## Latest Articles

### 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.

### Why Mathematical Proof Is a Social Compact

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.

### 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.

### Mathematicians Discover Novel Way to Predict Structure in Graphs

Mathematicians probe the limits of randomness in new work estimating quantities called Ramsey numbers.

### Flow Proof Helps Mathematicians Find Stability in Chaos

A series of new papers describes how to fully characterize key dynamical systems with relatively little data.

### New Proof Finds the ‘Ultimate Instability’ in a Solar System Model

For the first time, mathematicians have proved that planetary orbits in a solar system will always be unstable.

### Mathematicians Find Hidden Structure in a Common Type of Space

In 50 years of searching, mathematicians found only one example of a “subspace design” in a vector space. A new proof reveals that there are infinitely more out there.

### New Proof Distinguishes Mysterious and Powerful ‘Modular Forms’

Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical physics.