{"product_id":"a-random-walk-at-infinity","title":"A Random Walk at Infinity","description":"\u003cp class=\"text-base sm:text-sm\/6\"\u003e\u003cspan style=\"white-space-collapse: preserve;\"\u003eThis book presents the problem of the Riemann Hypothesis (and later the Generalised Riemann Hypothesis). It details the relevant developments from the work of Riemann (1859) to Littlewood (1912) and gives the comprehensive proofs proposed by Kumar Eswaran (2016-18) that use the probabilistic\u003c\/span\u003e\u003cem\u003e\u003cstrong\u003e\u003cstrong class=\"font-bold italic\" style=\"white-space-collapse: preserve;\"\u003e \u003c\/strong\u003e\u003c\/strong\u003e\u003c\/em\u003e\u003cem\u003e\u003cem class=\"italic\" style=\"white-space-collapse: preserve;\"\u003eLaw of the Iterated Logarithm\u003c\/em\u003e\u003c\/em\u003e\u003cspan style=\"white-space-collapse: preserve;\"\u003e of A.Y.Khinchin and A.N.Kolmogorov from the 1920's.\u003c\/span\u003e\u003cstrong\u003e\u003cstrong class=\"font-bold\" style=\"white-space-collapse: preserve;\"\u003e No mathematics discovered after 1930 is used in the proofs.\u003c\/strong\u003e\u003c\/strong\u003e\u003c\/p\u003e\u003cp class=\"text-base sm:text-sm\/6\"\u003e \u003c\/p\u003e\u003cp class=\"text-base sm:text-sm\/6\"\u003e\u003cspan style=\"white-space-collapse: preserve;\"\u003eThe book assumes no prior knowledge of the Riemann Hypothesis, or even advanced complex analysis. Starting from first principles, and free of jargon and abstract notation, \u003c\/span\u003e\u003cu\u003e\u003cem\u003e\u003cstrong\u003e\u003cstrong class=\"font-bold italic border-b border-black\" style=\"white-space-collapse: preserve;\"\u003ethe book can be read by undergraduate students of any mathematical discipline of science and engineering.\u003c\/strong\u003e\u003c\/strong\u003e\u003c\/em\u003e\u003c\/u\u003e\u003c\/p\u003e\u003cp class=\"text-base sm:text-sm\/6\"\u003e \u003c\/p\u003e\u003cp class=\"text-base sm:text-sm\/6\"\u003e\u003cspan style=\"white-space-collapse: preserve;\"\u003eWhile its tone and language are directed at STEM educated laypersons, \u003c\/span\u003e\u003cstrong\u003e\u003cstrong class=\"font-bold\" style=\"white-space-collapse: preserve;\"\u003ethe book contains the detailed complete proofs\u003c\/strong\u003e\u003c\/strong\u003e\u003cspan style=\"white-space-collapse: preserve;\"\u003e.\u003c\/span\u003e\u003cstrong\u003e\u003cstrong class=\"font-bold\" style=\"white-space-collapse: preserve;\"\u003e So mathematicians, scientists and graduate students are invited to read the book and critique the proofs (\u003c\/strong\u003e\u003c\/strong\u003e\u003cem\u003e\u003cstrong\u003e\u003cstrong class=\"font-bold italic\" style=\"white-space-collapse: preserve;\"\u003eafter reading, at least, Chapters 5 to 12 in their entirety\u003c\/strong\u003e\u003c\/strong\u003e\u003c\/em\u003e\u003cstrong\u003e\u003cstrong class=\"font-bold\" style=\"white-space-collapse: preserve;\"\u003e).\u003c\/strong\u003e\u003c\/strong\u003e\u003c\/p\u003e\u003cp class=\"text-base sm:text-sm\/6\"\u003e \u003c\/p\u003e\u003cp class=\"text-base sm:text-sm\/6\"\u003e\u003cspan style=\"white-space-collapse: preserve;\"\u003eThe implications of the simultaneous proof of these two problems, considered to be the greatest in Pure Mathematics, are staggering in ways totally unanticipated. \u003c\/span\u003e\u003cem\u003e\u003cstrong\u003e\u003cstrong class=\"font-bold italic\" style=\"white-space-collapse: preserve;\"\u003eForemost among these is that, contrary to universal expectation, the proofs say nothing at all new about prime numbers\u003c\/strong\u003e\u003c\/strong\u003e\u003c\/em\u003e\u003cspan style=\"white-space-collapse: preserve;\"\u003e. Further, they question the foundational promise and future prospects of Analytic Number theory.\u003c\/span\u003e\u003c\/p\u003e\u003cp class=\"text-base sm:text-sm\/6\"\u003e\u003cspan style=\"white-space-collapse: preserve;\"\u003eAn extended extract including the \u003cstrong\u003efirst seven chapters \u003c\/strong\u003eis downloadable (free or nominally charged) from https:\/\/leanpub.com\/A_Random_Walk_at_Infinity_extract \u003c\/span\u003e\u003c\/p\u003e","brand":"paperback","offers":[{"title":"Perfect Bound","offer_id":67416835686704,"sku":"9789376865604","price":17.99,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/www.thegreatbritishbookshop.co.uk\/products\/a-random-walk-at-infinity","provider":"The Great British Bookshop","version":"1.0","type":"link"}