A series of unsolved puzzles in number theory called Diophantine problems date back to 3,700 years ago. Over the years mathematicians have whittled away at them, and recent work has made significant ...

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 ...

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 ...

Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, Nouvelle Série, Vol. 60(108), No. 1 (2017), pp. 19-24 (6 pages) We investigate the properties of positive definite binary ...

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 ...

MATH30200 Number Theory, and MATH33300 Group Theory are recommended but not necessary. Integers and rational numbers are the first numbers we encounter, and as such they are, in a way the easiest ...

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 ...