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Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm that, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns), can decide whether the equation has a solution with all unknowns taking integer values.
As with the Hilbert problems, one of the prize problems (the Poincaré conjecture) was solved relatively soon after the problems were announced. The Riemann hypothesis is noteworthy for its appearance on the list of Hilbert problems, Smale's list, the list of Millennium Prize Problems, and even the Weil conjectures, in its geometric guise.
Julia Hall Bowman Robinson (December 8, 1919 – July 30, 1985) was an American mathematician noted for her contributions to the fields of computability theory and computational complexity theory—most notably in decision problems. Her work on Hilbert's tenth problem (now known as Matiyasevich's theorem or the MRDP theorem) played a crucial ...
In 1972, at the age of 25, he defended his doctoral dissertation on the unsolvability of Hilbert's tenth problem. [7] From 1974 Matiyasevich worked in scientific positions at LOMI, first as a senior researcher, in 1980 he headed the Laboratory of Mathematical Logic.
In mathematics, Hilbert's fourteenth problem, that is, number 14 of Hilbert's problems proposed in 1900, asks whether certain algebras are finitely generated. The setting is as follows: Assume that k is a field and let K be a subfield of the field of rational functions in n variables, k(x 1, ..., x n) over k.
The Entscheidungsproblem is related to Hilbert's tenth problem, which asks for an algorithm to decide whether Diophantine equations have a solution. The non-existence of such an algorithm, established by the work of Yuri Matiyasevich , Julia Robinson , Martin Davis , and Hilary Putnam , with the final piece of the proof in 1970, also implies a ...
The number of childfree women is at a record high: 48 percent of women between the ages of 18 and 44 don’t have kids, according to 2014 Census numbers. The Huffington Post and YouGov asked 124 women why they choose to be childfree.
Hilbert's 2nd and 10th problems introduced the "Entscheidungsproblem" (the "decision problem"). In his 2nd problem he asked for a proof that "arithmetic" is "consistent". Kurt Gödel would prove in 1931 that, within what he called "P" (nowadays called Peano Arithmetic), "there exist undecidable sentences [propositions]". [4]