Undecidability in Number Theory

Speaker: 
Bjorn Poonen
Date: 
Mon, May 26, 2014
Location: 
PIMS, University of British Columbia
Conference: 
2014 Niven Lecture
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.  However, 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.