modular forms – 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...

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New Proof Distinguishes Mysterious and Powerful ‘Modular Forms’

Jordana Cepelewicz — Thu, 09 Mar 2023 15:30:08 +0000

In a new proof, a long-neglected mathematical object has finally gotten its moment in the spotlight. At first glance, modular forms — functions whose abundant symmetries have intrigued mathematicians for centuries — seem to have garnered more than enough attention. They crop up in all sorts of problems: They were a key ingredient in Andrew Wiles’ 1994 proof of Fermat’s Last Theorem...

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In Times of Scarcity, War and Peace, a Ukrainian Finds the Magic in Math

Thomas Lin and Erica Klarreich — Tue, 05 Jul 2022 07:18:11 +0000

In late February, just weeks after Maryna Viazovska learned she had won a Fields Medal — the highest honor for a mathematician — Russian tanks and war planes began their assault on Ukraine, her homeland, and Kyiv, her hometown. Viazovska no longer lived in Ukraine, but her family was still there. Her two sisters, a 9-year-old niece and an 8-year-old nephew set out for Switzerland...

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John Conway Solved Mathematical Problems With His Bare Hands

Kevin Hartnett — Mon, 20 Apr 2020 15:50:14 +0000

In modern mathematics, many of the biggest advances are great elaborations of theory. Mathematicians move mountains, but their strength comes from tools, highly sophisticated abstractions that can act like a robotic glove, enhancing the wearer’s strength. John Conway was a throwback, a natural problem-solver whose unassisted feats often left his colleagues stunned. “Every top mathematician was in...

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Out of a Magic Math Function, One Solution to Rule Them All

Erica Klarreich — Mon, 13 May 2019 15:20:26 +0000

Three years ago, Maryna Viazovska, of the Swiss Federal Institute of Technology in Lausanne, dazzled mathematicians by identifying the densest way to pack equal-sized spheres in eight- and 24-dimensional space (the second of these in collaboration with four co-authors). Now, she and her co-authors have proved something even more remarkable: The configurations that solve the sphere-packing problem...

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