Telling the Life of a Mathematician: the Case of J.J. Sylvester
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The Cambridge Mathematical Journal and Its Descendants: the Linchpin of a Research Community in the Early and Mid-Victorian Age ✩
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Historia Mathematica 31 (2004) 455–497 www.elsevier.com/locate/hm The Cambridge Mathematical Journal and its descendants: the linchpin of a research community in the early and mid-Victorian Age ✩ Tony Crilly ∗ Middlesex University Business School, Hendon, London NW4 4BT, UK Received 29 October 2002; revised 12 November 2003; accepted 8 March 2004 Abstract The Cambridge Mathematical Journal and its successors, the Cambridge and Dublin Mathematical Journal,and the Quarterly Journal of Pure and Applied Mathematics, were a vital link in the establishment of a research ethos in British mathematics in the period 1837–1870. From the beginning, the tension between academic objectives and economic viability shaped the often precarious existence of this line of communication between practitioners. Utilizing archival material, this paper presents episodes in the setting up and maintenance of these journals during their formative years. 2004 Elsevier Inc. All rights reserved. Résumé Dans la période 1837–1870, le Cambridge Mathematical Journal et les revues qui lui ont succédé, le Cambridge and Dublin Mathematical Journal et le Quarterly Journal of Pure and Applied Mathematics, ont joué un rôle essentiel pour promouvoir une culture de recherche dans les mathématiques britanniques. Dès le début, la tension entre les objectifs intellectuels et la rentabilité économique marqua l’existence, souvent précaire, de ce moyen de communication entre professionnels. Sur la base de documents d’archives, cet article présente les épisodes importants dans la création et l’existence de ces revues. 2004 Elsevier Inc. -
James Joseph Sylvester1
Chapter 8 JAMES JOSEPH SYLVESTER1 (1814-1897) James Joseph Sylvester was born in London, on the 3d of September, 1814. He was by descent a Jew. His father was Abraham Joseph Sylvester, and the future mathematician was the youngest but one of seven children. He received his elementary education at two private schools in London, and his secondary education at the Royal Institution in Liverpool. At the age of twenty he entered St. John’s College, Cambridge; and in the tripos examination he came out sec- ond wrangler. The senior wrangler of the year did not rise to any eminence; the fourth wrangler was George Green, celebrated for his contributions to mathe- matical physics; the fifth wrangler was Duncan F. Gregory, who subsequently wrote on the foundations of algebra. On account of his religion Sylvester could not sign the thirty-nine articles of the Church of England; and as a consequence he could neither receive the degree of Bachelor of Arts nor compete for the Smith’s prizes, and as a further consequence he was not eligible for a fellowship. To obtain a degree he turned to the University of Dublin. After the theological tests for degrees had been abolished at the Universities of Oxford and Cam- bridge in 1872, the University of Cambridge granted him his well-earned degree of Bachelor of Arts and also that of Master of Arts. On leaving Cambridge he at once commenced to write papers, and these were at first on applied mathematics. His first paper was entitled “An analytical development of Fresnel’s optical theory of crystals,” which was published in the Philosophical Magazine. -
From Arthur Cayley Via Felix Klein, Sophus Lie, Wilhelm Killing, Elie Cartan, Emmy Noether and Superstrings to Cantorian Space–Time
Available online at www.sciencedirect.com Chaos, Solitons and Fractals 37 (2008) 1279–1288 www.elsevier.com/locate/chaos From Arthur Cayley via Felix Klein, Sophus Lie, Wilhelm Killing, Elie Cartan, Emmy Noether and superstrings to Cantorian space–time L. Marek-Crnjac Institute of Mathematics, Physics and Mechanics, Jadranska ulica 19, P.O. Box 2964, SI-1001 Ljubljana, Slovenia Abstract In this work we present a historical overview of mathematical discoveries which lead to fundamental developments in super string theory, super gravity and finally to E-infinity Cantorian space–time theory. Cantorian space–time is a hierarchical fractal-like semi manifold with formally infinity many dimensions but a finite expectation number for these dimensions. The idea of hierarchy and self-similarity in science was first entertain by Right in the 18th century, later on the idea was repeated by Swedenborg and Charlier. Interestingly, the work of Mohamed El Naschie and his two contra parts Ord and Nottale was done independently without any knowledge of the above starting from non- linear dynamics and fractals. Ó 2008 Published by Elsevier Ltd. 1. Introduction Many of the profound mathematical discovery and dare I say also inventions which were made by the mathemati- cians Arthur Cayley, Felix Klein, Sophus Lie, Wilhelm Killing, Elie Cartan and Emmy Noether [1] are extremely important for high energy particles in general [2] as well as in the development of E-infinity, Cantorian space–time the- ory [3,4]. The present paper is dedicated to the historical background of this subject. 2. Arthur Cayley – beginner of the group theory in the modern way Arthur Cayley was a great British mathematician. -
