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# Mathematics

## New Proof Settles How to Approximate Numbers Like Pi

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer.

## Color Me Polynomial

Polynomials aren’t just exercises in abstraction. They’re good at illuminating structure in surprising places.

## How Randomness Can Make Math Easier

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite.

## Random Surfaces Hide an Intricate Order

Mathematicians have proved that a random process applied to a random surface will yield consistent patterns.

# A 53-Year-Old Network Coloring Conjecture Is Disproved

In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible.

## A Mathematician Whose Only Constant Is Change

Amie Wilkinson searches for exotic examples of the mathematical structures that describe change.

## Why the Proof of Fermat’s Last Theorem Doesn’t Need to Be Enhanced

Decades after the landmark proof of Fermat’s Last Theorem, ideas abound for how to make it even more reliable. But such efforts reflect a deep misunderstanding of what makes the proof so important.