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Pierre de Fermat’s Link to a High School Student’s Prime Math Proof
How Fermat’s less famous “little theorem” got mathematicians young and old to play with prime-like Carmichael numbers.
The Hidden Connection That Changed Number Theory
Quadratic reciprocity lurks around many corners in mathematics. By proving it, number theorists reimagined their whole field.
A New Generation of Mathematicians Pushes Prime Number Barriers
New work attacks a long-standing barrier to understanding how prime numbers are distributed.
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.
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.
Why Mathematical Proof Is a Social Compact
Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.
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.
Elliptic Curves Yield Their Secrets in a New Number System
Ana Caraiani and James Newton have extended an important result in number theory to the imaginary realm.