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# Mathematics

## Latest Articles

### In Highly Connected Networks, There’s Always a Loop

Mathematicians show that graphs of a certain common type must contain a route that visits each point exactly once.

### 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.

### How Failure Has Made Mathematics Stronger

The topologist Danny Calegari discusses the inevitability of disappointment in math, and how to learn from it.

### 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.

### Mathematicians Marvel at ‘Crazy’ Cuts Through Four Dimensions

Topologists prove two new results that bring some order to the confoundingly difficult study of four-dimensional shapes.

### 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.