# 2013-14 Serge Lang Undergraduate Lecture

*The 2013-14 Serge Lang Undergraduate Lecture will be given on Thursday, January 30 at 4:10PM in room 60 Evans Hall on the Berkeley campus. Our lecturer this year is Bjorn Poonen.*

MUSA and the Department of Mathematics, University of California, Berkeley, present

The 2013-14 Serge Lang Undergraduate Lecture

Bjorn Poonen

Department of Mathematics

Massachusetts Institute of Technology

**Undecidability in number theory*** 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.