The first formal verification was suggested by Gengyi Ponggale.

  It's the first time in the history of the world.

It's just been a big news in the mathematical world.

In September, AI successfully formalized verification of the "Pongaly conjecture" has shocked the mathematical community.

Recently, a top academic team led by Ayush Khaitan, has joined forces.NVIDIA Humanfia teamIt was successful.Thurston geometrical conjectureThe full Lean formalization!

Hamilton-Perelman's "Proof of the Century" is hundreds of pages long and can be seen for years by even the best anthropologists.

Following the famous Pongaly conjecture in September this year, it was finally made into a line of code with the help of AI.

47.7 million lines of code in just about two weeks.

This is another milestone in the history of mathematics and marks the beginning of the era of AI-assisted high-level geometry analysis.

AI-assisted formalized mathematics has officially killed the "no man's land" in the deepest levels of human geometry.

If someone told you that a team had written 4.7 million lines of modern mathematical code in two weeks without a single error, you'd think he was crazy.

But that's exactly what just happened.

Jared Duker Lichtman, assistant professor of mathematics at Stanford University, recently shouted:

It's really amazing work.

Poincaré proved to be promoted to complete geometrical conjecture, and all of this is done in Lean!

The results were published by Princeton Mathematicians and AI Scholars.Ayush KhaitanIn his tweet, he introduced the ultra-powerful cross-border lineup.

Look at this list of hardcore teams:

• Bennett Chow (Jubei): Chu Cheng's apprentice, professor of mathematics at the University of California, San Diego, an absolute authority in the field of Ricci flow, and a Thai figure.
• Ziyang Qin and Yuan Liao: absolute leaders in project formalization.
• Ayush Khaitan: A scholar at Princeton University who is the driving force behind the project.
• The NVIDIA Humanfia team (Jui-Hui Chung & Ligeng Zhu): represents the frontline force of the world's most powerful AI computing giant, NVIDIA.

In the collaboration of this super-team, a miracle was born.

Ayush reveals that this proves that there are about 4.7 million lines of code.

In addition to Chow, Liao and Qin's previous work of about 2 million lines of code,The new 2.7 million lines of code were written in about two weeks!

At present, this great project is fully open source on GitHub.

Why are Stanford mathematicians so excited?

We need to know first.Thurston Geometry Guesses the DifficultyThe geometry.

We've all heard of it.「Ponggale speculates」 。

It explores: if all the closed curves in a three-dimensional space can shrink to a point, is that space necessarily equal to a three-dimensional sphere?

Between 2002 and 2003, Russian mathematical genius Gregory Perelman was born in Yokohama, Japan, who proved Pongaly's conjecture with three pre-print papers, and subsequently refused to accept a million-dollar prize.

But Pongaly's conjecture is actually a grand blueprint for the "corner of the iceberg" -- a blueprint called Thurston's geometrical conjecture.。

In other words, Pongaly's conjecture is to teach you how to identify a "circle", and Thurston's geometric conjecture is to give the entire three-dimensional universe a "cycle table of elements".

It states that any three-dimensional fluid can eventually be precisely cut into several pieces. More importantly, each piece must belong to one of the eight standard geometrical structures.

At the time, Perelman was proving Pongley's conjecture by proving Thurston's geometrical conjecture.

He used a tactic called「Ricci flow and surgical theory」 。

It's like using a "geometric wrestling" (Ricci flow equation) to flatten the distorted space.

This theory is so profound that it took two or three years for even the world's top ten mathematicians to fully validate Perelman's proof.

And today, a group of great university students and engineers have put this theory of the pinnacle of human intelligence into the minds of computers.

The complete Lean proof of Thurston's geometric conjecture means that machines already have the ability to process advanced differential geometry, topology, and partial differential equations.

The machines officially killed the "no man's land" of high-level geometry.

If you open a GitHub repository called differential-geometry, you're going to have a massive "hardcore attack".

