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Echoes of Electromagnetism Found in Number Theory
A new magnum opus posits the existence of a hidden mathematical link akin to the connection between electricity and magnetism.
How Simple Math Moves the Needle
The spatial intuition behind a three-point turn offers an on-ramp to a century-old geometry problem.
Mathematicians Cross the Line to Get to the Point
A new paper establishes a long-conjectured bound about the size of the overlap between sets of lines and points.
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?
A Tower of Conjectures That Rests Upon a Needle
On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics.
The Biggest Smallest Triangle Just Got Smaller
A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square.
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.
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.