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Langlands program

A visualization of the tower formed by the 3-adic numbers
Abstractions blog

An Infinite Universe of Number Systems

October 19, 2020

The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory.

Diagram showing a colorful visualization of the simple Lie group
Abstractions blog

The ‘Useless’ Perspective That Transformed Mathematics

June 9, 2020

Representation theory was initially dismissed. Today, it’s central to much of mathematics.

Langlands program

‘Amazing’ Math Bridge Extended Beyond Fermat’s Last Theorem

April 6, 2020

Mathematicians have figured out how to expand the reach of a mysterious bridge connecting two distant continents in the mathematical world.

Photo illustration of Akshay Venkatesh
2018 Fields Medal and Nevanlinna Prize

A Number Theorist Who Bridges Math and Time

August 1, 2018

Akshay Venkatesh, a former prodigy who struggled with the genius stereotype, has won a Fields Medal for his “profound contributions to an exceptionally broad range of subjects in mathematics.”

Photo of Dr. Peter Scholze
2018 Fields Medal and Nevanlinna Prize

A Master of Numbers and Shapes Who Is Rewriting Arithmetic

August 1, 2018

The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.”

520px photo of Robert Langlands
Abstractions blog

Robert Langlands, Mathematical Visionary, Wins the Abel Prize

March 20, 2018

Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.

Abstractions blog

Handicapping the 2018 Fields Medal

June 28, 2016

Peter Scholze is a favorite to win one of the highest honors in mathematics for his contributions in number theory and geometry.


The Oracle of Arithmetic

June 28, 2016

At 28, Peter Scholze is uncovering deep connections between number theory and geometry.


Math Quartet Joins Forces on Unified Theory

December 8, 2015

A new breakthrough that bridges number theory and geometry is just the latest triumph for a close-knit group of mathematicians.