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Portrait of Mathematician Prof. Günter M. Ziegler

In Search of God’s Perfect Proofs

The mathematicians Günter Ziegler and Martin Aigner have spent the past 20 years collecting some of the most beautiful proofs in mathematics.

Photograph of Albert Einstein in his office at the University of Berlin, published in the USA in 1920.
Abstractions blog

How Einstein Lost His Bearings, and With Them, General Relativity

By 1913, Albert Einstein had nearly completed general relativity. But a simple mistake set him on a tortured, two-year reconsideration of his theory. Today, mathematicians still grapple with the issues he confronted.

Animated illustration of a black hole in a cube of jelly
mathematical physics

To Test Einstein’s Equations, Poke a Black Hole

Two teams of researchers have made significant progress toward proving the black hole stability conjecture, a critical mathematical test of Einstein’s theory of general relativity.

520px illustration of a man falling and missing a hay stack to land on.
insights puzzle

Solution: ‘When Probability Meets Real Life’

When our brains don’t have a good intuition for reasoning with numbers, explicit probabilistic thinking can lead to improved decision-making.

520px illustration for scale=free networks
network science

Scant Evidence of Power Laws Found in Real-World Networks

A new study challenges one of the most celebrated and controversial ideas in network science.

520px illustration of a man falling and missing a hay stack to land on.
insights puzzle

When Probability Meets Real Life

When faced with a difficult decision, should you go with your gut or carefully calculate the attendant risks?

520px photo of Gil Kalai
The Future of Quantum Computing

The Argument Against Quantum Computers

The mathematician Gil Kalai believes that quantum computers can’t possibly work, even in principle.

520px illustration for herd immunity
Quantized Academy

How Math (and Vaccines) Keep You Safe From the Flu

Simple math shows how widespread vaccination can disrupt the exponential spread of disease and prevent epidemics.

Illustration: man using rulers stacked on a compass as a telescope
insights puzzle

Solution: ‘Triangulation and Motion Sickness’

A method for estimating distances in sailing and astrophysics helps explain why riding on buses and boats can make us nauseous.