Where results make sense

About us   |   Why use us?   |   Reviews   |   PR   |   Contact us

Topic: Hilbert's tenth problem

    Note: these results are not from the primary (high quality) database.

Ads by Google

Related Topics

Hilary Putnam

Hilberts sixth problem, - The Honors BOOK REVIEWS Hilbert's ..Problems and Their Solvers In fact, there is a connection between Hilbert's sixth question dealing with probability theory and his tenth problem of solving algebraic equations in Hilbert's 6th problem, the proposal that the axioms of mathematical physics should be developed, had paid off for Einstein. He became Hilbert's assistant in 1905, continuing to attend lectures by Klein and the axiomatization of physics and the Sixth Problem (Spanish), Gac. linkhighway.com /?q=hilberts-sixth-problem   (430 words)

Hilbert 10 Hilbert's tenth problem: what was done and and was is to be done. Matjasevich: Hilbert's tenth problem: what was done and and was is to be done. Work on Hilbert's 10th problem, for various rings and fields, over the past decades. cage.rug.ac.be /~hilbrt10/hilbert10.html   (618 words)

Clay Mathematics Institute: Encyclopedia topic Hilbert's tenth problem (Hilbert's tenth problem: more facts about this subject) dealt with a more general type of equation, and in that case it was proved that there is no way to decide whether a given equation even has any solutions. This was Hilbert's eighth problem (Hilbert's eighth problem: in mathematics, the riemann hypothesis (aka riemann zeta hypothesis), first formulated... The problem is to establish the existence of the Yang-Mills theory and a mass gap. www.absoluteastronomy.com /reference/clay_mathematics_institute   (1002 words)

COMP3310 Theory of Computation For Hilberts tenth problem see Martin Davis, Hilbert's tenth problem is unsolvable. Thursday: PSPACE-completeness, the TQBF problem, L, NL and the Immerman Szelepscenyi theorem Monday: Turing machines, Church-Turing thesis, decidable problems for regular and context free languages, the halting problem www.it.usyd.edu.au /~comp3310/notes.html   (295 words)

Hilbert Tenth Problem: database index Extensions of Hilbert's Tenth Problem (March 21 to March 25, 2005) at the American Institute of Mathematics, Palo Alto, California organized by Bjorn Poonen, Alexandra Shlapentokh, Xavier Vidaux, and Karim Zahidi. This workshop, sponsored by AIM and the NSF, will be devoted to extensions of Hilbert's Tenth Problem and related questions in Number Theory and Geometry. The aim of this page is to promote research connected with the negative solution of Hilbert's Tenth Problem. logic.pdmi.ras.ru /Hilbert10   (214 words)

Hilbert Tenth Problem: database index Extensions of Hilbert's Tenth Problem (March 21 to March 25, 2005) at the American Institute of Mathematics, Palo Alto, California organized by Bjorn Poonen, Alexandra Shlapentokh, Xavier Vidaux, and Karim Zahidi. This workshop, sponsored by AIM and the NSF, will be devoted to extensions of Hilbert's Tenth Problem and related questions in Number Theory and Geometry. The aim of this page is to promote research connected with the negative solution of Hilbert's Tenth Problem. logic.pdmi.ras.ru /Hilbert10   (214 words)

Hilbert's Tenth Problem. Diophantine Equations. By K.Podnieks Matiyasevich solved the problems 1), 2) in 1970, Julia Robinson - the problems 3) and 4) in 1952, the problem 5) was solved by Davis, Putnam and Julia Robinson in 1961. For example, the problem of determining, is n a prime number or not, is a mass problem, since it must be solved for an infinite set of values of n. Problems that can be solved by finding solutions of algebraic equations in the domain of integer numbers are known since the very beginning of mathematics. www.ltn.lv /~podnieks/gt4.html   (4248 words)

Salvador Vera: Directorio - Teoría de Números Hilbert's Tenth Problem Given a Diophantine equation with any number of unknowns and with rational integer coefficients: devise a process, which could determine by a finite number of operations whether the equation is solvable in rational integers. Hilbert's Tenth Problem Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites. The Beal Conjecture $75,000 prized problem pertaining to the Diophantine equation of the form A^x + B^y = C^z where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common factor. www.satd.uma.es /matap/svera/links/matnet14.html   (4248 words)

