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A simple, step-by-step breakdown of two “perfect” math proofs.

Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.

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

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.

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.

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

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

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

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