LEADER 03737nam 22005535 450 001 996418266103316 005 20200724143114.0 010 $a3-030-50876-5 024 7 $a10.1007/978-3-030-50876-0 035 $a(CKB)4100000011354693 035 $a(DE-He213)978-3-030-50876-0 035 $a(MiAaPQ)EBC6273696 035 $a(PPN)260832839 035 $a(EXLCZ)994100000011354693 100 $a20200724d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCan Mathematics Be Proved Consistent?$b[electronic resource] $eGödel's Shorthand Notes & Lectures on Incompleteness /$fby Jan von Plato 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (IX, 263 p.) 225 1 $aSources and Studies in the History of Mathematics and Physical Sciences,$x2196-8810 300 $aIncludes index. 311 $a3-030-50875-7 327 $aI. Gödel's Steps Toward Incompleteness -- II. The Saved Sources on Incompleteness -- III. The Shorthand Notebooks -- IV. The Typewritten Manuscripts -- V. Lectures and Seminars on Incompleteness -- Index -- References. 330 $aKurt Gödel (1906?1978) shook the mathematical world in 1931 by a result that has become an icon of 20th century science: The search for rigour in proving mathematical theorems had led to the formalization of mathematical proofs, to the extent that such proving could be reduced to the application of a few mechanical rules. Gödel showed that whenever the part of mathematics under formalization contains elementary arithmetic, there will be arithmetical statements that should be formally provable but aren?t. The result is known as Gödel?s first incompleteness theorem, so called because there is a second incompleteness result, embodied in his answer to the question "Can mathematics be proved consistent?" This book offers the first examination of Gödel?s preserved notebooks from 1930, written in a long-forgotten German shorthand, that show his way to the results: his first ideas, how they evolved, and how the jewel-like final presentation in his famous publication On formally undecidable propositions was composed.The book also contains the original version of Gödel?s incompleteness article, as handed in for publication with no mentioning of the second incompleteness theorem, as well as six contemporary lectures and seminars Gödel gave between 1931 and 1934 in Austria, Germany, and the United States. The lectures are masterpieces of accessible presentations of deep scientific results, readable even for those without special mathematical training, and published here for the first time. 410 0$aSources and Studies in the History of Mathematics and Physical Sciences,$x2196-8810 606 $aMathematics 606 $aHistory 606 $aMathematical logic 606 $aHistory of Mathematical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M23009 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 615 0$aMathematics. 615 0$aHistory. 615 0$aMathematical logic. 615 14$aHistory of Mathematical Sciences. 615 24$aMathematical Logic and Foundations. 676 $a511.3 700 $avon Plato$b Jan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0766770 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418266103316 996 $aCan Mathematics Be Proved Consistent$92083320 997 $aUNISA