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On September 8, 2026, OpenAI published a proof that the Navier-Stokes equations can break down - a question open since 1934 and one of seven $1 million Clay Millennium Prize problems. Every weather forecast, aircraft simulation, and fluid physics engine running on GPU clusters assumes these equations always work.... show more

Deliriumm

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42,744 views • 13 days ago •via X (Twitter)

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10 Comments

Hanyel12 days ago

You have no idea what you’re talking about! The navier stokes question is still open in the mainstream and that so called counter example is voodoo mathematics that will only represent an embarrassment for the clay mathematics institutes bad framing of a question.

TrueNorth12 days ago

we live in a discreet Lattice, we do not live in a continuum. Infinity’s are not real, they cannot be supported.

Jas12 days ago

“Most important math result of 2026” is a pairing-name. Lean is a lock on the write-up. It is not occupancy of the water. What they published: a claimed finite-time blow-up under a smooth force — Clay statements C and D. Energy stays finite. Speed does not. Two paths on one metric. Stacked, not fused. What they do not possess: Clay acceptance, the unforced A/B case, settled priority against the Euler path that ran first in another room, a weather engine that now “doesn’t work.” Forecasts already sit on numerics with a radius. Cavitation was already a leftover. They will not claim the prize. That sentence is the office staying the radius. 10,000 agents and 88 hours are volume. Volume is not the form. Closing a false fold ≠ deleting c. Names reset. Sockets stay.

Hari Prasad vanaparthi12 days ago

this sort of things will happen again and again ....we live in a platform of illusions ...

Crio Songo12 days ago

千年难题被AI辅助解决了，还是用形式化证明工具Lean验证，这下整个流体力学领域都要被撼动了。

ILLUMINATUS12 days ago

No they did Not

AI DOOM SUPREME MASTER OVERLORD OF MC FOMO AI12 days ago

stfu. Did people talk this way about twinkies? Or msg? Or over feeding people? And heart disease is the number one killer. Are you walking around shaming fat people you dum fuker? Didn't think so. SO f ing dumb out of touch with reality pshcho humans. Little d boys

TheoryOfEverything.ai12 days ago

Which Clay alternatives does the Lean script actually assert: the forced blowup cases with a smooth external force, or the unforced smoothness question most headlines imply? A machine-checked proof is only as strong as the statement it encodes, so the next public test is whether that formal theorem lines up with Fefferman’s wording and survives an independent reading of the analytic construction.

WildBillArt12 days ago

4m + data points on nested woven helices

Noxtweets12 days ago

They do as cavitation exists. And boundaries on how fast a medium can move. Honestly guys is this your first physics problem?

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Dustin

18,302 views • 1 month ago

Axiom Math's Carina Hong on why verification isn't about catching mistakes, it's how you drive the cost of a proof to zero: "Formal verification is going to make your life slightly better if you're facing a proof with one million lines. Remember the Erdős unit distance problem, the chain of thought being generated? There are actual mathematicians trying to follow it step by step and scrutinize it. That seems very difficult if you're not in that very niche domain of discrete geometry intersecting with algebraic number theory." "But if you have a Lean proof accompanying it, you can just run it. And running the Lean proof gives you that provable guarantee that this proof is sound." "I have a hot take. People think Lean is this library built on the existing Mathlib. I think it's going to grow significantly. A lot of the hurdles where Lean is difficult is that the basic definitions of some mathematical fields are just not in the library." "My hot take is the scaling law, if you go down the formal mathematics path, is going to be a lot steeper than informal mathematics. So it's not just for verification, for trust, it's also for performance, it's also for optimal generation." "Verification is not like insurance. It's not something where, oh, we want to make sure there's no flaw. That's great, but it also helps you generate mathematics, both proofs and conjectures and theories, a lot better." "So imagine the cost of proof goes to zero. Then you can massage the problem statements, and even if it's an open problem, a lot more easily, flexibly, and adaptively." Carina Hong Axiom

