Let D be a global domain whose quotient field F does not have characteristic 2, let U be a quaternion algebra over F, and let D be an order on U over D. A right D-module M which is simultaneously a ...

Inspired by Stark's analytic proof of class number finiteness of a ring of integers in an algebraic number field, we give a new proof of the finiteness of the number of classes of ideals in a maximal ...

Two apparently disjoint subjects discussed in the same issue – quantum uncertainty and the Riemann hypothesis – have a surprising and important mathematical connection. Louis de Branges’s purported ...

As in recent numbers of NATURE my views on analysis have been quoted, and not very correctly, I ask for space to state them more explicitly. I see truth in the quaternion analysis and in the vector ...

SMALL PRINT:DANIEL O'CONNELL may have been known as The Liberator, but another important figure in 19th-century Ireland earned a similar title – mathematician William Rowan Hamilton (right) is ...