There is a major development reported on the Navier-Stokes equation, driven by AI agents
A couple of thoughts on N-S buzz:
1] Energy and resource expenditure are finite and constrained. AI companies dominate in LLM domains, and not (yet) in the physical 3D domain. That transition will perhaps be a greater leap, but probably the most challenging one. A great bridge built in America does not solve a problem in India, even when we have the complete knowledge and tools to build the bridge. Transferable solutions are easier to transfer in the software domain compared to hardware.
2] Human intervention is still needed. The definition of a scientific problem can be objective, but the pursuit of science (or maths) has to be anchored in the historical, philosophical and sociological setting. Humans will play a dominant role there, and a complete transition towards machines will be of lesser interest to humans.
We are in interesting and exhilarating times driven by AI info-tech, but we must pause to reflect as humans and ask what the implications are on our thinking and living. The answer will be interesting to study.
ps:
Below is the message from the American Mathematical Society, and it puts the humans at the center of this development, which was heartening to read.
“The news today of progress on resolving the Navier–Stokes problem, one of mathematics’ great longstanding challenges concerning the equations that govern the flow of fluids, represents a milestone advance in human knowledge. This story began with Navier, Stokes, Leray, and Ladyzhenskaya and has culminated in the recent breakthroughs of Córdoba and Martínez-Zoroa, then — assisted by new technologies — Alpöge and Buckmaster, with the final steps taken by OpenAI mathematicians. The purpose of mathematics is human understanding, and this achievement, and the process that led to it, will bear fruit for a long time to come.”
Ravi Vakil, President of the AMS
John Meier, CEO of the AMS