Rouse Ball Lecture - Undecidability in Number Theory

Duration: 57 mins 7 secs

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Description:	This year's Rouse Ball lecture was held on Thursday 13 May at 4pm BST, and was given by Professor Bjorn Poonen of MIT.


Created:	2021-05-31 17:53
Collection:	Rouse Ball Lecture
Publisher:	University of Cambridge
Copyright:	Deryck Thake
Language:	eng (English)


Abstract:	Hilbert’s tenth problem asked for an algorithm that, given a multivariable polynomial equation with integer coefficients, would decide whether there exists a solution in integers. Around 1970, Matiyasevich, building on earlier work of Davis, Putnam, and Robinson, showed that no such algorithm exists. But the answer to the analogous question with integers replaced by rational numbers is still unknown, and there is not even agreement among experts as to what the answer should be.

Abstract:

Hilbert’s tenth problem asked for an algorithm that, given a multivariable polynomial equation with integer coefficients, would decide whether there exists a solution in integers. Around 1970, Matiyasevich, building on earlier work of Davis, Putnam, and Robinson, showed that no such algorithm exists. But the answer to the analogous question with integers replaced by rational numbers is still unknown, and there is not even agreement among experts as to what the answer should be.

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