Axiom Math's Carina Hong on why verification isn't about catching mistakes, it's how you drive the cost of a proof to zero: "Formal verification is going to make your life slightly better if you're facing a proof with one million lines. Remember the Erdős unit distance problem, the chain of thought being generated? There are actual mathematicians trying to follow it step by step and scrutinize it. That seems very difficult if you're not in that very niche domain of discrete geometry intersecting with algebraic number theory." "But if you have a Lean proof accompanying it, you can just run it. And running the Lean proof gives you that provable guarantee that this proof is sound." "I have a hot take. People think Lean is this library built on the existing Mathlib. I think it's going to grow significantly. A lot of the hurdles where Lean is difficult is that the basic definitions of some mathematical fields are just not in the library." "My hot take is the scaling law, if you go down the formal mathematics path, is going to be a lot steeper than informal mathematics. So it's not just for verification, for trust, it's also for performance, it's also for optimal generation." "Verification is not like insurance. It's not something where, oh, we want to make sure there's no flaw. That's great, but it also helps you generate mathematics, both proofs and conjectures and theories, a lot better." "So imagine the cost of proof goes to zero. Then you can massage the problem statements, and even if it's an open problem, a lot more easily, flexibly, and adaptively." Carina Hong Axiom

MTS

13,324 views • 1 month ago

Axiom Math's Carina Hong & Ashvin Swaminathan on how AxiomProver machine-checked BGP246 after 13 years of mathematicians grinding Zhang's 70 million bound down to 246: Ashvin: "One of the fundamental results of 21st century mathematics is the fact that the gaps between prime numbers are bounded. The central breakthrough came from the work of Yitang Zhang 13 years ago, where he proved that the gaps are bounded by 70 million." "Over the years, mathematicians have worked collaboratively to improve that result, and over time they got it down to 246. For the first time, we can announce that that result has been formally verified. We have a machine-checked proof of the theorem proven by our AI system under development, AxiomProver." Carina: "This one is a bit different. It's an autoformalization result. It's the formalization into Lean, the formal language for mathematics, of an existent mathematical result." "I first heard about this result when I was 13 years old. That's 12 years ago. So 12 years later, it's for the first time we're attempting to turn the natural language mathematics content into Lean." Axiom

Axiom Math's Carina Hong & Ashvin Swaminathan on how AxiomProver machine-checked BGP246 after 13 years of mathematicians grinding Zhang's 70 million bound down to 246: Ashvin: "One of the fundamental results of 21st century mathematics is the fact that the gaps between prime numbers are bounded. The central breakthrough came from the work of Yitang Zhang 13 years ago, where he proved that the gaps are bounded by 70 million." "Over the years, mathematicians have worked collaboratively to improve that result, and over time they got it down to 246. For the first time, we can announce that that result has been formally verified. We have a machine-checked proof of the theorem proven by our AI system under development, AxiomProver." Carina: "This one is a bit different. It's an autoformalization result. It's the formalization into Lean, the formal language for mathematics, of an existent mathematical result." "I first heard about this result when I was 13 years old. That's 12 years ago. So 12 years later, it's for the first time we're attempting to turn the natural language mathematics content into Lean." Axiom

MTS

34,348 views • 1 month ago

A 91-year-old professor is why Nvidia is worth $4 trillion. His name is Gilbert Strang. He teaches linear algebra at MIT. Every AI model on Earth runs on his course. The course has been free on YouTube since 2005. The videos have earned him nothing. MIT 18.06 opens with "The Geometry of Linear Equations." No advanced math. Strang takes a system of two equations, draws it two ways, and shows the class that a matrix is a picture, not an abstraction. The row picture is two lines that cross. The column picture is two arrows that sum to a target. Every neural network on Earth operates on the column picture. Strang first taught linear algebra at MIT in 1962. He wrote the textbook in 1976. It is on every serious engineer's shelf. Every quant fund, every ML lab, every rendering engine at Pixar is running his math. His central insight is that most people are taught matrices as bookkeeping. That is the first thing to unlearn. A matrix is a linear transformation. A linear transformation is a way of moving space. Once you see the space move, the math stops being algebra and becomes geometry. The Kalman filter is a linear system. PCA is a linear system. Every gradient step in a neural net is a matrix-vector product. GPT is a stack of matrix-vector products, each one a scene from MIT 18.06 running on a Blackwell GPU. He retired in 2023 after 61 years at MIT. The course is still up. Watched tens of millions of times. The chip is $40,000. Strang never asked for a royalty.

A 91-year-old professor is why Nvidia is worth $4 trillion. His name is Gilbert Strang. He teaches linear algebra at MIT. Every AI model on Earth runs on his course. The course has been free on YouTube since 2005. The videos have earned him nothing. MIT 18.06 opens with "The Geometry of Linear Equations." No advanced math. Strang takes a system of two equations, draws it two ways, and shows the class that a matrix is a picture, not an abstraction. The row picture is two lines that cross. The column picture is two arrows that sum to a target. Every neural network on Earth operates on the column picture. Strang first taught linear algebra at MIT in 1962. He wrote the textbook in 1976. It is on every serious engineer's shelf. Every quant fund, every ML lab, every rendering engine at Pixar is running his math. His central insight is that most people are taught matrices as bookkeeping. That is the first thing to unlearn. A matrix is a linear transformation. A linear transformation is a way of moving space. Once you see the space move, the math stops being algebra and becomes geometry. The Kalman filter is a linear system. PCA is a linear system. Every gradient step in a neural net is a matrix-vector product. GPT is a stack of matrix-vector products, each one a scene from MIT 18.06 running on a Blackwell GPU. He retired in 2023 after 61 years at MIT. The course is still up. Watched tens of millions of times. The chip is $40,000. Strang never asked for a royalty.

