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Mathematics The Millennium Problem
Amélie Dupont
[long_description] Amélie Dupont examines how an OpenAI mathematical model resolved the Navier–Stokes Millennium Problem by constructing a smooth external force that drives a fluid from rest to finite-time singularity. Moving from vorticity and vortex stretching to oscillatory disturbances and shear amplification, Dupont explains how unbounded velocity can coexist with finite energy and argues that the construction answers one of the alternatives explicitly permitted in Charles Fefferman’s original formulation of the problem.
Mathematics AI will not make mathematicians obsolete
Sergiu Klainerman
[short_description] Sergiu Klainerman examines what AI’s recent mathematical breakthroughs really mean for mathematicians. Revisiting the Navier–Stokes problem, he distinguishes exhaustive machine search from the deeper human task of deciding which questions matter and what meaningful answers should look like.
Astronomy Twin Universes and Bimetric Gravity
Jean-Pierre Luminet
[short_description] Jean-Pierre Luminet traces twin-universe cosmology from Sakharov to modern bimetric gravity, examining negative mass, quantum-cosmological models, and the Janus model, and argues that ambitious alternatives to standard cosmology must meet the demands of mathematical consistency, stability, and rigorous observational testing.

Recent Articles

Imagine an Organism
David Lobina
[long_description] David J. Lobina takes up Blaise Agüera y Arcas’s What is Intelligence?, which argues that advances in AI have resolved longstanding questions about intelligence, language, and cognition. Drawing on research into infant development, linguistics, and cognitive science, Lobina challenges the book’s identification of intelligence with prediction and its parallels between neural networks and the human brain, arguing instead that modern AI and human cognition operate in fundamentally different ways.
An Abecedary Of Scientific Serendipity
Sheldon Lee Glashow
[long_description] The word serendipity, the art of stumbling on fortunate discoveries while searching for something else, was coined by Horace Walpole in 1754. In an alphabetical tour running from the first aniline dye to the science of fermentation, Nobel laureate Sheldon Lee Glashow recounts twenty-six episodes in which accident and a prepared mind reshaped science, among them Botox, dynamite, gamma-ray bursts, LSD, the microwave oven, pulsars, radioactivity and Viagra.
A Truncated Manuscript
Pierre Schapira
[long_description] In the mid-1980s, an enigmatic document began circulating in French mathematical circles. Entitled Récoltes et Semailles, it was a lengthy, philosophical and deeply personal tract from the elusive mathematician Alexander Grothendieck, by then living in self-imposed seclusion. Now published officially for the first time, Pierre Schapira casts a critical eye over the book and some notable omissions.
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Letters to the Editors

Mechanical Thinking
Sylvia Berryman
reply by Mike Edmunds
[short_description] Could a single implement, such as the Antikythera mechanism, change the understanding of the cosmos? Sylvia Berryman is wary of viewing mechanistic pictures as unique keys to historical worldviews.
Archaeology and Armageddon
Erin Hall
[short_description] In the interwar period, a team from the University of Chicago oversaw an archaeological dig in Megiddo, modern day Israel. The dig’s findings, and shortcomings, proved foundational for archaeology.
A Riddling Mirror of Nature
Paul Keyser
reply by Mike Edmunds
[short_description] When studying the origins and nature of the Antikythera mechanism, Paul Keyser cautions scholars to be mindful not to “retroject things seen or deduced from one era back into times well prior.”
Translating Theory into Technology
Paul Cartledge
reply by Mike Edmunds
[short_description] Paul Cartledge describes how the discovery of the Antikythera mechanism has challenged long-held views about the ability of Greek scholars in antiquity to translate theory into technology.
The First Computer
Kyriakos Efstathiou
reply by Mike Edmunds
[short_description] Was the Antikythera mechanism the first computer in world history? Kyriakos Efstathiou makes the case for the predictive powers of the device, which have now been tested in detail.
Neither Denouncing nor Celebrating
Richard Noakes
reply by David Kordahl
[short_description] Is scientific advancement entrapped by its historical context, or could history be the driving force behind such progress? Richard Noakes and David Kordahl discuss.
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From the Archives
State of the Union
Michael Fumento
[long_description] Is fusion really the energy of the future? Michael Fumento explores some of the many false starts in the development of controlled nuclear fusion and considers its current prospects, including inertial and magnetic confinement, inertial electrostatic confinement, and compact reactors.
The Fourth State of Water
Marc Henry
[short_description] What is water that is not ice, liquid, or vapor? Marc Henry explains the unfolding discovery of water’s elusive fourth state, which could bring a revolution for biology and medicine.
From Conception to Kamchatka
Joshua Socolar
[short_description] In The Second Kind of Impossible, Paul Steinhardt tells the story of his first encounters with quasicrystals and his subsequent decades-long search for a naturally formed example.
Divine Medicine
George Scialabba
[short_description] In reviewing A Natural History of Beer by Rob DeSalle & Ian Tattersall, George Scialabba summarizes beer’s story, including its major historical moments, the science of its components, and its future.
The Concept of Self
Neeraja Sankaran
[short_description] In 1960, Macfarlane Burnet became Australia’s second winner of the Nobel Prize for Medicine. Neeraja Sankaran examines his wide body of work and enduring significance, both at home and abroad.
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