LMS – EPSRC Durham Symposium
LMS – EPSRC Durham Symposium Anthony Byrne Grants and Membership Administrator 12th July 2016, Durham The work of the LMS for mathematics The charitable aims of the Society: Funding the advancement of mathematical knowledge Encouraging mathematical research and collaboration ’, George Legendre Celebrating mathematical 30 Pieces achievements Publishing and disseminating mathematical knowledge Advancing and promoting mathematics The attendees of the Young Researchers in Mathematics Conference 2015, held at Oxford Historical Moments of the London Mathematical Society 1865 Foundation of LMS at University College London George Campbell De Morgan organised the first meeting, and his father, Augustus De Morgan became the 1st President 1865 First minute book list of the 27 original members 1866 LMS moves to Old Burlington House, Piccadilly J.J. Sylvester, 2nd President of the Society. 1866 Julius Plûcker Thomas Hirst Plûcker Collection of boxwood models of quartic surfaces given to Thomas Archer Hirst, Vice- President of LMS, and donated to the Society 1870 Move to Asiatic Society, 22 Albemarle Street William Spottiswoode, President 1874 Donation of £1,000 from John William Strutt (Lord Rayleigh) Generous donation enabled the Society to publish volumes of the Proceedings of the London Mathematical Society. J.W. Strutt (Lord Rayleigh), LMS President 1876-78 1881 First women members Charlotte Angas Scott and Christine Ladd 1884 First De Morgan medal awarded to Arthur Cayley 1885 Sophie Bryant First woman to have a paper published in LMS Proceedings 1916 Return to Burlington House the home of LMS until 1998 1937 ACE ’s Automatic Turing LMS Proceedings, 1937 Computing Engine, published Alan Turing’s first paper 1950 On Computable Numbers 1947 Death of G.H. -
Arthur Cayley English Version
ARTHUR CAYLEY (August 16, 1821 – January 26, 1895) by HEINZ KLAUS STRICK, Germany Born in Richmond (Surrey), ARTHUR CAYLEY, the son of the English merchant HENRY CAYLEY, initially grew up in St Petersburg, Russia. When the family returned to England, he attended King's College in London. He entered Trinity College, Cambridge University at 17, graduated in mathematics at the age of 21 (as senior wrangler) and won the Smith's Prize, an award for students who have shown exceptional performance throughout their studies. During his studies, he published three articles in the Cambridge Mathematical Journal. In the two years after the bachelor's degree, during which he supervised new students as a tutor, there were another 28 contributions. After passing his master's degree, he decided to become a lawyer in order to earn a better living. In the following five years he worked for a well-known London notary before he was admitted to the bar in 1849. During this time he met JAMES JOSEPH SYLVESTER, who had the same interests as him. The two became friends; their conversations were always and almost exclusively about mathematical topics. CAYLEY worked as a lawyer for 14 years – and published over 250 scientific papers during this time, before he was appointed to the SADLEIRian Chair, a chair for pure mathematics at the University of Cambridge, in 1863. Although he now had only a fraction of the income he previously had as a lawyer, he was happy with the work he was able to do until his death in 1895. In total, he published 967 articles that dealt with topics from all current research areas of mathematics, and including one textbook (on JACOBI's elliptical functions). -
Math Horizons Math Horizons
"Searching for the 'true tree' for twenty species is like trying to find a needle in very large haystack. Yet biologists are now routinely attempting to build trees with hundreds and sometimes thousands of species." Mathematical Aspects of the'Tree of Life' Charles Semple and Mike Steel University of Canterbury, New Zealand rees have long been used for illustrating certain phe- nomena in nature. They describe the structure of braid- Ted rivers, classify acyclic hydrocarbons in chemistry, and model the growth of cell division in physiology. In evolu- tionary biology, trees describe how species evolved from a common ancestor. Evolutionary trees date back (at least) to Charles Darwin, who made an early sketch of one in a note- book from 1837, more than 20 years before his Origin of Species. In Darwin's day, the main evidence available for reconstructing such trees, apart from some fossils, was mor- phology and physiology- the physical details of different species (does an animal have wings or not, how many petals does a plant have, and so forth). As Darwin wrote in 1872: We possess no pedigrees or amorial bearings; and we have to discover and trace the many diverging lines of descent in our natural genealogies, by characters ofany kind which have long been inherited. A phylogenetic (evolutionary) tree of 42 representative mammals The problem with morphological and fossil data is that they reconstructed using a Bayesian approach by concatenating 12 pro- are patchy, and can be misleading. Also the evolution of mor- tein coding mitochondrial genes. The main mammalian groups are phological characters is often compleX: tind difficult to model. -
