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A Victory for Dark Matter in a Galaxy Without Any
Paradoxically, a small galaxy that seems to contain none of the invisible stuff known as “dark matter” may help prove that it exists.
Brains Cling to Old Habits When Learning New Tricks
Using a brain-computer interface, scientists are beginning to learn why learning is hard.
The Infinite Primes and Museum Guard Proofs, Explained
A simple, step-by-step breakdown of two “perfect” math proofs.
Black Hole Echoes Would Reveal Break With Einstein’s Theory
Gravitational waves have opened up new ways to test the properties of black holes — and Einstein’s theory of gravity along with them.
Complex Animals Led to More Oxygen, Says Maverick Theory
For decades, researchers have commonly assumed that higher oxygen levels led to the sudden diversification of animal life 540 million years ago. But one iconoclast argues the opposite: that new animal behaviors raised oxygen levels and remade the environment.
Robert Langlands, Mathematical Visionary, Wins the Abel Prize
Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.
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.
Why Stephen Hawking’s Black Hole Puzzle Keeps Puzzling
The renowned British physicist, who died at 76, left behind a riddle that could eventually lead his successors to the theory of quantum gravity.
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.