Wolf DeVoon 24 Posted November 20, 2015 Share Posted November 20, 2015 I have no dog in this hunt, because I'm a math dodo. Natural language predicate logic, sure. But not this stuff.http://www.claymath.org/millennium-problemsMillennium ProblemsYang–Mills and Mass GapExperiment and computer simulations suggest the existence of a "mass gap" in the solution to the quantum versions of the Yang-Mills equations. But no proof of this property is known.Riemann HypothesisThe prime number theorem determines the average distribution of the primes. The Riemann hypothesis tells us about the deviation from the average. Formulated in Riemann's 1859 paper, it asserts that all the 'non-obvious' zeros of the zeta function are complex numbers with real part 1/2.P vs NP ProblemIf it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? This is the essence of the P vs NP question. Typical of the NP problems is that of the Hamiltonian Path Problem: given N cities to visit, how can one do this without visiting a city twice? If you give me a solution, I can easily check that it is correct. But I cannot so easily find a solution.Navier–Stokes EquationThis is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding.Hodge ConjectureThe answer to this conjecture determines how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations. The Hodge conjecture is known in certain special cases, e.g., when the solution set has dimension less than four. But in dimension four it is unknown.Poincaré Conjecture In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston's geometrization conjecture. Perelman's proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries.Birch and Swinnerton-Dyer ConjectureSupported by much experimental evidence, this conjecture relates the number of points on an elliptic curve mod p to the rank of the group of rational points. Elliptic curves, defined by cubic equations in two variables, are fundamental mathematical objects that arise in many areas: Wiles' proof of the Fermat Conjecture, factorization of numbers into primes, and cryptography, to name three. Link to post Share on other sites

Brant Gaede 192 Posted November 20, 2015 Share Posted November 20, 2015 No idea why you posted this. My understanding of zero is it's not a number. It's a place-holder which revolutionized arithmetical computations.--Brantonly Bob can help us now Link to post Share on other sites

Wolf DeVoon 24 Posted November 20, 2015 Author Share Posted November 20, 2015 No idea why you posted this. My understanding of zero is it's not a number. It's a place-holder which revolutionized arithmetical computations.--Brantonly Bob can help us nowI always ask for help when I see something I don't understand. Link to post Share on other sites

Brant Gaede 192 Posted November 20, 2015 Share Posted November 20, 2015 Either that or shoot it.--Joke alert! Link to post Share on other sites

BaalChatzaf 60 Posted February 21, 2016 Share Posted February 21, 2016 On 11/20/2015 at 10:47 PM, Brant Gaede said: No idea why you posted this. My understanding of zero is it's not a number. It's a place-holder which revolutionized arithmetical computations. --Brant only Bob can help us now Zero is the identity element for the additive subgroup of the rationals, reals, complex number 0 + x = x. x - x = 0 zero is a genuine number but during the renaissance the mathematicians considered negative numbers and zero as fantastical elements, not to be taken seriously. The bankers were the first to catch on that zero and negative balances were as real as rain. Link to post Share on other sites

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