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 ...

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 ...

In the literature there has been considerable attention given to the exploration of relationships between certain diophantine equations and class numbers of quadratic fields. In this paper we provide ...

Let (X, μ) be a probability measure space and $T_{1},\ldots ,T_{n}$ be a family of commuting, measure preserving invertible transformations on X. Let $Q(m_{1},\ldots ...

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 ...

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 ...

For decades, a math puzzle has stumped the smartest mathematicians in the world. x 3 +y 3 +z 3 =k, with k being all the numbers from one to 100, is a Diophantine equation that's sometimes known as ...