# Poonen undecidability in number theory concepts

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Undecidability in number theory Bjorn Poonen Rademacher Lecture 1 November 6, Undecidability in number theory Bjorn Poonen H10 Polynomial equations Hilbert’s 10th problem Diophantine sets Listable sets DPRM theorem Consequences of DPRM Prime-producing polynomials Riemann hypothesis Related problems H10 over Ok. Undecidability in Number Theory Andrew Gilroy June 23, In the study of number theory the question often arises: does an equation have a solution? This question can address any given equation, but in the true spirit of mathematics, it can address a general situation. In David. Undecidability in number theory Bjorn Poonen University of California at Berkeley (on sabbatical at Harvard and MIT in Fall ) September 20, Undecidability in number theory Bjorn Poonen H10 Polynomial equations Hilbert’s 10th problem Diophantine sets Listable sets DPRM theorem Consequences of DPRM.

# Poonen undecidability in number theory concepts

Undecidability in number theory Bjorn Poonen University of California at Berkeley (on sabbatical at Harvard and MIT in Fall ) September 20, Undecidability in number theory Bjorn Poonen H10 Polynomial equations Hilbert’s 10th problem Diophantine sets Listable sets DPRM theorem Consequences of DPRM. Undecidability in Number Theory Andrew Gilroy June 23, In the study of number theory the question often arises: does an equation have a solution? This question can address any given equation, but in the true spirit of mathematics, it can address a general situation. In David. Undecidability in number theory Bjorn Poonen Rademacher Lecture 1 November 6, Undecidability in number theory Bjorn Poonen H10 Polynomial equations Hilbert’s 10th problem Diophantine sets Listable sets DPRM theorem Consequences of DPRM Prime-producing polynomials Riemann hypothesis Related problems H10 over Ok. • some of the concepts in the proof, • a few by-products of the proof, and • current research on related problems that are still open, such as the analogue for rational number solutions. Bjorn Poonen is professor of mathematics at the Uni-versity of California at Berkeley. His email address is [email protected] Undecidability in number theory Bjorn Poonen MIT Novos Talentos em Matem´atica Lisboa July 15, Undecidability in number theory Bjorn Poonen H10 Polynomial equations Hilbert’s 10th problem Diophantine sets Listable sets DPRM theorem Consequences of DPRM Prime-producing polynomials Riemann hypothesis.discusses the concepts behind Matiyasevich's negative answer to the .. Bjorn Poonen is professor of mathematics at the Uni- versity of. in number theory1. Bjorn Poonen Of course, number theory does not end with the study of cubic some of the concepts in the proof,. • a few by-products of . A basic, old result is the decidability of Presburger arithmetic, i.e. the theory of the .. The ring-theories of Qp (p is a prime number) are decidable (results of ..  B. Poonen, Hilbert's Tenth Problem over rings of number-theoretic interest, ob-. Conceptual Analysis and Phenomenology Yoshitsugu Oono For Hilbert's 10th problem see B. Poonen, “Undecidability in number theory,” Notices Am. Math. In computability theory, an undecidable problem is a type of computational problem that (encoding some mathematical concept or object) represent the same object or not. For undecidability in axiomatic mathematics, see List of statements undecidable . Poonen, Bjorn (2 April ), Undecidable problems: a sampler.

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42 is the new 33 - Numberphile, time: 13:40
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