That's one.It was built in machine language.「The modern micro-geometric digital wall」。

In Lean's interactive proof of theorem, the computer doesn't understand what is "obviously possible", it recognizes only the most basic logical axioms. In order for the machine to understand Thurston's geometric conjecture, the team must start from scratch and define the rules of the entire universe in code.

In terms of the technical details of the warehouse, the team's hard core filled in a large number of missing basic building blocks in the official Lean mathematics library (Mathlib).

They're rebuilding from the ground up.The Geometry of Le Mans。

The code defines extremely complex fluid types such as manifolds, tangent bundles, tensor fields, and Riemannian metrics.

The team used rigorous generic programming to allow the machine to finally "know" what space is curved.

In traditional mathematical papers, the Ricci flow is merely a partial differential equation.。

But in GitHub's warehouse, the team needed thousands of lines of code to pinpoint the existential boundaries of "time-dependent measurement evolution", "local computation of the tension of the Ricci curve", and extremely complex partial differential equations.

Perelman demonstrates that the hardest part of it is being"The theory of surgery".

How to make a "cut" and a "coup" of an abstract space in code?

The team introduced complex topological connectivity and geometric decomposition algorithms into the codebase, transforming the processing of odd points in geometry into a logical tree that can be run step by step by a computer.

The most exciting thing is this set of data: in two weeks, nearly 2.7 million lines of code were added, totaling 4.7 million lines.

In software engineering, a project of 2.7 million runs is enough to keep a senior development team of a dozen people working overtime all year long.

In a lean language where every line of code takes a very long time to compile and validate, two weeks of writing is absolutely impossible with human effort alone!

How did they do it?

The answer is obvious: The NVIDIA Humanfia team has come up with a big model with automated reasoning called "reduction impact".

Invidia not only provides the most powerful computing capabilities on the planet, but they are exploring how AI can directly support cutting-edge basic scientific research.

Although all the details of AI generated have not yet been officially disclosed, an explosion in the amount of code over a short period of time can be deduced from the evidence of this "industrialisation" pipeline.

Top mathematicians such as Chow, Liao, and Qin were responsible for drawing "tactical maps", breaking down huge geometrical conjectures into thousands of arguments and sub-objectives.

Using LLM and automated scripts, the NVIDIA team delivers a huge amount of underlying proof of code based on human-provided contexts, complementing complex algebraic derivations and boundary conditions.

Finally, all the code is sent to the Lean compiler for a relentless "logical quality check" without having to rewrite it until the green light comes on.

It's not just a big thing in mathematics, it's an absolute focus in the history of AI evolution!

Current big language models still exist as "illusions" in complex long chain logical reasoning, and the ultimate weapon for solving big model logical flaws is mathematical formalization.

If AI could master the production of Lean code to prove the peak of human intelligence of "Shurst's geometrical conjecture", it would be only one step away from "setting up new conjectures and proving them".

The complete formalization of Thurston's geometrical conjecture was not merely the completion of a difficult "code translation". It left a valuable digital treasure to the world.

Through the differential-geometry project on GitHub, the team left a database of differential geometry codes for all human beings that have been "absolutely verified".

This means that when mathematicians around the world want to study the geometry of multi-dimensional fluids, the geometry of black holes and even the evolution of time and space in a computer, they can directly call upon the libraries they have written!

This is the great work that the former planted trees, and the latter planted them.

From Pongaly's famous speculation over a hundred years ago to Thurston's large blueprint of the three-dimensional universe.

From Perelman's apartment in St. Petersburg to the present day, scholars such as Ayush Khaitan, Hanukkah, Fountain of Youth, and Jubei Power have joined forces with the United Kingdom to make the machine fully "aware" with 4.7 million lines of code.

Humanity's pursuit of truth is like a race against time.

Instead of robbing mathematicians of their dishes, AI gave them a set of "star ships" to explore the universe.

Human progress in solving complex problems will explode at an unprecedented rate.