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# Geometry

## Latest Articles

### Echoes of Electromagnetism Found in Number Theory

A new magnum opus posits the existence of a hidden mathematical link akin to the connection between electricity and magnetism.

### How Simple Math Moves the Needle

The spatial intuition behind a three-point turn offers an on-ramp to a century-old geometry problem.

### Mathematicians Cross the Line to Get to the Point

A new paper establishes a long-conjectured bound about the size of the overlap between sets of lines and points.

### Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math

Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?

### A Tower of Conjectures That Rests Upon a Needle

On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics.

### The Biggest Smallest Triangle Just Got Smaller

A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square.

### An Old Conjecture Falls, Making Spheres a Lot More Complicated

The telescope conjecture gave mathematicians a handle on ways to map one sphere to another. Now that it has been disproved, the universe of shapes has exploded.

### Mathematicians Solve Long-Standing Coloring Problem

A new result shows how much of the plane can be colored by points that are never exactly one unit apart.

### New Proof Threads the Needle on a Sticky Geometry Problem

A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures.