Automorphisms such as this are the 'fearless symmetries' of the title of Avner Ash and Robert Gross's book. They can be thought of as symmetries because they are transformations of a mathematical ...

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them. Problems in ...

Complex numbers seem to have an almost mystical aura surrounding them. Perhaps it’s because of the terminology used for them – for example, they have a ‘real part’ and an ‘imaginary part’, and they ...