03639nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001200172072001600184072002300200072001500223100008500238245015700323250001800480264006900498300004600567336002600613337002600639338003600665347002400701505030300725520168201028650002402710650001302734650003602747650002502783650004502808650003802853650005402891710003402945773002602979776003603005776003603041856004603077912001403123912001503137999001703152978-3-031-74224-8DE-He21320251030114553.0cr nn 008mamaa241130s2024    sz |    s    |||| 0|eng d  a97830317422489978-3-031-74224-87 a10.1007/978-3-031-74224-82doi 4aQA21-27 7aPBX2bicssc 7aMAT0150002bisacsh 7aPBX2thema1 aAgarwal, Ravi P.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98828910aMathematics Before and After Pythagorash[electronic resource] :bExploring the Foundations and Evolution of Mathematical Thought /cby Ravi P. Agarwal.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXXIX, 658 p. 104 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aPreface -- Foreword -- Life and Teaching of Pythagoras -- Numbers and Number Mysticism -- Mathematics, Mathematicians, and Proofs -- Prime Numbers -- Pythagorean Theorem -- Pythagorean Triples -- Pythagorean Figurative Numbers -- Pythagorean Irrationality of Numbers -- Name Index -- Subject Index.  aThis book provides the reader with a comprehensive account of the contributions of Pythagoras to mathematics and philosophy, using them as a starting point to compare pre-Pythagorean accomplishments with the myriad mathematical developments that followed. It begins with a thorough study of Pythagoreanism and the early Pythagoreans, including the major events in Pythagoras' life and the origins of the mystical significance attributed by Pythagoreans to natural numbers. From Chapter 3 onward, the book describes how mathematical thinking works and prepares the reader for the subsequent chapters, which cover mathematical logic and proofs, their application to the study of natural and prime numbers, the investigation of Pythagorean triples, figurative numbers, and irrational numbers, all interwoven with rich historical context. Aimed at students and teachers at all levels, this work is accessible to non-mathematicians as well, with the main prerequisite being an avid curiosity about some of the ideas and thinkers that helped to forge the mathematical world as we know it. Early praises for “Mathematics Before and After Pythagoras”: “Your book is charming and fun to read. It would be fine to be able to teach from it.” (Steve Krantz, USA) “...your new book, an obvious labor of love... I can see that it will be an inspiration for young students.” (Bruce Berndt, USA) “It is an excellent book, and I am deeply grateful for sending it to me. It is an extraordinary gift, and I am so grateful for this.” (Carlo Cattani, Italy) “I am really impressed by the wealth of interesting material you have collected and presented.” (Rainer Kress, Germany). 0aMathematics.965523 0aHistory. 0aMathematicsxPhilosophy.969649 0aProof theory.98829014aHistory of Mathematical Sciences.96619724aPhilosophy of Mathematics.96965024aProof Theory and Constructive Mathematics.9882912 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303174223108iPrinted edition:z978303174225540uhttps://doi.org/10.1007/978-3-031-74224-8  aZDB-2-SMA  aZDB-2-SXMS  c65340d65340