Mathematics

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AI will not make mathematicians obsolete

Sergiu Klainerman

[long_description] Recent breakthroughs have fueled fears that artificial intelligence could make mathematicians obsolete. Sergiu Klainerman examines what AI has actually achieved in mathematics, taking the Navier–Stokes problem as a revealing case. However powerful its ability to search for solutions, he argues, AI still depends on human mathematicians to identify the questions that matter—and to determine what a meaningful answer should look like.

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The Millennium Problem

Amélie Dupont

[short_description] Amélie Dupont examines how an OpenAI model resolved the Navier–Stokes Millennium Problem. Tracing vortex stretching, singularity formation, and external forcing, she explains how the construction satisfies one of the alternatives allowed by the original problem.

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A Truncated Manuscript

Pierre Schapira

[short_description] In the mid-1980s, an enigmatic document began circulating in French mathematical circles. Pierre Schapira casts a critical eye over Alexander Grothendieck's Récoltes et Semailles, now published officially for the first time.

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Reflections on an Essay by Wigner

Sergiu Klainerman

[short_description] In a new essay, Sergiu Klainerman retraces the development of modern mathematics, unexpected consequences in physics, and the perennial question of whether mathematics is itself a science.

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A Christmas Chrestomathy

The Editors

[short_description] As the year draws to a close, we are delighted to present our second annual Christmas Chrestomathy, highlighting the essays that best represent our aims, ambitions, attitudes, and even our animadversions.

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The Game of Life

Daniel Kleitman

[short_description] The late John Horton Conway had a gift for making complicated mathematics appear simple. His contributions included a solution for the major problem of group theory and the concept of surreal numbers.

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At Lunch with Freeman Dyson

William Press

[short_description] The prisoner’s dilemma, played once, involves limited strategy. But consider the iterated prisoner’s dilemma. Using information from the previous plays, each player can try to outwit their accomplice.

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Exponential Growth

Sheldon Lee Glashow

[short_description] Exponential growth features frequently in epidemiological projections. Because of carelessness or ignorance, its implications can be easily, and sometimes grievously, underestimated.

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A Gentle Giant

Robert MacLean Losee

[short_description] Claude Shannon was an unmatched problem-solver, whether in electrical engineering, mathematics, or cryptography, but he is chiefly implicated in the creation of information theory.

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Points and Lines

Daniel Kleitman

[short_description] In Forbidden Configurations in Discrete Geometry, David Eppstein examines simple problems in plain geometry. Although most of the problems are relatively easy to grasp, general solutions are unknown.

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The Unity of Partial Differential Equations

Sergiu Klainerman & Jean-Michel Kantor

[short_description] Sergiu Klainerman is interviewed about his education in Romania; his interest in partial differential equations, general relativity, fluid mechanics; and his expectations for research in the future.

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A Remembrance

David Campbell

[short_description] On June 30, 2019, the physicist Mitchell Feigenbaum died in New York City at the age of 74. His friend and colleague David Campbell offers this tribute to Feigenbaum’s life and work.

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