Math is always reinventing itself. In the late 19th century, its foundations were still shaky, its definitions and assumptions vague and uncertain. Mathematicians spent decades fixing the problem, setting the course of the modern era. But they never stopped questioning their most basic assumptions. This special issue explores how mathematicians are still renovating and rebuilding the core pillars of their field today.
Intuition breaks down once we’re dealing with the endless. To begin with: Some infinities are bigger than others.
For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.
David Dunning explores the social effects of notation.
Explore the “deplorable evil” that helped transform math.
Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core principles didn’t come easily.
His two theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.
One of the strangest results in mathematics explains how it’s possible to turn one sphere into two identical copies, simply by rearranging its pieces.
Grothendieck is revered in the world of math; outside of it, he’s known for his unusual life, if he’s known at all. But what were his actual mathematical contributions?
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.
