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.

Arithmetic Geometry and Manin's Conjecture Publication Trend The graph below shows the total number of publications each year in Arithmetic Geometry and Manin's Conjecture.

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 ...

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 ...

Mathematicians have illuminated what sets of points can look like if the distances between them are all whole numbers. On its ...

Annals of Mathematics, a distinguished journal of research papers in pure mathematics, was founded in 1884. Annals of Mathematics is published bimonthly with the cooperation of Princeton University ...

D. B. A. Epstein, V. Markovic, The Logarithmic Spiral: A Counterexample to the K = 2 Conjecture, Annals of Mathematics, Second Series, Vol. 161, No. 2 (Mar., 2005 ...

Pierre Deligne netted the prize, one oft he most prestigious in mathematics and worth about $1 million, for proving a deep conjecture about algebraic geometry which has helped to transform number ...

In early 20th-century Paris, there was a boy so mesmerized by math that when his parents took his paper and pencil away, urging him to play, he found a rock and scribbled algebra equations on the ...

Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program. The grandest project in mathematics has ...