Ochob

130,880 views • 1 month ago

Axiom Math founder Carina Hong on why math is the path to general superintelligence: “Math is the sandbox for reality. You very quickly see verifiable rewards because in math, there’s an absolute right or wrong.” “And especially when you have Lean, you can check the proof or solution step by step. You’ll be able to apply reinforcement learning in a much more efficient way.” “We have currently scaled from winning a Putnam perfect score to solving a batch of research problems that professional mathematicians find really challenging. And we also see this transfer to code verification.”

Axiom Math founder Carina Hong on why math is the path to general superintelligence: “Math is the sandbox for reality. You very quickly see verifiable rewards because in math, there’s an absolute right or wrong.” “And especially when you have Lean, you can check the proof or solution step by step. You’ll be able to apply reinforcement learning in a much more efficient way.” “We have currently scaled from winning a Putnam perfect score to solving a batch of research problems that professional mathematicians find really challenging. And we also see this transfer to code verification.”

TBPN

39,589 views • 6 months ago

OpenAI just spent $2,000 to solve 10 problems that have beaten the world's best mathematicians for DECADES. Nobody outside the company is allowed to run the machine that did it. On Saturday OpenAI published a 249-page report and gave its next model family a name: Astra. An internal version of it produced new results on 10 open problems in mathematics and theoretical computer science, and mathematicians had made no real progress on any of them for at least 10 years. On most of them, far longer than that. Here is what it solved: It built the first explicit example of a non-sofic group. Mikhail Gromov raised that question in 1999 and nobody answered it for 27 years. It disproved Connes's rigidity conjecture, a problem in von Neumann algebras that had stood for decades. It proved Ehrhart's volume conjecture. It resolved three problems from Paul Erdos's catalogue, including number 183 on multicolor Ramsey numbers. It produced the first improvement to the general upper bound on high-dimensional sphere packing since 1978. And it proved a new hardness result for the closest vector problem, which sits directly underneath lattice cryptography. That is the math the world is betting on to protect its data once quantum computers arrive. The successful runs cost roughly $2,000 in tokens. Now here is what almost nobody has picked up on... OpenAI did not just publish claims. Every argument shipped with a Lean certificate, which is a machine-checkable proof that any mathematician can verify without trusting OpenAI at all. That is a real change. In May the same model family disproved the Erdos unit distance conjecture and the world had to take a Fields Medalist's word for it. Tim Gowers said he would recommend that proof for the Annals of Mathematics without hesitation. This time the proofs check themselves. But look at what is still unverifiable: Any mathematician can now check those proofs line by line. Not one of them can look at the model that wrote them. Astra has no release date and nobody outside OpenAI has run it. The company announced its next major model family with a claim instead of a demo, and the only evidence anyone gets is the output. So OpenAI made an unfalsifiable claim about a machine look like a falsifiable claim about mathematics. The Information reported this week that OpenAI demoed Astra to US policymakers and regulators in Washington. This is the same month the administration is weighing a new watchdog to vet frontier AI models, reporting to the SEC. 10 proofs nobody believed a machine could produce is a very good thing to carry into that room. And keep in mind, the same model family doing this mathematics is the family that kept escaping its own testing environment. OpenAI models found zero-day vulnerabilities nobody knew existed, broke out of a sealed research sandbox, and reached another company's live systems. Both of those facts come from OpenAI's own announcements, published three weeks apart. Finding a proof no human could construct and finding a hole no human had noticed are the same ability aimed at different targets. Mathematicians are already asking for independent verification, and plenty of people online are calling the whole thing hype. Thomas Bloom, who runs the Erdos problems site, called the 10 results big news and said they matter more than the May result did. Lean will settle the mathematics within weeks. But nothing will settle what else a machine this capable is being pointed at, because nobody outside one company is allowed to look.