Research The oustanding problem of the area is whether the existential theory of the field of rational numbers is decidable, that is, the analogue of Hilbert’s tenth problem for the rationals. The decidability problem for theories and existential theories of algebraic domains and analogues to Hilbert’s tenth problem especially for the following domains: polynomial rimgs, number rings, formal power series rings, rings of analytic functions (complex and/or p-adic), fields of rational functions, fields of meromorphic functions. Population genetics, phase transition problems, multiphase geometrical optics in underwater acoustics, direct and inverse problems in underwater acoustics, wave propagation in layered media. www.math.uoc.gr /~www-old/2000-01/research.html   (4248 words)

Hilbert's Tenth Problem. Diophantine Equations. By K.Podnieks If we could construct an equation with a parameter such that that set S would be unsolvable, then we had proved that Hilbert's tenth problem is unsolvable. Thus, in 1961 the unsolvability of (modified) Hilbert's 10th problem for exponential Diophantine equations was proved. The idea that problems like Hilbert's, maybe, have negative solutions could appear only in 1930s, when the notion of algorithm ("process, which could determine by a finite number of operations...") was formalized. www.ltn.lv /~podnieks/gt4.html   (4227 words)

Hilbert's Tenth Problem. Diophantine Equations. By K.Podnieks If we could construct an equation with a parameter such that that set S would be unsolvable, then we had proved that Hilbert's tenth problem is unsolvable. Thus, in 1961 the unsolvability of (modified) Hilbert's 10th problem for exponential Diophantine equations was proved. The idea that problems like Hilbert's, maybe, have negative solutions could appear only in 1930s, when the notion of algorithm ("process, which could determine by a finite number of operations...") was formalized. www.ltn.lv /~podnieks/gt4.html   (4241 words)

Mathematical Problems by David Hilbert Maxim Vsemirnov's Hilbert's Tenth Problem page at the Steklov Institute of Mathematics at St.Petersburg. Leo Corry's article "Hilbert and the Axiomatization of Physics (1894-1905)" in the research journal Archive for History of Exact Sciences, 51 (1997). Lie's concept of a continuous group of transformations without the assumption of the differentiability of the functions defining the group. aleph0.clarku.edu /~djoyce/hilbert/toc.html   (309 words)

Bibliography on Hilbert's Tenth Problem The ultimate goal of this bibliography would be to contain references to all publications connected with the undecidability of Hilbert's Tenth Problem. liinwww.ira.uka.de /bibliography/Math/Hilbert10.html   (114 words)

Mathematical Problems by David Hilbert Maxim Vsemirnov's Hilbert's Tenth Problem page at the Steklov Institute of Mathematics at St.Petersburg. Leo Corry's article "Hilbert and the Axiomatization of Physics (1894-1905)" in the research journal Archive for History of Exact Sciences, 51 (1997). Lie's concept of a continuous group of transformations without the assumption of the differentiability of the functions defining the group. deptinfo.unice.fr /~fedou/ENSEIGNEMENT/OFI/GODEL/toc.html   (283 words)

[BilgiMath] Bibliography on Hilbert's Tenth Problem and on some Decidability Questions Thanases Pheidas, Hilbert's Tenth Problem for a class of rings of algebraic integers, Proceedings of the American Mathematical Society, 104(2), pp. Goodstein Hilbert's Tenth Problem and the independence of recursive difference, The Journal of the London Mathematical Society (Second Series), 10(2), pp. Goodstein, Hilbert's Tenth Problem and the independence of recursive difference, The Journal of the London Mathematical Society (Second Series), 10(2), pp. math.bilgi.edu.tr /pipermail/math/2002-September/000148.html   (2137 words)

Tenth - House of Commons - Science and Technology - Tenth Report The AIM Research Conference Center (ARCC) will host a focused workshop on Extensions of Hilbert's Tenth Problem, March 21 to March 25, 2005. The tenth planet in the solar system has a moon at least a tenth of its size. The Tenth National Green Power Marketing Conference is scheduled for October 24-26, 2005 in Austin, TX. globalinfoplus.com /?q=tenth   (205 words)

