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A exploration of using LLM chain-of-thought reasoning to tackle the final step of a Navier-Stokes mathematical argument, blending AI-driven reasoning with open problems in fluid dynamics and the Millennium Problems.
A link to Lobsters comments discussing Vi Hart's big post about the Navier-Stokes equations, sparking community discussion about the math and fluid dynamics.
Scientists at the University of Pittsburgh used swimming brine shrimp to demonstrate that the direction of the energy cascade in two-dimensional turbulence can be reversed by a small, properly angled obstacle, challenging a longstanding assumption in fluid dynamics with possible applications in pollution control and drug design.
A single-authored arXiv paper proposes a data-free physics-informed neural operator for level-set interface advection, trained only on transport residuals and a geometric constraint without any reference solutions, outperforming supervised baselines in area conservation while quantifying the accuracy cost of refusing labels.
This paper proposes a minimal transverse-subspace representation that encodes a D-component divergence-free vector field as a D−1-component field, enabling end-to-end divergence-free operator learning without projection or auxiliary potentials, achieving lower error and greater robustness.
OpenAI's claimed solution to the Navier-Stokes problem has sparked controversy, with experts questioning whether it addresses the correct variant of the mathematical problem.
Greg Brockman discusses how OpenAI used 10,000 AI agents to solve the Navier-Stokes problem, highlighting AI's potential to drive scientific discoveries and advance towards AGI.
OpenAI claims to have produced a proof that singularities can form in the Navier-Stokes equations using AI agents. The article discusses the potential impact on AI-driven mathematics research and future scientific methods.
Anima Anandkumar describes a guest post on Terence Tao's blog detailing a method using Physics-Informed Neural Networks to find singular solutions for the Euler equations in fluid dynamics, highlighting its earlier release and broader applications in scientific computing.
A simulation of an evolving vortex using Navier-Stokes equations has gone viral, showcasing impressive fluid dynamics visualization.
This article summarizes the current debates in pro-AI and anti-AI online spaces concerning the use of artificial intelligence in relation to the Navier-Stokes equations.
OpenAI has reportedly used Anthropic's Claude model in their efforts to prove the Navier-Stokes equations, a major unsolved problem in mathematics and physics.
OpenAI announced solving the Navier-Stokes problem using AI, but controversy erupted over accusations of not crediting mathematicians Tristan Buckmaster and Levent Alpöge. This event signals a potential shift in mathematical research with AI's growing influence.
OpenAI announces a solution to the Navier-Stokes Millennium Prize Problem using an advanced internal AI model, proving that smooth three-dimensional fluid motion can develop a singularity in finite time.
This paper examines finite-time blowup with smooth forcing for three-dimensional incompressible Euler, Boussinesq, and IPM equations.
Bubeck denies allegations made by Buckmaster in a dispute concerning the Navier-Stokes equations.
This article is an academic paper by Tristan Buckmaster on the Navier-Stokes equations, likely exploring mathematical solutions or properties.
Buckmaster and Alpoge present a counterexample to Euler's equation, showing that 3D Euler equations can develop singularities in fluid dynamics.
Introduces VATO, a vortex-force-aware transformer operator that improves predictions of unsteady separated aerodynamic flows by reducing errors in velocity, pressure, and vorticity through force-aware neural operator learning.
The paper proposes a self-augmented diffusion guidance method to incorporate physical laws into diffusion models, reducing deviations from true dynamics and enabling faster generation.