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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.
Ninth Dedekind Number Found by Two Independent Groups
The numbers count a variety of seemingly unrelated mathematical structures.
New Proof Shows That ‘Expander’ Graphs Synchronize
The proof establishes new conditions that cause connected oscillators to sway in sync.
Mathematicians Solve Long-Standing Coloring Problem
A new result shows how much of the plane can be colored by points that are never exactly one unit apart.
New Proof Threads the Needle on a Sticky Geometry Problem
A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures.