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 ...

Arithmetic geometry and Diophantine geometry lie at the confluence of number theory and algebraic geometry, exploring the deep connections between the arithmetic properties of numbers and the ...

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 ...

This is a preview. Log in through your library . Journal Information The Mathematical Gazette is the original journal of the Mathematical Association and it is now over a century old. Its readership ...