century. The volume begins shortly before the restoration of the monarchy in 1660 and witnesses the emergence of the Royal Society from scientific circles, which had existed earlier in London and Oxford. Wallis's involvement in the Royal Society stretches back to its beginnings. After its official establishment, he became one of its most active members, corresponding regularly with its secretary Henry Oldenburg and attending meetings whenever he was in London. Wallis contributed extensively to contemporary scientific debate both in England and on the continent, and many of his letters to Oldenburg on mathematical and physical topics were edited and published in the journal Philosophical Transactions to this purpose. The correspondence contained in the volume, much of which is previously unpublished, throws new light on the background to the scientific revolution and on university politics during this time. As Keeper of the Archives, Wallis was often called upon to prepare papers aimed at defending the University of Oxford's ancient rights and privileges, and was also required to spend a considerable amount of his time in London. To this extent, at least his university commitments and scientific interests were able to go hand-in-hand.
Jacqueline A. Stedall
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198524953
- eISBN:
- 9780191711886
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198524953.001.0001
- Subject:
- Mathematics, History of Mathematics
This book provides an accessible account of the rise of algebra in England from the medieval period to the later years of the 17th century. The book includes new research and is the most detailed ...
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This book provides an accessible account of the rise of algebra in England from the medieval period to the later years of the 17th century. The book includes new research and is the most detailed study to date of early modern English algebra. In its structure and content this book builds on a much earlier history of algebra, A treatise of algebra, published in 1685 by John Wallis (Savilian Professor of Geometry at Oxford). This book both analyses Wallis' text and moves beyond it. Thus, it explores the reception and dissemination of important ideas from continental Europe up to the end of the 16th century, and the subsequent revolution in English mathematics in the 17th century. In particular, the book includes chapters on the work of Thomas Harriot, William Oughtred, John Pell, and William Brouncker, as well as of Wallis himself.Less
This book provides an accessible account of the rise of algebra in England from the medieval period to the later years of the 17th century. The book includes new research and is the most detailed study to date of early modern English algebra. In its structure and content this book builds on a much earlier history of algebra, A treatise of algebra, published in 1685 by John Wallis (Savilian Professor of Geometry at Oxford). This book both analyses Wallis' text and moves beyond it. Thus, it explores the reception and dissemination of important ideas from continental Europe up to the end of the 16th century, and the subsequent revolution in English mathematics in the 17th century. In particular, the book includes chapters on the work of Thomas Harriot, William Oughtred, John Pell, and William Brouncker, as well as of Wallis himself.
Catherine Jami
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199601400
- eISBN:
- 9780191729218
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199601400.001.0001
- Subject:
- Mathematics, History of Mathematics
This book explores how the mathematics the Jesuits brought to China was reconstructed as a branch of imperial learning so that the emperor Kangxi (r. 1662–1722) could consolidate his power over the ...
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This book explores how the mathematics the Jesuits brought to China was reconstructed as a branch of imperial learning so that the emperor Kangxi (r. 1662–1722) could consolidate his power over the most populous empire in the world. Kangxi forced a return to the use of what became known as ‘Western’ methods in official astronomy. In his middle life he studied astronomy, musical theory, and mathematics in person, with Jesuits as his teachers. In his last years he sponsored a book that was intended to compile these three disciplines, and he set several of his sons to work on this project. All this activity formed a vital part of his plan for establishing Manchu authority over the Chinese. This book sets out to explain how and why Kangxi made the sciences a tool for laying the foundations of empire, and to show how, as part of this process, mathematics was reconstructed as a branch of imperial learning.Less
This book explores how the mathematics the Jesuits brought to China was reconstructed as a branch of imperial learning so that the emperor Kangxi (r. 1662–1722) could consolidate his power over the most populous empire in the world. Kangxi forced a return to the use of what became known as ‘Western’ methods in official astronomy. In his middle life he studied astronomy, musical theory, and mathematics in person, with Jesuits as his teachers. In his last years he sponsored a book that was intended to compile these three disciplines, and he set several of his sons to work on this project. All this activity formed a vital part of his plan for establishing Manchu authority over the Chinese. This book sets out to explain how and why Kangxi made the sciences a tool for laying the foundations of empire, and to show how, as part of this process, mathematics was reconstructed as a branch of imperial learning.
Joseph Mazur
- Published in print:
- 2016
- Published Online:
- January 2018
- ISBN:
- 9780691173375
- eISBN:
- 9781400850112
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691173375.001.0001
- Subject:
- Mathematics, History of Mathematics
While all of us regularly use basic mathematical symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did ...
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While all of us regularly use basic mathematical symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? This book explains the fascinating history behind the development of our mathematical notation system. It shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, the book looks at how historians have disagreed over the origins of the number system for the past two centuries. It follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. It also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. It considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.Less
While all of us regularly use basic mathematical symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? This book explains the fascinating history behind the development of our mathematical notation system. It shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, the book looks at how historians have disagreed over the origins of the number system for the past two centuries. It follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. It also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. It considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.
Jacqueline A. Stedall
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198526025
- eISBN:
- 9780191712364
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526025.001.0001
- Subject:
- Mathematics, History of Mathematics
This book casts new light on the work of Thomas Harriot (c.1560-1621), an innovative thinker and practitioner in several branches of the mathematical sciences, including navigation, astronomy, ...
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This book casts new light on the work of Thomas Harriot (c.1560-1621), an innovative thinker and practitioner in several branches of the mathematical sciences, including navigation, astronomy, optics, geometry, and algebra. On his death Harriot left behind over 4,000 manuscript sheets, but most of his work still remains unpublished. This book focuses on 140 of those sheets, those concerned with the structure and solution of equations. The original material has been carefully ordered, translated, and annotated to provide the first complete edition of Harriot's treatise, and an extended introduction provides the reader with a lucid background to the work. Illustrations from the manuscripts provide additional interest. The appendices discuss correlations between Harriot's manuscripts and those of this contemporaries, Viète, Warner, and Torporley.Less
This book casts new light on the work of Thomas Harriot (c.1560-1621), an innovative thinker and practitioner in several branches of the mathematical sciences, including navigation, astronomy, optics, geometry, and algebra. On his death Harriot left behind over 4,000 manuscript sheets, but most of his work still remains unpublished. This book focuses on 140 of those sheets, those concerned with the structure and solution of equations. The original material has been carefully ordered, translated, and annotated to provide the first complete edition of Harriot's treatise, and an extended introduction provides the reader with a lucid background to the work. Illustrations from the manuscripts provide additional interest. The appendices discuss correlations between Harriot's manuscripts and those of this contemporaries, Viète, Warner, and Torporley.
