Number Theory is one of the oldest branches of modern mathematics. It is motivated by the study of properties of integers and solutions to equations in integers. Many of its problems can be stated ...

Arithmetic dynamics investigates the behaviour of iterated functions—often polynomials or rational maps—over number fields and function fields, while Galois theory provides the framework to analyse ...

Simon Singh likes to work against the grain. He decides to write about a mathematical problem that gained iconic status because of a teasing, 300-year-old note in the margin of a book, but won't seem ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science has been ...

One of the first collaborations Xinyi Yuan and Wei Zhang ever undertook was a trip to the Social Security office. It was the fall of 2004 and the two of them were promising young graduate students in ...

Canadian-American wins ‘maths Nobel’ for the Langlands program, which predicts unexpected connections between different fields Some mathematicians are immortalised by a theorem. Others by a conjecture ...

Science advances by overturning theories, replacing them by better ones. Sometimes the old theories continue to serve as valuable approximations, as with Newton’s laws of motion. Sometimes the older ...

The grandest project in mathematics has received a rare gift, in the form of a mammoth 350-page paper posted in February that will change the way researchers around the world investigate some of the ...

Number theorist Peter Scholze, who became Germany’s youngest ever full professor aged 24, and geometrician Caucher Birkar—a Kurdish refugee—are among the winners of this year’s Fields Medals, the most ...