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.
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 ...
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 ...
In an old Indian parable, six blind men each touch a different part of an elephant. They disagree about what the elephant must look like: Is it smooth or rough? Is it like a snake (so thinks the man ...
One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...
Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong. One of the oldest and simplest ...
Some results have been hidden because they may be inaccessible to you
Show inaccessible results
Feedback