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number theory

Art for "In the Universe of Equations, Virtually All Are Prime"
number theory

In the Universe of Equations, Virtually All Are Prime

Equations, like numbers, cannot always be split into simpler elements.

abstractions blog

New Proof Shows Infinite Curves Come in Two Types

Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.

number theory

Without a Proof, Mathematicians Wonder How Much Evidence Is Enough

A new statistical model appears to undermine long-held assumptions in number theory. How much should it be trusted when all that really matters is proof?

Art for "Titans of Mathematics Clash Over Epic Proof of ABC Conjecture"
number theory

Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years.

Photo illustration of Akshay Venkatesh
2018 Fields Medal and Nevanlinna Prize Winners

A Number Theorist Who Bridges Math and Time

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 Winners

A Master of Numbers and Shapes Who Is Rewriting Arithmetic

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.”

Crystal diffraction art for "A Chemist Shines Light on a Surprising Prime Number Pattern"
prime numbers

A Chemist Shines Light on a Surprising Prime Number Pattern

When a crystallographer treated prime numbers as a system of particles, the resulting diffraction pattern created a new view of existing conjectures in number theory.

520px photo of Robert Langlands
Abstractions blog

Robert Langlands, Mathematical Visionary, Wins the Abel Prize

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

Jennifer Balakrishnan and Sachi Hashimoto, plotted using SageMath
Abstractions blog

Mathematicians Crack the Cursed Curve

A famously difficult mathematical problem resisted solution for over 40 years. Mathematicians have finally resolved it by following an intuition that links number theory to physics.