Sergiu Klainerman examines OpenAI’s claim that an internal AI system solved the Navier-Stokes problem, explaining that the announced result addresses a weaker, forced version of the question rather than the unforced equations that underlie physical fluid flow. The machine constructed a smooth external force that drives a fluid from rest to a finite-time blowup - a technically impressive feat requiring coordinated agents and massive computing - and that construction falls within a permissive formulation previously allowed by Charlie Fefferman. However, the forced example leaves untouched the central physical question: whether smooth, unforced fluids can develop singularities. Such singular behavior would contradict the physical assumptions used to derive the equations and has never been observed experimentally or numerically; Klainerman believes unforced singularities may exist but, if so, are likely extremely unstable and undetectable in practice.
The essay argues that recent AI successes chiefly produce intricate examples found by exhaustive, machine-driven searches guided by human ideas, not by independently posing the deep questions or deciding what counts as a meaningful answer. Choosing which problems matter and framing what a genuine mathematical resolution looks like remains the creative core of mathematics and a distinctly human task, so mathematicians are not made obsolete. AI is portrayed as a powerful tool built upon mathematics itself, useful for constructing examples but not for replacing the conceptual work of formulating and validating fundamental theory.
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Open-source framework scikit-decide, combined with aircraft performance models and wind data, can optimize flight paths to reduce jet fuel consumption. This approach has the potential to save airlines thousands of dollars on long-haul flights. (tech.marksblogg.com)
Jean-Pierre Serre is a French mathematician celebrated for his work in algebraic topology, algebraic geometry, and number theory, turning 100 years old. He developed an early passion for mathematics, studying advanced problems in high school and earning top honors in competitions. (mathshistory.st-andrews.ac.uk)
Quantum computers will not instantly solve hard problems by trying all solutions in parallel, contrary to some misconceptions. AI progress over the past decade has confirmed many wild predictions, indicating that the Singularity has already begun in uneven ways. (scottaaronson.blog)
Medieval mathematicians kept their discoveries secret to secure social and professional advantages, often delaying publication. Today, the culture encourages open publication and sharing, though issues with academic publishing persist. (mathoverflow.net)
A new study suggests Venus may have once had a moon that was eventually pulled in and destroyed by the planet. The models indicate that Venus's early rotation and the moon's mass likely caused the moon to spiral into Venus over time. (nautil.us)
Periodic Labs has developed a high-throughput physical lab infrastructure integrated with AI to accelerate scientific discovery. They trained a trillion-parameter model, Periodic Neon, to analyze experimental results, outperforming some frontier models in scientific tasks. (periodic.com)
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