Video Credit: Star Talk
When Deep Thought Meets Deep Blue: Did AI Really "Solve" Navier-Stokes?
There is something fascinating, and perhaps a little unsettling, about the prospect of artificial intelligence solving a mathematical problem that has challenged some of the finest human minds for generations.
Recently, while watching Neil deGrasse Tyson's StarTalk discussion about AI and the Navier–Stokes equations, featuring astrophysicist Mark McLoughlin, I found Neil deGrasse Tyson leaning into his microphone to grapple with a bizarre milestone in modern science: an AI system producing a mathematical proof with fuzzy logic for one of the hardest questions in physics
If AI produces the correct mathematical answer, does that necessarily mean it understands the physical problem it has supposedly solved?
And, more importantly, if the answer is 42, how do we know that the journey leading to 42 is mathematically sound, physically meaningful and not merely a clever manipulation of symbols?
The distinction is important. Mathematics is not simply about arriving at a number or producing a collection of statements that appear logically connected. In physics, mathematics is a language through which we describe nature. A mathematical solution must satisfy the conditions of the problem, and when it represents a physical system, we must also understand what those conditions mean.
The recent AI achievement involving the Navier–Stokes equations makes this distinction particularly interesting.
Continuous Physics vs. Symbolic Logic
The Traditional Physics Route: Physicists treat fluids as smooth, continuous fields described by partial differential equations (PDEs). Solving these equations involves differential calculus, limits, and infinite-dimensional spaces - calculating how continuous quantities like pressure, velocity, and viscosity change seamlessly over time.
The AI's Translation Step: Automated theorem provers (using formal proof systems like Lean) do not perform calculus or simulate fluid movement. Instead, they translate mathematical axioms, theorems, and rules of inference into discrete symbolic structures.
The Core Disconnect
The AI did not "think" in terms of fluid dynamics, turbulence, or geometric intuition. It generated a structured, machine-verified string of logical steps that satisfied the formal requirements of the problem- proving a specific outcome mechanically without having to "feel" or model the continuous physical universe.Final Thoughts: The Future of AI in Theoretical Physics
We are entering a strange era in theoretical science. For centuries, humans used calculus and differential equations as the primary tools to translate physical phenomena into human thought.
AI is showing us that there might be an alternative route to mathematical truth - one paved with discrete set theory, formal logic, and massive combinatorial searches.
If AI gives us the "42" to the Navier–Stokes equations, the math community might accept the check, but physicists will spend the next century trying to figure out what the question actually meant.
