The original version of this story appeared in Quanta Magazine. The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the ...

An American mathematician has cracked part of a problem that had remained unsolved for 64 years. Andrew Booker, Reader of Pure Mathematics at the University of Bristol in the U.K., worked out how to ...

Research in group theory has long embraced equations as a means to elucidate the structure and behaviour of groups. In particular, Diophantine problems—those surrounding the existence and ...

A polynomial parametrization for the group of integer two-by-two matrices with determinant one is given, solving an old open problem of Skolem and Beurkers. It follows that, for many Diophantine ...

Mathematics of Computation, Vol. 47, No. 176 (Oct., 1986), pp. 713-727 (15 pages) We show how the Gelfond-Baker theory and diophantine approximation techniques can be ...

The set of solutions to a diophantine equation is strongly influenced by the geometry of the associated algebraic variety. This paradigm, for example, suggests that an elementary proof of Fermat’s ...

Your mathematics teacher at school will have told you that you can only solve a set of simultaneous equations if there are as many equations as there are variables, but that is because they don’t ...