Equiangular lines are an elemental part of geometry. Mathematicians have discovered a tighter limit on the number of such lines that exist in every dimension.

# Mathematics

### How to Quantify (and Fight) Gerrymandering

Powerful new quantitative tools are now available to combat partisan bias in the drawing of voting districts.

### Quantum Questions Inspire New Math

In order to fully understand the quantum world, we may have to develop a new realm of mathematics.

### A Long-Sought Proof, Found and Almost Lost

When a German retiree proved a famous long-standing mathematical conjecture, the response was underwhelming.

### New Number Systems Seek Their Lost Primes

For centuries, mathematicians tried to solve problems by adding new values to the usual numbers. Now they’re investigating the unintended consequences of that tinkering.

### In Mathematics, ‘You Cannot Be Lied To’

For Sylvia Serfaty, mathematics is all about truth and beauty and building scientific and human connections.

### A Fight to Fix Geometry’s Foundations

When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry.

### To Live Your Best Life, Do Mathematics

The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them.

### 3-D Fractals Offer Clues to Complex Systems

By folding fractals into 3-D objects, a mathematical duo hopes to gain new insight into simple equations.

### Strange Numbers Found in Particle Collisions

An unexpected connection has emerged between the results of physics experiments and an important, seemingly unrelated set of numbers in pure mathematics.