The Legacy of Felix Klein
The Legacy of Thematic Afternoon Felix Klein The Legacy of Felix Klein The Legacy of The legacy of Felix Klein Felix Klein First Hour: Panel (15.00–16.00 h) 1. Introduction: What is and what could be the legacy of Felix Klein? Hans-Georg Weigand (Würzburg, GER) 2. Felix Klein - Biographical Notes Renate Tobies (Jena, GER): 3. Introduction to the Two Hour Session (16.30–18.30 h): • Strand A: Functional thinking Bill McCallum (Arizona, USA). • Strand B: Intuitive thinking and visualization Michael Neubrand (Oldenburg, GER). • Strand C: Elementary Mathematics from a higher standpoint Marta Menghini (Rome, IT) & Gert Schubring (Bielefeld, GER). 1 The Legacy of The legacy of Felix Klein Felix Klein First Hour: Panel (15.00–16.00 h) 1. Introduction: What is and what could be the legacy of Felix Klein? Hans-Georg Weigand (Würzburg, GER) 2. Felix Klein - Biographical Notes Renate Tobies (Jena, GER): 3. Introduction to the Two Hour Session (16.30–18.30 h): • Strand A: Functional thinking Bill McCallum (Arizona, USA). • Strand B: Intuitive thinking and visualization Michael Neubrand (Oldenburg, GER). • Strand C: Elementary Mathematics from a higher standpoint Marta Menghini (Rome, IT) & Gert Schubring (Bielefeld, GER). The Legacy of The legacy of Felix Klein Felix Klein First Hour: Panel (15.00–16.00 h) 1. Introduction: What is and what could be the legacy of Felix Klein? Hans-Georg Weigand (Würzburg, GER) 2. Felix Klein - Biographical Notes Renate Tobies (Jena, GER): 3. Introduction to the Two Hour Session (16.30–18.30 h): • Strand A: Functional thinking Bill McCallum (Arizona, USA). -
Full History of The
London Mathematical Society Historical Overview Taken from the Introduction to The Book of Presidents 1865-1965 ADRIAN RICE The London Mathematical Society (LMS) is the primary learned society for mathematics in Britain today. It was founded in 1865 for the promotion and extension of mathematical knowledge, and in the 140 years since its foundation this objective has remained unaltered. However, the ways in which it has been attained, and indeed the Society itself, have changed considerably during this time. In the beginning, there were just nine meetings per year, twenty-seven members and a handful of papers printed in the slim first volume of the ’s Society Proceedings. Today, with a worldwide membership in excess of two thousand, the LMS is responsible for numerous books, journals, monographs, lecture notes, and a whole range of meetings, conferences, lectures and symposia. The Society continues to uphold its original remit, but via an increasing variety of activities, ranging from advising the government on higher education, to providing financial support for a wide variety of mathematically-related pursuits. At the head of the Society there is, and always has been, a President, who is elected annually and who may serve up to two years consecutively. As befits a prestigious national organization, these Presidents have often been famous mathematicians, well known and respected by the mathematical community of their day; they include Cayley and Sylvester, Kelvin and Rayleigh, Hardy and Littlewood, Atiyah and Zeeman.1 But among the names on the presidential role of honour are many people who are perhaps not quite so famous today, ’t have theorems named after them, and who are largely forgotten by the majority of who don modern-day mathematicians. -
Arthur Cayley1
Chapter 5 ARTHUR CAYLEY1 (1821-1895) Arthur Cayley was born at Richmond in Surrey, England, on August 16, 1821. His father, Henry Cayley, was descended from an ancient Yorkshire family, but had settled in St. Petersburg, Russia, as a merchant. His mother was Maria Antonia Doughty, a daughter of William Doughty; who, according to some writers, was a Russian; but her father’s name indicates an English origin. Arthur spent the first eight years of his life in St. Petersburg. In 1829 his parents took up their permanent abode at Blackheath, near London; and Arthur was sent to a private school. He early showed great liking for, and aptitude in, numerical calculations. At the age of 14 he was sent to King’s College School, London; the master of which, having observed indications of mathematical genius, advised the father to educate his son, not for his own business, as he had at first intended, but to enter the University of Cambridge. At the unusually early age of 17 Cayley began residence at Trinity College, Cambridge. As an undergraduate he had generally the reputation of being a mere mathematician; his chief diversion was novel-reading. He was also fond of travelling and mountain climbing, and was a member of the Alpine Club. The cause of the Analytical Society had now triumphed, and the Cambridge Mathematical Journal had been instituted by Gregory and Leslie Ellis. To this journal, at the age of twenty, Cayley contributed three papers, on subjects which had been suggested by reading the M´ecanique analytique of Lagrange and some of the works of Laplace. -
