{"title":"John Stillwell","description":"\u003cp\u003eWelcome to the world of John Stillwell — a profound thinker and esteemed author in the realm of \u003cem\u003eScience \u0026amp; Nature\u003c\/em\u003e. Known for his captivating approach to unpacking the complexities of mathematics, Stillwell offers readers an enlightening journey through the wonders of the mathematical universe.\u003c\/p\u003e\n\n\u003cp\u003eIn \u003cstrong\u003eElements of Mathematics\u003c\/strong\u003e, Stillwell breaks down intricate theories into understandable concepts, making mathematics accessible and engaging. His talent lies in weaving together historical insights with modern perspectives, creating a tapestry that is both educational and inspiring.\u003c\/p\u003e\n\n\u003cp\u003eWith \u003cstrong\u003eReverse Mathematics\u003c\/strong\u003e, readers are treated to a fresh perspective on mathematical logic. This book delves into the interplay between classical mathematics and reverse mathematics, guiding readers through its nuances with clarity and precision.\u003c\/p\u003e\n\n\u003cp\u003e\u003cstrong\u003eThe Story of Proof\u003c\/strong\u003e offers an intriguing exploration into the essence and evolution of mathematical proofs. Stillwell skillfully narrates the development of proof techniques, allowing readers to appreciate the art and science behind this fundamental aspect of mathematics.\u003c\/p\u003e\n\n\u003cp\u003eJohn Stillwell's works are not just books; they are gateways to understanding the language of the universe. Whether you're a seasoned mathematician or a curious mind eager to delve into the world of numbers, Stillwell's writings promise a rewarding and enlightening experience.\u003c\/p\u003e","products":[{"product_id":"reverse-mathematics-by-john-stillwell-9780691177175","title":"Reverse Mathematics","description":"\u003cdiv class=\"book-description\"\u003e\n\u003cp\u003eThis book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem?\u003c\/p\u003e\n\n\u003cp\u003eOnly in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In \u003cem\u003eReverse Mathematics\u003c\/em\u003e, John Stillwell gives a representative view of this field, emphasizing basic analysis—finding the \"right axioms\" to prove fundamental theorems—and giving a novel approach to logic. \u003c\/p\u003e\n\n\u003cp\u003eStillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic, in some sense, underlies analysis, logic, and computation.\u003c\/p\u003e\n\n\u003cp\u003eReverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the \"right axiom\" to prove it.\u003c\/p\u003e\n\n\u003cp\u003eBy using a minimum of mathematical logic in a well-motivated way, \u003cem\u003eReverse Mathematics\u003c\/em\u003e will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"NewSouth Books","offers":[{"title":"Default Title","offer_id":46854812008684,"sku":"9780691177175","price":67.99,"currency_code":"NZD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0705\/7784\/8556\/files\/9aa09e2ba304df92932c4958248aea1a.jpg?v=1759264629"},{"product_id":"the-story-of-proof-by-john-stillwell-9780691234366","title":"The Story of Proof","description":"\u003cdiv class=\"book-description\"\u003e\n\u003cp\u003e\u003cstrong\u003eHow the concept of proof has enabled the creation of mathematical knowledge.\u003c\/strong\u003e\u003c\/p\u003e\n\n\u003cp\u003e\u003cem\u003eThe Story of Proof\u003c\/em\u003e investigates the evolution of the concept of proof—one of the most significant and defining features of mathematical thought—through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge.\u003c\/p\u003e\n\n\u003cp\u003eStillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as 'infinitesimal algebra,' and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid.\u003c\/p\u003e\n\n\u003cp\u003eStillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved.\u003c\/p\u003e\n\n\u003cp\u003eShedding light on the workings of mathematics at its most fundamental levels, \u003cem\u003eThe Story of Proof\u003c\/em\u003e offers a compelling new perspective on the field's power and progress.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"NewSouth Books","offers":[{"title":"Default Title","offer_id":46855268597996,"sku":"9780691234366","price":155.0,"currency_code":"NZD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0705\/7784\/8556\/files\/9780691234366.jpg?v=1759266090"},{"product_id":"elements-of-mathematics-by-john-stillwell-9780691178547","title":"Elements of Mathematics","description":"\u003cdiv class=\"book-description\"\u003e\n\u003cp\u003e\u003ci\u003eElements of Mathematics\u003c\/i\u003e takes readers on a fascinating tour that begins in elementary mathematics—but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become \"elementary.\"\u003c\/p\u003e\n\n\u003cp\u003eStillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole.\u003c\/p\u003e\n\n\u003cp\u003eThrough a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of \"reverse mathematics\" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics.\u003c\/p\u003e\n\n\u003cp\u003e\u003ci\u003eElements of Mathematics\u003c\/i\u003e gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of maths beyond its boundaries.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"NewSouth Books","offers":[{"title":"Default Title","offer_id":46998054338796,"sku":"9780691178547","price":77.0,"currency_code":"NZD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0705\/7784\/8556\/files\/1772613482434.jpg?v=1763206656"},{"product_id":"reverse-mathematics-by-john-stillwell-9780691196411","title":"Reverse Mathematics","description":"\u003cdiv class=\"book-description\"\u003e\n\u003cp\u003eThe first book surveying the history and ideas behind reverse mathematics, \u003cem\u003eReverse Mathematics\u003c\/em\u003e is a new field that seeks to find the axioms needed to prove given theorems.\u003c\/p\u003e\n\n\u003cp\u003eIn \u003cem\u003eReverse Mathematics\u003c\/em\u003e, John Stillwell offers a historical and representative view, emphasizing basic analysis and providing a novel approach to logic. By using a minimum of mathematical logic in a well-motivated way, \u003cem\u003eReverse Mathematics\u003c\/em\u003e will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"NewSouth Books","offers":[{"title":"Default Title","offer_id":46998570795244,"sku":"9780691196411","price":72.0,"currency_code":"NZD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0705\/7784\/8556\/files\/d39565703578d14e1ca044a0374f8615.jpg?v=1773005151"}],"url":"https:\/\/bookhero.live\/collections\/john-stillwell.oembed","provider":"Book Hero","version":"1.0","type":"link"}