LEADER 03563nam 22005175 450 001 9910644259003321 005 20230522102335.0 010 $a9783031136788$b(electronic bk.) 010 $z9783031136771 024 7 $a10.1007/978-3-031-13678-8 035 $a(MiAaPQ)EBC7179168 035 $a(Au-PeEL)EBL7179168 035 $a(CKB)26020957100041 035 $a(DE-He213)978-3-031-13678-8 035 $a(PPN)267811144 035 $a(EXLCZ)9926020957100041 100 $a20230116d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLogos and Alogon $eThinkable and the Unthinkable in Mathematics, from the Pythagoreans to the Moderns /$fby Arkady Plotnitsky 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (307 pages) 300 $aIncludes index. 311 08$aPrint version: Plotnitsky, Arkady Logos and Alogon Cham : Springer International Publishing AG,c2023 9783031136771 327 $a1 The Ghost and the Spirit of Pythagoras in Modern and Modernist Mathematics -- 2 Plato?s Ghosts: Pythagorean Mathematics, Socratic Philosophy, and Tragic Art -- 3 ?Comprehending the Connection of Things?: Bernhard Riemann and the Architecture of Mathematical Concepts -- 4 What is a Curve?: From Geometry to Algebra, from Modern to Modernist Mathematics -- 5 Returns of Geometry: From the Pythagoreans to Mathematical Modernism and Beyond -- 6 Who Thinks Abstractly: Emmy Noether and Modernist Mathematics -- 7 Mathematical Practice as Philosophy, with Galois, Riemann, Poincaré, and Grothendieck. 330 $aThis book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the book?s title, an alogon in the logos of mathematics. The outcome of this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields. 606 $aMathematics?Philosophy 606 $aPhilosophy of Mathematics 606 $aFilosofia de la matemātica$2thub 608 $aLlibres electrōnics$2thub 615 0$aMathematics?Philosophy. 615 14$aPhilosophy of Mathematics. 615 7$aFilosofia de la matemātica 676 $a551.48 676 $a510.1 700 $aPlotnitsky$b Arkady$0814131 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910644259003321 996 $aLogos and Alogon$93004756 997 $aUNINA