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Theory of distributions (Functional analysis) --- Distributions, Théorie des (Analyse fonctionnelle) --- 51 <09> --- Distribution (Functional analysis) --- Distributions, Theory of (Functional analysis) --- Functions, Generalized --- Generalized functions --- Functional analysis --- Mathematics--Geschiedenis van ... --- Theory of distributions (Functional analysis). --- 51 <09> Mathematics--Geschiedenis van ... --- Distributions, Théorie des (Analyse fonctionnelle) --- Mathematics--Geschiedenis van .. --- Analyse fonctionnelle --- History. --- Histoire. --- Mathematics--Geschiedenis van . --- Mathematics--Geschiedenis van --- Distributions, Théorie des (analyse fonctionnelle) --- Histoire des mathematiques --- 20e siecle

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"Mathematical theorems stating that a problem cannot be solved using specific means are numerous. This book follows the history of such impossibility theorems from Greek antiquity through the early 20th century. It reveals that many impossibility statements started out as meta-statements but ended up as mathematical theorems that were proved by mathematical methods. Until the 19th century, impossibility theorems were often considered of secondary interest compared with positive results. This changed during the 19th century and today impossibility results are among the most famous and popular theorems of mathematics. The book will deal with some of the celebrated impossibility theorems in pure mathematics such as the quadrature of the circle, the duplication of the cube, the trisection of the angle, Fermat's last theorem, the impossibility of proving the parallel postulate and Gödel's theorem, as well as some theorems from applied mathematics such as Arrow's impossibility theorem. Although an impossibility may sound as a negative result, impossibilities have in fact acted as a creative force in the history of mathematics challenging mathematicians to circumvent the impossibility. The introduction of complex numbers is a case in point"--

Analyse mathématique --- Mathematical analysis --- Histoire. --- History. --- Analyse mathématique

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Mathematicians --- Biography --- Liouville, Joseph, --- Biography. --- France --- Liouville, Joseph, 1809-1882. --- Mathematicians - France - Biography. --- Mathematicians - France - Biography --- Liouville, Joseph, - 1809-1882

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This is an outstanding collection of original essays. All of them concern the history and philosophy of mathematics and physics in the years from 1870 to 1930. More specifically, they are intellectual histories of the interactions between the three disciplines, philosophy, mathematics and physics, in that period. And as the essays bring out, what a period it was: of both ferment and synergy, heat and light! Most of the giants - especially Helmholtz, Hertz, Poincare, Hilbert, Einstein and Weyl - are here: engaging not just in physics and mathematics but also in philosophy, often together, or with figures like Schlick. The editors are to be congratulated on a major contribution to our understanding of one of the most complex but fertile periods in the history of all three disciplines. - Jeremy Butterfield, University of Cambridge This stimulating volume covers a wide range of topics which are of direct interest to anyone who thinks about the curious relation between mathematics and the natural world. Philosophers often pose interesting questions about the "dispensability" of mathematics to science. But they too often overlook the wealth of philosophical perplexities that can arise in detailed examples and case studies, both contemporary and historical. This volume refocuses our attention by addressing a number of topics connected to applied mathematics, any one of which is worthy of every philosopher’s attention. - James Robert Brown, University of Toronto What to make of neo-Kantianism in its hey-day, from 1840-1940? It was the most prolific of times and the most seminal, it was the most muddled and confused, it is philosophy working at its hardest with science and most damagingly against science. It is examined here episodically, as it engaged individual scientists: Helmholtz, , Hertz, Poincare, Minkowski, Hilbert, Eddington and Weyl. If Einstein is not in their number, he had to contend with their influence, and anyway he transformed their agenda. The essays on these figures are glinting in their focus and scholarship. Whatever one thinks of neo-Kantianism, this book is history and philosophy of science at its best: mathematically and physically informed, historically engaged, and philosophically driven. - Simon Saunders, University of Oxford Ten first-rate philosopher-historians probe insightfully into key conceptual questions of pre-quantum mathematical physics, from Helmholtz and Boltzmann, through Hertz and Lorentz, to Einstein, Weyl and Eddington, with an interesting aside on the rarely studied philosophy of Federigo Enriques. A rich and effective display of what the critical history of science can do for our understanding of scientific thought and its achievements. Roberto Torretti, University of Puerto Rico.

History of philosophy --- Pure sciences. Natural sciences (general) --- Theory of knowledge --- History of physics --- filosofie --- epistomologie --- Mathematics --- geschiedenis --- Philosophy of science --- wetenschapsgeschiedenis --- wiskunde --- epistemologists --- fysica --- Philosophy. --- History. --- Philosophy and science. --- Mathematics. --- Physics. --- Philosophy, general. --- History of Mathematical Sciences. --- History of Science. --- Philosophy of Science. --- History and Philosophical Foundations of Physics. --- History of Philosophy. --- Science and philosophy --- Science --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Math --- Annals --- Auxiliary sciences of history --- Mental philosophy --- Humanities --- Mathematical analysis --- Physics --- Causality (Physics) --- Foundations. --- 517.1 --- Philosophy and science --- Normal science --- Logic of mathematics --- Mathematics, Logic of --- Causality --- Heisenberg uncertainty principle --- Nuclear physics --- Quantum theory --- 517.1 Mathematical analysis --- Philosophy --- Causality (Physics). --- Philosophy (General). --- Foundations