Fermat’s Last Theorem – Quanta Magazine

Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math

Jordana Cepelewicz — Thu, 21 Sep 2023 06:44:56 +0000

“There are five fundamental operations in mathematics,” the German mathematician Martin Eichler supposedly said. “Addition, subtraction, multiplication, division and modular forms.” Part of the joke, of course, is that one of those is not like the others. Modular forms are much more complicated and enigmatic functions, and students don’t typically encounter them until graduate school. But “there...

Source

Elliptic Curves Yield Their Secrets in a New Number System

Kevin Hartnett — Thu, 06 Jul 2023 14:24:50 +0000

Many complicated advances in research mathematics are spurred by a desire to understand some of the simplest questions about numbers. How are prime numbers distributed in the integers? Are there perfect cubes (like 8 = 23 or 27 = 33) that can be written as the sum of two other cubes? More generally, mathematicians might want to solve an equation. But it is often impossible to do so by tinkering...

Source

Can Computers Be Mathematicians?

Steven Strogatz — Wed, 29 Jun 2022 21:05:04 +0000

How do you teach mathematics to an artificial intelligence? AI has already bested humans at problem-solving tasks that include games like chess and Go. But before any task can be tackled by a machine, it must be reinterpreted as directions in a language that computers can understand. For the last few years, researchers and amateurs all over the world have worked together to translate the essential...

Source

The Mathematician Who Delights in Building Bridges

Steve Nadis — Wed, 17 Nov 2021 17:22:13 +0000

For her senior thesis at Princeton University, Ana Caraiani was given a challenging problem from her adviser, the mathematician Andrew Wiles. He’d recently garnered fame for his 1994 proof of Fermat’s Last Theorem, but Caraiani had less luck with her assigned problem. Still, although she ended up making no significant headway, she remained undaunted. “The point of the exercise wasn’t necessarily...

Source

A Number Theorist Who Connects Math to Other Creative Pursuits

Steve Nadis — Thu, 27 May 2021 14:37:45 +0000

“There are many different pathways into mathematics,” said Jordan Ellenberg, a mathematician at the University of Wisconsin, Madison. “There is the stereotype that interest in math displays itself early. That is definitely not true in general. It’s not the universal story — but it is my story.” That account was backed up by a biostatistician at the University of Pennsylvania — his mother...

Source