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Big Advance on Simple-Sounding Math Problem Was a Century in the Making
A new proof about prime numbers illuminates the subtle relationship between addition and multiplication — and raises hopes for progress on the famous abc conjecture.
Elliptic Curve ‘Murmurations’ Found With AI Take Flight
Mathematicians are working to fully explain unusual behaviors uncovered using artificial intelligence.
The Year in Math
Landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.
The Astonishing Behavior of Recursive Sequences
Some strange mathematical sequences are always whole numbers — until they’re not. The puzzling patterns have revealed ties to graph theory and prime numbers, awing mathematicians.
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?
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.
Mathematical Trio Advances Centuries-Old Number Theory Problem
The work — the first-ever limit on how many whole numbers can be written as the sum of two cubed fractions — makes significant headway on “a recurring embarrassment for number theorists.”
A Mathematician Dancing Between Algebra and Geometry
Wei Ho, the first director of the Women and Mathematics program at the Institute for Advanced Study, combines algebra and geometry in her work on an ancient class of curves.
‘Post-Quantum’ Cryptography Scheme Is Cracked on a Laptop
Two researchers have broken an encryption protocol that many saw as a promising defense against the power of quantum computing.