Hilbert's Tenth Problem. Diophantine Equations. By K.Podnieks David Hilbert stated his famous 23 mathematical problems for the coming XX century (see full text at Thus, in 1961 the unsolvability of (modified) Hilbert's 10th problem for exponential Diophantine equations was proved. The idea that problems like Hilbert's, maybe, have negative solutions could appear only in 1930s, when the notion of algorithm ("process, which could determine by a finite number of operations...") was formalized. www.ltn.lv /~podnieks/gt4.html   (4248 words)

Mathematical Problems by David Hilbert Maxim Vsemirnov's Hilbert's Tenth Problem page at the Steklov Institute of Mathematics at St.Petersburg. Leo Corry's article "Hilbert and the Axiomatization of Physics (1894-1905)" in the research journal Archive for History of Exact Sciences, 51 (1997). (Philosophy of problems, relationship between mathematics and science, role of proofs, axioms and formalism.) aleph0.clarku.edu /~djoyce/hilbert/toc.html   (309 words)

[BilgiMath] Calendar Lou ven den Dries speaks about Hilbert Tenth Problem. math.bilgi.edu.tr /pipermail/math/2002-September/000152.html   (108 words)

h76 (11) Hilbert's Tenth Problem and related Diophantine questions. (4) The Halting Problem (HP) for Tm's: Post Correspondence Problem (PCP), Word Problems, Thue's Problem, Dehn's Word Problem, the Post-Markov Theorem, the Novikov-Boone Theorem. (8) Primality testing, integer factorization,and randomized algorithms: certifcate of primality,applications to cryptography (9) Mersenne numbers, Mersenne primes, Lucas-Lehmer Test (10) An arithmetic research question: The 3X+1 Problem. www-cs.engr.ccny.cuny.edu /~csmma/cs5722/h76   (108 words)

h78 Carefully explain each of the following: (A) Thue's Problem, the Post- Markov Theorem and their relationship.(B) Hilbert's Tenth Problem and its relationship to Fermat's Problem.(C) NP is the class of languages that have polynomial time verifiers.(D) SAT is an NP-complete problem. Prove that the Halting Problem (HP) for M is undecidable. (B) How is HP used in proving the Post Correspondence Problem (PCP) is undecidable? www-cs.engr.ccny.cuny.edu /~csmma/cs5722/h78   (380 words)

The Math Forum - Math Library - History/Biography Contents include: Platonism, intuition and the nature of mathematics; Axiomatic set theory; First order arithmetic; Hilbert's Tenth problem; Incompleteness theorems; Around the Goedel's...more>> A draft translation of Podnieks' book, published in 1992 in Russian. www.mathforum.org /library/topics/history   (380 words)

Matiyasevich's theorem -- Facts, Info, and Encyclopedia article Matiyasevich's theorem, proven in 1970 by Yuri Matiyasevich, implies that (Click link for more info and facts about Hilbert's tenth problem) Hilbert's tenth problem is unsolvable. The conjunction of Matiyasevich's theorem with a result discovered in the 1930s implies that a solution to Hilbert's tenth problem is impossible. Matiyasevich's theorem has since been used to prove that many problems from (A hard lump produced by the concretion of mineral salts; found in hollow organs or ducts of the body) calculus and (An equation containing differentials of a function) differential equations are unsolvable. www.absoluteastronomy.com /encyclopedia/M/Ma/Matiyasevichs_theorem.htm   (713 words)

E-unification Consequently the unification problem for commutative rings is precisely the problem of the solvability of Diophantine systems in the integers, known as Hilbert's Tenth problem. Such a system was studied by Franzen in Hilbert's tenth problem is of unification type zero, J. Automated Reasoning 9 (1992), 169-178, where he shows the unification type is nullary. When Plotkin originally proposed that the notion of unification be extended to E-unification in 1972 he presented the example of the associative law for a binary operation -- this of course defines semigroups. www.math.uwaterloo.ca /~snburris/htdocs/scav/e_unif/e_unif.html   (2066 words)