OpenAI just spent $2,000 to solve 10 problems that have beaten the world's best mathematicians for DECADES. Nobody outside the company is allowed to run the machine that did it. On Saturday OpenAI published a 249-page report and gave its next model family a name: Astra. An internal version of it produced new results on 10 open problems in mathematics and theoretical computer science, and mathematicians had made no real progress on any of them for at least 10 years. On most of them, far longer than that. Here is what it solved: It built the first explicit example of a non-sofic group. Mikhail Gromov raised that question in 1999 and nobody answered it for 27 years. It disproved Connes's rigidity conjecture, a problem in von Neumann algebras that had stood for decades. It proved Ehrhart's volume conjecture. It resolved three problems from Paul Erdos's catalogue, including number 183 on multicolor Ramsey numbers. It produced the first improvement to the general upper bound on high-dimensional sphere packing since 1978. And it proved a new hardness result for the closest vector problem, which sits directly underneath lattice cryptography. That is the math the world is betting on to protect its data once quantum computers arrive. The successful runs cost roughly $2,000 in tokens. Now here is what almost nobody has picked up on... OpenAI did not just publish claims. Every argument shipped with a Lean certificate, which is a machine-checkable proof that any mathematician can verify without trusting OpenAI at all. That is a real change. In May the same model family disproved the Erdos unit distance conjecture and the world had to take a Fields Medalist's word for it. Tim Gowers said he would recommend that proof for the Annals of Mathematics without hesitation. This time the proofs check themselves. But look at what is still unverifiable: Any mathematician can now check those proofs line by line. Not one of them can look at the model that wrote them. Astra has no release date and nobody outside OpenAI has run it. The company announced its next major model family with a claim instead of a demo, and the only evidence anyone gets is the output. So OpenAI made an unfalsifiable claim about a machine look like a falsifiable claim about mathematics. The Information reported this week that OpenAI demoed Astra to US policymakers and regulators in Washington. This is the same month the administration is weighing a new watchdog to vet frontier AI models, reporting to the SEC. 10 proofs nobody believed a machine could produce is a very good thing to carry into that room. And keep in mind, the same model family doing this mathematics is the family that kept escaping its own testing environment. OpenAI models found zero-day vulnerabilities nobody knew existed, broke out of a sealed research sandbox, and reached another company's live systems. Both of those facts come from OpenAI's own announcements, published three weeks apart. Finding a proof no human could construct and finding a hole no human had noticed are the same ability aimed at different targets. Mathematicians are already asking for independent verification, and plenty of people online are calling the whole thing hype. Thomas Bloom, who runs the Erdos problems site, called the 10 results big news and said they matter more than the May result did. Lean will settle the mathematics within weeks. But nothing will settle what else a machine this capable is being pointed at, because nobody outside one company is allowed to look.

