Nature

Arithmetic Geometry and Manin's Conjecture

Arithmetic geometry is a vibrant field at the intersection of number theory and algebraic geometry, focussing on the study of polynomial equations and the distribution of their rational solutions.
Scientific American

Gerd Faltings, mathematician who proved the Mordell conjecture, wins the Abel Prize at age 71

This year’s Abel Prize, an annual lifetime achievement award for mathematics that is bestowed by the Norwegian Academy of ...
The Conversation

Millennium Prize: the Hodge Conjecture

Arun Ram receives funding from the Australian Research Council. MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in 2000 ...
Wired

‘Nasty’ Geometry Breaks a Decades-Old Tiling Conjecture

They made some progress, re-proving the conjecture in two dimensions using different techniques—ones they hoped would be applicable to the three-dimensional case. But then they hit a wall. “At some ...