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Roads to Infinity: The Mathematics of Truth and Proof (AK Peters/CRC Recreational Mathematics Series)
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About Roads To Infinity: The Mathematics Of Truth And
Product Description Winner of a CHOICE Outstanding Academic Title Award for 2011!This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is historical and partly informal, but with due attention to the subtleties of the subject. Ideas are shown to evolve from natural mathematical questions about the nature of infinity and the nature of proof, set against a background of broader questions and developments in mathematics. A particular aim of the book is to acknowledge some important but neglected figures in the history of infinity, such as Post and Gentzen, alongside the recognized giants Cantor and Gödel. Review "The text is nicely presented, with many illuminating and/or entertaining quotes and diagrams. … The wide scope of the work and the way that the author manages to show the connections between the different topics are the main strength of the book, making it a good place to start if you have some interest in logic, set theory, or just challenging ideas in general."―Yann Peresse, London Mathematical Society Newsletter, June 2013 "The book follows essentially two roads to infinity: Cantor’s diagonal argument and Cantor’s construction of the ordinals. Stillwell shows how these two themes intertwine and influence a wide range of mathematical questions … The scope of this book is breathtaking, but Stillwell has masterfully presented and developed a wide range of mathematics as a coherent narrative. … He is able to pack a lot of information and ideas into a few well-chosen paragraphs without sacrificing clarity. Stillwell is an accomplished historian of mathematics who doesn’t limit himself to the work of the well-known. I appreciated the appearance of some of the lesser known contributors to the study of the infinite. … It is well-conceived and well-written, and covers a large amount of material on logic, transfinite set theory, provability, combinatorics, and the histories of these fields."―James V. Rauff, Mathematics and Computer Education, Winter 2012 "Stillwell is a master expositor and does a very good job explaining and weaving together many core issues in mathematical logic and foundational studies. … Stillwell’s book is highly commendable, very informative and well organized. It is very carefully produced."―José Ferreirós, American Mathematical Monthly, February 2012 "I highly recommend it for undergraduates in mathematics and other young mathematicians who are looking for historical context or a different angle to their studies. Readers who have experience with theoretical analysis or a foundation in abstract mathematics will find the examples wonderfully illustrative. For these readers, Stillwell’s words will flow smoothly, almost like a novel."―Joyance Meechai, Mathematics Teacher, October 2011 "Stillwell has produced an excellent book on infinity for the motivated lay reader. … The author does a masterful job of painting a historical portrait of logic, set theory, incompleteness, computable functions, and many associated foundational questions. His lively style and clear exposition of the relationship between proof and truth will engage both the novice and the expert. Although there are numerous books on the topic of infinity, Stillwell tells a story which motivates the ideas he introduces. This is a book that anyone with an interest in mathematics should have in their library. Highly recommended."―R.L. Pour, CHOICE, March 2011 "This book is an accessible, but also a scholarly and extremely well-written introduction to the great ideas of modern logic. While the central results are the famed proofs of Gödel, Stillwell does a masterful job of relating that work not only to Gödel’s contemporaries, such as Post, Turing, Church, Tarski, Gentzen, and von Neumann, but also to modern resea
