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# geometry

## Latest Articles

### Monumental Proof Settles Geometric Langlands Conjecture

In work that has been 30 years in the making, mathematicians have proved a major part of a profound mathematical vision called the Langlands program.

### What Can Tiling Patterns Teach Us?

If you cover a surface with tiles, repetitive patterns always emerge — or do they? In this week’s episode, mathematician Natalie Priebe Frank and co-host Janna Levin discuss how recent breakthroughs in tiling can unlock structural secrets in the natural world.

### Why Is This Shape So Terrible to Pack?

Two mathematicians have proved a long-standing conjecture that is a step on the way toward finding the worst shape for packing the plane.

### Mathematicians Attempt to Glimpse Past the Big Bang

By studying the geometry of model space-times, researchers offer alternative views of the universe’s first moments.

### Strangely Curved Shapes Break 50-Year-Old Geometry Conjecture

Mathematicians have disproved a major conjecture about the relationship between curvature and shape.

### A Rosetta Stone for Mathematics

In 1940 André Weil wrote a letter to his sister, Simone, outlining his vision for translating between three distinct areas of mathematics. Eighty years later, it still animates many of the most exciting developments in the field.

### To Pack Spheres Tightly, Mathematicians Throw Them at Random

Four mathematicians broke a 75-year-old record by finding a denser way to pack high-dimensional spheres.

### Geometers Engineer New Tools to Wrangle Spacecraft Orbits

Mathematicians think abstract tools from a field called symplectic geometry might help with planning missions to far-off moons and planets.

### Number of Distances Separating Points Has a New Bound

Mathematicians have struggled to prove Falconer’s Conjecture, a simple, but far-reaching, hypothesis about the distances between points. They’re finally getting close.