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In the Universe of Equations, Virtually All Are Prime
Equations, like numbers, cannot always be split into simpler elements.
New Proof Shows Infinite Curves Come in Two Types
Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.
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?
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.
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.”
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.”
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.
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.
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.