Profiles of Women in Mathematics: Julia Robinson In 1948 Robinson began work on the tenth problem on Hilbert's famous list: "to find an effective method for determining if a given diophantine equation is solvable in integers." Although she also published papers on a variety of questions, the tenth problem was to occupy the largest portion of her professional career. In view of her earlier proof that exponentiation is existentially definable in terms of any function of roughly exponential growth, the negative solution of Hilbert's problem was reduced to finding an existential definition of such a function. In 1975, Robinson became the first woman mathematician to be elected to the National Academy of Sciences, and, in 1983, she became the first woman president of the American Mathematical Society. www.awm-math.org /noetherbrochure/Robinson82.html   (500 words)

Background to Richard Kaye's research interests Matiyasevich's theorem on Hilbert's tenth problem also has important applications to the fine structure of models of arithmetic, especially weak fragments of PA. A typical sort of application shows that the addition and/or multiplication in a nonstandard model cannot be computable. Hilbert's tenth problem (posed in 1900) asks for an algorithm to decide which diophantine equations (polynomial equations of the form p(x1,...,xn)=0 in several variables but with integer coefficients) can be solved in the integers. The fine structure theory of such models is in many ways analogous to Galois theory, and the automorphism groups of recursively saturated models of PA and Pres are studied as well. web.mat.bham.ac.uk /R.W.Kaye/backgr.htm   (500 words)

PIMS Distinguished Chair Lectures Matiyasevich presented a series of 75 minute lectures on Hilbert's tenth problem as a PIMS Distinguished Chair at the University of Calgary. It was 70 years later before a solution was found for Hilbert's tenth problem. Matiyasevich is a distinguished logician and mathematician based at the Steklov Institute of Mathematics at St. Petersburg. www.pims.math.ca /science/2000/distchair/matiyasevich   (500 words)

Oscar Ibarra Bibliography Applications of the Unsolvability of Hilbert's Tenth Problem to Decision Questions Concerning Programs and Abstract Machines, invited chapter for the "Handbook on Hilbert's Tenth Problem", co-edited by M. Davis and Y. Matiyasevich, to be published by the AMS as a volume in the Advances in Mathematical Sciences. On the Equivalence of Two-way Pushdown Automata and Counter Machines over Bounded Languages (with T. Jiang, N. Tran, and H. Wang), Proceedings of the 1993 Symposium on Theoretical Aspects of Computer Science, Germany, February 1993. Relating the Degree of Ambiguity of Finite Automata to Succinctness of their Representation (with B. Ravikumar), Proceedings of the 7th Conference on Foundations of Software Technology and Theoretical Computer Science, Pune, India, 1987. www.cs.ucsb.edu /~ibarra/bib.html   (3753 words)

Church integer from LiveJournal Tien D. Kieu Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into problems involving either a set of infinitely-coupled non-linear differential equations or a class of linear Schr\"odinger equations with some appropriate time-dependent Hamiltonians... [math.GM/0507109] Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into problems involving either a set of infinitely-coupled non-linear differential equations or a class of linear Schr\"odinger equations with some appropriate time-dependent Hamiltonians... Really, I'm referring to two things: The (computational) intractability of, say, integer linear programming versus straight-up linear programming, and everything that entails about their being hard (in the sense of, we cannot be good at them, as in, NP Complete) problems like combinatorial... www.ljseek.com /search/Church%20integer   (668 words)

Matiyasevich's theorem: Definition and links. Matiyasevich's theorem, proven in 1970 by Yuri Matiyasevich[?], implies that Hilbert's tenth problem is unsolvable. Matiyasevich's theorem itself is somewhat more general than the unsolvability of the Tenth Problem; it can be stated as "Every recursively enumerable set is Diophantine ". Matiyasevich's theorem has since been used to prove that many problems from calculus and differential equations are unsolvable. www.encyclopedian.com /ma/Matiyasevichs-theorem.html   (668 words)

Try your search on: Qwika (all wikis)

About us   |   Why use us?   |   Reviews   |   Press   |   Contact us   Copyright © 2005-2007 www.factbites.com Usage implies agreement with terms.