> 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 field’s deepest questions.
> The work is a collaboration between Laurent Fargues of the Institute of Mathematics of Jussieu in Paris and Peter Scholze of the University of Bonn.
> It opens a new front in the long-running “Langlands program,” which seeks to link disparate branches of mathematics — like calculus and geometry — to answer some of the most fundamental questions about numbers.
> The Langlands program is a sprawling research vision that begins with a simple concern: finding solutions to polynomial equations like x2 − 2 = 0 and x4 − 10x2 + 22 = 0.
> “The Langlands program is a network of conjectures that touch upon almost every area of pure mathematics,” said Caraiani.