THIS is a philosophical thesis by a writer who is really familiar with the subject of non-Euclidean geometry, and as such it is well worth reading. The first three chapters are historical; the ...

In February, I wrote about Euclid's parallel postulate, the black sheep of the big, happy family of definitions, postulates, and axioms that make up the foundations of Euclidean geometry. I included ...

Hyperbolic geometry studies spaces of constant negative curvature, where the parallel postulate is replaced and geodesics exhibit exponential divergence. This framework underpins a rich theory of ...

Science and maths skills are widely celebrated as keys to economic and technological progress, but abstract mathematics may seem bafflingly far from industrial optimisation or medical imaging. Pure ...