{"product_id":"2940013341388","title":"MATHEMATICAL PROBLEMS","description":"Scanned, proofed and corrected from the original magazine edition for enjoyable reading. (Worth every penny spent!)\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e***\u003cbr\u003e\u003cbr\u003eHilbert put forth a most influential list of 23 unsolved problems at the International Congress of Mathematicians in Paris in 1900. This is generally reckoned the most successful and deeply considered compilation of open problems ever to be produced by an individual mathematician.\u003cbr\u003e\u003cbr\u003e— Excerpted from David Hilbert on Wikipedia.\u003cbr\u003e\u003cbr\u003e***\u003cbr\u003e\u003cbr\u003eIn 1902 David Hilbert lectured on mathematical problems which were at that time awaiting solutions by the hands of competent mathematicians. This piece has been translated into English by Dr. Mary Newson \u003cbr\u003e\u003cbr\u003efor the Bulletin of the American Mathematical Society. \u003cbr\u003e\u003cbr\u003eSome of the problems are as follows: \u003cbr\u003e\u003cbr\u003eCantor's problem of the cardinal number of the continuum;\u003cbr\u003e\u003cbr\u003eThe compatibility of the axioms of arithmetic;\u003cbr\u003e\u003cbr\u003eThe equality of the volumes of two tetrahedra of equal bases and equal altitudes;\u003cbr\u003e\u003cbr\u003eThe problem of the straight line as the shortest distance between two points\u003cbr\u003eLie's concept of a continuous group of transformations without assuming that the functions defining the group are capable of differentiation;\u003cbr\u003e\u003cbr\u003eThe treatment of the axioms of physics as we treat the axioms of mathematics, placing in the first rank probabilities and mechanics;\u003cbr\u003e\u003cbr\u003eThe irrationality and transcendence of certain numbers;\u003cbr\u003e\u003cbr\u003eRiemann's prime number formula;\u003cbr\u003e\u003cbr\u003eGoldback's theorem, that every integer is expressible as the sum of two primes;\u003cbr\u003e\u003cbr\u003eIs there an infinite number of pairs of primes differing by 2? \u003cbr\u003e\u003cbr\u003eIs ax+by+c=o soluble in prime numbers x and y, where a, b are integral and a prime to b? \u003cbr\u003e\u003cbr\u003eto apply the results obtained for the distribution of rational prime numbers to the theory of the distribution of ideal primes in a given number field k;\u003cbr\u003e\u003cbr\u003e...and so on.\u003cbr\u003e\u003cbr\u003e***\u003cbr\u003e\u003cbr\u003ePoincaré is discoursed on the role of intuition and logic in mathematics, showing how, while intuition is often the source of discovery, it is logic which harmonizes and consolidates the creations of intuition. \u003cbr\u003e\u003cbr\u003eIt is a delightful collection.","brand":"OGB","offers":[{"title":"Default Title","offer_id":47082686578928,"sku":"2940013341388","price":2.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/2940013341388_p0.jpg?v=1763580103","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/2940013341388","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}