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algebraic geometry
Langlands program
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.
combinatorics
A Mathematician’s Unanticipated Journey Through the Physical World
Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.
Q&A
Conducting the Mathematical Orchestra From the Middle
Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.
Abstractions blog
Mathematicians Will Never Stop Proving the Prime Number Theorem
Why do mathematicians enjoy proving the same results in different ways?
Multimedia
The Map of Mathematics
Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.
geometry
Mathematicians Cut Apart Shapes to Find Pieces of Equations
New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.
foundations of mathematics
With Category Theory, Mathematics Escapes From Equality
Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.
prime numbers
Big Question About Primes Proved in Small Number Systems
The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems.
Q&A
A Movement to Close the Gender Gap in Mathematics
The Brazilian mathematician Carolina Araujo, who calls herself “a bit of an anarchist,” is organizing meetings and building a support network to study and solve the problems women face in mathematics.