OpenAI's unreleased Astra model has produced what its October 2025 announcement only pretended to: genuine solutions to ten long-standing open problems in mathematics and theoretical computer science, ...

Learn to apply statistical methods to solve problems facing financial services industries. This course aims to present you with a wide range of mathematical ideas in a way that develops your critical ...

Explore our campus, meet lecturers and current students, and learn more about what it's like to study at Manchester. We place social responsibility at the heart of your learning which means you can ...

Explore our campus, meet lecturers and current students, and learn more about what it's like to study at Manchester. Tailor your learning with a flexible degree programme offering a wide range of ...

Mathematical truths are often born of the conflict between order and disorder. Mathematicians discover patterns, and, to better understand the mysterious forces at play, they look for countervailing ...

Extreme Mass Ratio Inspirals (EMRIs) are one of the key sources for future space-based gravitational wave interferometers. Measurements of EMRI gravitational waves are expected to determine the ...

Various statistical models have been used in estimating inputs to mean-variance efficient portfolio construction since the mid-1960s. One can argue how many factors are necessary, but there appears to ...

At the frontiers of theoretical physics, many of the most popular ideas have one thing in common: they begin from a mathematical framework that seeks to explain more things than our currently ...