Jeremy Gray

Bio: Jeremy Gray is an academic researcher from Open University. The author has contributed to research in topics: Non-Euclidean geometry & Riemann hypothesis. The author has an hindex of 22, co-authored 160 publications receiving 1921 citations. Previous affiliations of Jeremy Gray include University of Warwick.

Linear Differential Equations and Group Theory from Riemann to Poincare

Abstract: Hypergeometric equations and modular equations - Euler and Gauss, Jacobi and Kummer, Riemann's approach to complex analysis, Riemann's P-function, interlude -Cauchy's theory of differential equations Lazarus Fuchs - Fuchs's theory of linear equations, generalisation of the hypergeometric equation, conclusion, the new methods of Frobenius and other algebraic solutions to a differential equation -Scharz, generalisations, Klein and Gordan, the solutions of Gordan and Fuchs, Jordan's solution, equations of higher order modular equations - Fuchs and Hermite, Dedekind, Galois theory, groups and fields, the Galois theory of module equations, c.1858, Klein some algebraic curves - algebraic curves, particularly quartics, function-theoretic geometry, Klein automorphic functions - Lame's equation, Poincare, Klein, 1881, Klein's response, Poincare's papers of 1883 and 1884. Appendices: Riemann, Schottky, and Schwarz on conformal representation Riemann's lectures and the Riemann-Hilbert problem Fuchs's analysis of the nth order equation on the history of non-Euclidean geometry the uniformisation theorem Picard-Vessiot theory the hypergeometric equation in several variables - Appell and Picard. Notes on chapters and appendices. Bibliography.

Plato's Ghost: The Modernist Transformation of Mathematics

Abstract: This book presents the development of mathematics between 1880 and 1920 as a modernist transformation similar to those in art, literature, and music. It is the first to trace the growth of mathematical modernism from its roots in explicit mathematical practice – problem solving and theory building – down to the foundations of mathematics and out to its interactions with physics, philosophy, and theology, the popularisation of mathematics, psychology, and ideas about real and artificial languages. It shows that modernism succeeded in mathematics because it connected fruitfully with what mathematicians were doing and with the image they were creating for themselves as an autonomous body of professionals, but also that it steadily raised the stakes by forcing deeper and ultimately unanswerable questions onto the agenda. Novel objects, definitions, and proofs in mathematics coming from the use of naive set theory and the revived axiomatic method animated debates that spilled over into contemporary arguments in philosophy, and drove an upsurge of popular writing on mathematics and the psychology of learning mathematics. A final chapter looks at mathematics after the First World War: the so-called Foundational crisis, the mechanisation of thought, and mathematical Platonism. Prominent figures in these debates who are seen here for the first time in a broad web of influences include, among the mathematicians, Borel, Dedekind, du Bois-Reymond, Enriques, Hilbert, Holder, Klein, Kronecker, Lebesgue, Minkowski, Peano, and Poincare, as well as Helmholtz, Hertz, Maxwell, and the neglected but important figures of Paul Carus and Wilhelm Wundt.

Ideas of space : Euclidean, non-Euclidean, and relativistic

Abstract: PART I: Early geometry Euclidean geometry and the parallel postulate Investigations by Islamic mathematicians. PART II: Saccheri and his Western Predecessors J H Lambert's work Legendre's work Gauss' contribution Trigonometry the first new geometries the discoveries of Lobachevskii and Bolyai Curves and surfaces Riemann on the foundations of geometry Beltrami's ideas New models and old arguments Resume. PART III: Non-Euclidean mechanics The question of absolute space Space, time and space-time Paradoxes of special relativity Gravitation and non-Euclidean geometry Speculations Some last thoughts.

The history of mathematics : a reader

Abstract: In 1922 Barnes Wallis, who later invented the bouncing bomb immortalized in the movie The Dam Busters, fell in love for the first and last time, aged 35. The object of his affection, Molly Bloxam, was 17 and setting off to study science at University College London. Her father decreed that the two could correspond only if Barnes taught Molly mathematics in his letters. Mathematics with Love presents, for the first time, the result of this curious dictat: a series of witty, tender and totally accessible introductions to calculus, trigonometry and electrostatic induction that remarkably, wooed and won the girl. Deftly narrated by Barnes and Molly's daughter Mary, Mathematics with Love is an evocative tale of a twenties courtship, a surprising insight into the early life of a World War Two hero, and a great way to learn a little mathematics.

A Complete Bibliography of Publications in Isis, 2000{2009

Abstract: accademiche [38]. Ada [45]. Adrian [45]. African [56]. Age [39, 49, 61]. Al [23]. Al-Rawi [23]. Aldous [68]. Alex [15]. Allure [46]. America [60, 66]. American [49, 69, 61, 52]. ancienne [25]. Andreas [28]. Angela [42]. Animals [16]. Ann [26]. Anna [19, 47]. Annotated [46]. Annotations [28]. Anti [37]. Anti-Copernican [37]. Antibiotic [64]. Anxiety [51]. Apocalyptic [61]. Archaeology [26]. Ark [36]. Artisan [32]. Asylum [48]. Atri [54]. Audra [65]. Australia [41]. Authorship [15]. Axelle [29].

Galois theory of linear differential equations

Abstract: Linear differential equations form the central topic of this volume, Galois theory being the unifying theme. A large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, the inverse problem and linear differential equations in positive characteristic. The appendices aim to help the reader with concepts used, from algebraic geometry, linear algebraic groups, sheaves, and tannakian categories that are used. This volume will become a standard reference for all mathematicians in this area of mathematics, including graduate students.

Remarks on the Foundations of Mathematics. By L. Wittgenstein. Edited by G. H. Von Wright, R. Rhees and G. E. M. Anscombe. Translated by G. E. M. Anscombe. Pp. 400. 37s. 6d. 1956. (Basil Blackwell, Oxford)

Abstract: Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.

Geometry of Quantum States

Abstract: a ) p. 131 The discussion between eqs. (5.14) and (5.15) is incorrect (dA should be made as large as possible!). b ) p. 256 In the figure, the numbers 6) and 7) occur twice. c ) p. 292 At the end of section 12.5, it should be the space of isospectral 0Hermitian matrices. d ) p. 306 A ”Tr” is missing in eq. (13.43). e ) p. 327, Eq. (14.64b) is 〈Trρ〉B = N(14N+10) (5N+1)(N+3) should be 〈Trρ〉B = 8N+7 (N+2)(N+4)