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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?
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.
How Math Achieved Transcendence
Transcendental numbers include famous examples like e and π, but it took mathematicians centuries to understand them.
The Simple Geometry That Predicts Molecular Mosaics
By treating molecules as geometric tessellations, scientists devised a new way to forecast how 2D materials might self-assemble.
Math Patterns That Go On Forever but Never Repeat
Simple math can help explain the complexities of the newly discovered aperiodic monotile.