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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?
New Proof Distinguishes Mysterious and Powerful ‘Modular Forms’
Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical physics.
Probability and Number Theory Collide — in a Moment
Mathematicians are taking ideas developed to study random numbers and applying them to a broad range of categories.
Mathematicians Crack a Simple but Stubborn Class of Equations
Ever since Archimedes, mathematicians have been fascinated by equations that involve a difference between squares. Now two mathematicians have proven how often these equations have solutions, concluding a decades-old quest.
New Shape Opens ‘Wormhole’ Between Numbers and Geometry
Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program.
Mathematician Disproves 80-Year-Old Algebra Conjecture
Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses.
The ‘Useless’ Perspective That Transformed Mathematics
Representation theory was initially dismissed. Today, it’s central to much of mathematics.