OpenAI solves decades-old math puzzle

OpenAI said it used thousands of agents to solve the Navier-Stokes existence and smoothness problem, a puzzle that has intrigued mathematicians for decades.

Math has always been an art form

Mathematicians typically follow a thoughtful, deliberate process to develop ideas, resembling artistic exploration akin to inventing a game or puzzle, not racing for quick answers.

Hardy saw math as pattern-making

English mathematician G. H. Hardy wrote in his nineteen forty essay A Mathematician's Apology that a mathematician, like a painter or poet, is a maker of patterns.

“A mathematician, like a painter or poet, is a maker of patterns”

Navier-Stokes equations describe fluid flow

Nineteenth-century scientists developed the Navier-Stokes equations to describe the flow of viscous fluids. Engineers use them to model airflow for airplane design.

Mathematicians loved the puzzle itself

Mathematicians became enamored with the Navier-Stokes equations themselves, not their applications. They pursued answers because of the mathematical richness and puzzle aspect of it.

The puzzle had no practical purpose

The puzzle's solution will not help anybody design a more aerodynamic airplane wing. Mathematicians imagined how the equations would apply in unrealistic, almost science-fiction contexts.

AI used brute force, not understanding

OpenAI approached the proof with brute force, which shortcut the process in a way that threatens to undermine human understanding of the mathematics involved.

The proof lacks transparency and clarity

The one hundred sixty-six-page proof remains under peer review. Mathematicians have criticized OpenAI's lack of transparency in how it arrived at the solution and possible improper attribution.

Nobody understands what happened

Jared Speck, a mathematician at Vanderbilt University, says basically nobody in the mathematics community really understands what is going on with the AI proof.

“basically nobody in my community really understands what's going on”

Mathematicians fear loss of understanding

Juspreet Singh Sandhu signed a declaration titled A Severe Misalignment of AI in Mathematics, warning that mass-producing proofs could destroy fertile ground instead of breathing life into new ideas.

Twenty-five Fields Medal winners signed on

The declaration's initial signatories were twenty-five winners of the Fields Medal, often called the Nobel Prize in mathematics, expressing concern about AI's impact on mathematical culture.

Struggle drives mathematical breakthroughs

Lorenzo Gavassino, a theoretical physicist at the University of Cambridge, says when a calculation becomes discouraging, that is when the greatest progress is possible. Struggle inspires new concepts.

“When a calculation turns out to be harder than expected, to the point of it being discouraging, that is when the greatest progress is possible”

Imaginary numbers came from struggle

Mathematicians invented the imaginary number i in the sixteenth century after generations of trying to solve cubic equations. This gave birth to complex analysis, later used in quantum mechanics.

AI threatens the apprenticeship model

The mathematics community has long relied on a teacher-apprentice structure to discover new ideas sustainably. AI threatens to scoop younger researchers and deprive students of training opportunities.

AI companies built on mathematical foundations

The study of differential equations and complex analysis enabled the invention of lasers for etching computer chips. Neural networks use linear algebra, a field at least as old as the seventeenth century.

Companies may trample their creators

Now that AI models are fed with generations of human insight and trillion-dollar valuations must be sought, companies may very well trample the mathematics community that created their product.