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Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math
Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?
An Old Conjecture Falls, Making Spheres a Lot More Complicated
The telescope conjecture gave mathematicians a handle on ways to map one sphere to another. Now that it has been disproved, the universe of shapes has exploded.
Math Proof Draws New Boundaries Around Black Hole Formation
For a half century, mathematicians have tried to define the exact circumstances under which a black hole is destined to exist. A new proof shows how a cube can help answer the question.
Two Students Unravel a Widely Believed Math Conjecture
Mathematicians thought they were on the cusp of proving a conjecture about the ancient structures known as Apollonian circles. But a summer project would lead to its downfall.