View This Volume's Front and Back Matter
Titles in This Series Volume 8 Kare n Hunger Parshall and David £. Rowe The emergenc e o f th e America n mathematica l researc h community , 1876-1900: J . J. Sylvester, Felix Klein, and E. H. Moore 1994 7 Hen k J. M. Bos Lectures in the history of mathematic s 1993 6 Smilk a Zdravkovska and Peter L. Duren, Editors Golden years of Moscow mathematic s 1993 5 Georg e W. Mackey The scop e an d histor y o f commutativ e an d noncommutativ e harmoni c analysis 1992 4 Charle s W. McArthur Operations analysis in the U.S. Army Eighth Air Force in World War II 1990 3 Pete r L. Duren, editor, et al. A century of mathematics in America, part III 1989 2 Pete r L. Duren, editor, et al. A century of mathematics in America, part II 1989 1 Pete r L. Duren, editor, et al. A century of mathematics in America, part I 1988 This page intentionally left blank https://doi.org/10.1090/hmath/008 History of Mathematics Volume 8 The Emergence o f the American Mathematical Research Community, 1876-1900: J . J. Sylvester, Felix Klein, and E. H. Moor e Karen Hunger Parshall David E. Rowe American Mathematical Societ y London Mathematical Societ y 1991 Mathematics Subject Classification. Primary 01A55 , 01A72, 01A73; Secondary 01A60 , 01A74, 01A80. Photographs o n th e cove r ar e (clockwis e fro m right ) th e Gottinge n Mathematisch e Ges - selschafft, Feli x Klein, J. J. Sylvester, and E. H. Moore. -
Unpublished Letters of James Joseph Sylvester and Other New Information Concerning His Life and Work Author(S): Raymond Clare Archibald Source: Osiris, Vol
Unpublished Letters of James Joseph Sylvester and Other New Information concerning His Life and Work Author(s): Raymond Clare Archibald Source: Osiris, Vol. 1 (Jan., 1936), pp. 85-154 Published by: The University of Chicago Press on behalf of The History of Science Society Stable URL: http://www.jstor.org/stable/301603 . Accessed: 06/03/2014 07:56 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The University of Chicago Press and The History of Science Society are collaborating with JSTOR to digitize, preserve and extend access to Osiris. http://www.jstor.org This content downloaded from 159.237.12.82 on Thu, 6 Mar 2014 07:56:26 AM All use subject to JSTOR Terms and Conditions UnpublishedLetters of JamesJoseph Sylvesterand othernew Information concerninghis Life and Work CONTENTS 1. - Introductory. II. -Curriculum Vitae. III. Publications dealing with SYLVEsTER'sLife and Work. IV. SyLv1EsTER'sFirst Mathematical Publication. V. -SYLvESTER and the Universityof Virginia. VI. SYLVESTER, i842-I855. VII. SYLVEsTER'S Poetry. VIII. Letters of SyLvEsTER. I. - INTRODUCTORY In yesteryearsthere were two gloriously inspiring centers of mathematical study in America. One of these was at -the University of Chicago, when BOLZA, and MASCHKE and E. -
Triangulating the Contributions of George Salmon to Victorian Disputes on Mathematics, Evolution, and Liberal Theology K
Nineteenth-Century Contexts Vol. 31, No. 3, September 2009, pp. 251–269 Triangulating the Contributions of George Salmon to Victorian Disputes on Mathematics, Evolution, and Liberal Theology K. G. Valente Department of Mathematics, Colgate University, Hamilton, NY, USA GivenTaylorGNCC_A_418389.sgm10.1080/08905490903182162Nineteenth-Century0890-5495Original20090000000002009Drkvalente@mail.colgate.edu K. G.Valente and& Article Francis (print)/1477-2663Francis Contexts (online) the intellectual potential represented by interdisciplinary investigations, it is disheartening to note the lack of scholarly attention paid to examining a conspicuous intersection of themes: the reception of Darwinism, the promotion of non-Euclidean geometry, and the contentious implications both engendered for religious belief. It would be unusual to find a Victorianist who could not claim some degree of familiarity with Darwinism and its reception; indeed, a wealth of literature attests to the profound nexus of cultural concerns embracing evolution and theology. Yet an essential, if gener- ally acknowledged, dimension of this discourse is typically overlooked: mathematical debates over the necessary truths of geometry have fundamental relationships with better-known disputes between science and religion. Questioning the primacy of Euclidean geometry directly threatened the notion of absolute truth and precipitated a paradigmatic dilemma as unsettling as any attending the dissemination of evolutionary theories. Furthermore, Victorians representing various ideological constituencies adopted diverse strategies in responding to the spiritual challenges emanating from Darwin’s terrestrial observations as well as deliberations on the transcendental nature of geometric reasoning. In this essay I emphasize the analytic potential of a framework that integrates mathematical discourses and more familiar post-Darwinian debates by adopting such in order to establish a definite location for the intellectual legacy of George Salmon (1819–1904).