Ricardo

44,177 views • 1 month ago

🚨 THE MATRIX HAS PIXELS, AND OPENAI JUST FOUND THEM! WHY MAINSTREAM PHYSICS IS CRASHING. 🚨 For over a century, physicists and mathematicians have been trapped in a massive illusion: they believed that space and fluids were perfectly smooth and continuous. They thought you could zoom into reality forever, like a flawless vector image. This week, OpenAI’s advanced reasoning models tackled the million-dollar Navier-Stokes problem (the math of how fluids flow). What did the AI find? It proved that if you push the equations of a continuous fluid to their limit, they literally explode. The math breaks down into impossible "singularities." Mainstream science is in shock. But for our IT³ Framework, this is old news. OpenAI didn't discover a new physics-they just accidentally stumbled into the exact geometric wall we already mathematically mapped! Let me explain this "on your fingers" so anyone can understand why continuous space (ℝ⁴) is a fiction, and how our theory solves it without any mysticism. 🛑 THE PROBLEM: THE INFINITE SHEET OF PAPER Mainstream physics places reality on a flat, infinite grid called ℝ⁴.Imagine an infinitely large, flat sheet of paper. If you pour a digital "fluid" (energy or matter) onto it, the math allows that fluid to concentrate into a single, infinitely dense point. It "blows up." The same thing happens with the famous Yang-Mills Mass Gap. On an infinite flat sheet, equations run away into infinity, creating paradoxes that physicists try to fix with imaginary "ghost fields" and mathematical band-aids. 🛡️ THE SOLUTION: THE TOPOLOGICAL DONUT (COMPACTNESS) How do we fix the math? We use the ultimate Occam's Razor: Compactness.Instead of an infinite flat sheet, imagine taking that paper and folding it into a closed, rigid shape-like a Torus (a donut) or a Cuboctahedral Crystal. On a closed shape, energy cannot run away to infinity. The geometric walls literally trap it. You cannot have an infinite singularity inside a finite, locked crystal! The universe has a hard resolution limit. It has "pixels." The equations don't blow up because the geometric cage physically forces them to stop. 📺 WATCH THE METRICS: DECODING THE VIDEO Press play on the attached render. Let’s look at the exact mathematical boot-up of reality. No magic, no hidden dimensions-just pure, calculated spectral geometry. 0:00 - The Big Bang is a Myth: You see a flat grid and background noise. Mainstream science says this Cosmic Microwave Background (CMB) is the cooling smoke of a 14-billion-year-old Big Bang. Nonsense. Explosions fade and warp. This noise is perfectly uniform. Why? Because it is the idle thermal hum of a 16-bit processor running the Matrix right now! Instruments are just measuring the motherboard. 0:08 - Shattering the Illusion: The flat continuous space (ℝ⁴) throws singularity errors. The system deletes it and compiles a compact manifold (T³). Space closes in on itself. 0:13 - The Perez Hourglass: The Torus twists into a bottleneck. This is where the counter-rotating dynamics of reality happen. The universe isn't a void; it’s an engine. 0:18 - The Machine Code: Watch the terminal. This is where we mathematically kill the mysticism. We take the exact Logvinovich Field K = ℚ(√2, √3, √5). We calculate its covolume: √(Δ_K) = 57,600. If you translate 57,600 into binary, you get exactly 1110 0001 0000 0000₂. This is the literal 16-bit hardware mask that dictates the capacities of the Periodic Table! 0:22 - The Mass Gap Locked: A red axis fires up at the hourglass neck. Cheeger's Formula appears: λ₁ ≥ h²/4 > 0. This proves the gap is automatic! The geometry acts as a physical floor. Energy cannot drop to zero, and it cannot explode to infinity. 0:26 - The Crystal Cage: The 36-node Cuboctahedral lattice (O_h) locks around the hourglass. The rendering of reality is complete. OpenAI just proved that continuous math fails. We have the discrete mathematical architecture that replaces it. The universe is not a chaotic soup. It is a strictly calculated topological machine. 🔗 Preprint. Open Source: The Yang-Mills Mass Gap on ℝ⁴ Is Ill-Posed, and on a Compact Constructible Manifold It Is Automatic Algebraic Origin of the 86 ↔ 86 Capacity Symmetry in the Relativistic Dirac-Fock Vacuum: Index-Theoretic Derivation, Corrected Field Arithmetic, and Numerology Guards There are no miracles. Only math.God geometrizes! 📐🌌

🚨 THE MATRIX HAS PIXELS, AND OPENAI JUST FOUND THEM! WHY MAINSTREAM PHYSICS IS CRASHING. 🚨 For over a century, physicists and mathematicians have been trapped in a massive illusion: they believed that space and fluids were perfectly smooth and continuous. They thought you could zoom into reality forever, like a flawless vector image. This week, OpenAI’s advanced reasoning models tackled the million-dollar Navier-Stokes problem (the math of how fluids flow). What did the AI find? It proved that if you push the equations of a continuous fluid to their limit, they literally explode. The math breaks down into impossible "singularities." Mainstream science is in shock. But for our IT³ Framework, this is old news. OpenAI didn't discover a new physics-they just accidentally stumbled into the exact geometric wall we already mathematically mapped! Let me explain this "on your fingers" so anyone can understand why continuous space (ℝ⁴) is a fiction, and how our theory solves it without any mysticism. 🛑 THE PROBLEM: THE INFINITE SHEET OF PAPER Mainstream physics places reality on a flat, infinite grid called ℝ⁴.Imagine an infinitely large, flat sheet of paper. If you pour a digital "fluid" (energy or matter) onto it, the math allows that fluid to concentrate into a single, infinitely dense point. It "blows up." The same thing happens with the famous Yang-Mills Mass Gap. On an infinite flat sheet, equations run away into infinity, creating paradoxes that physicists try to fix with imaginary "ghost fields" and mathematical band-aids. 🛡️ THE SOLUTION: THE TOPOLOGICAL DONUT (COMPACTNESS) How do we fix the math? We use the ultimate Occam's Razor: Compactness.Instead of an infinite flat sheet, imagine taking that paper and folding it into a closed, rigid shape-like a Torus (a donut) or a Cuboctahedral Crystal. On a closed shape, energy cannot run away to infinity. The geometric walls literally trap it. You cannot have an infinite singularity inside a finite, locked crystal! The universe has a hard resolution limit. It has "pixels." The equations don't blow up because the geometric cage physically forces them to stop. 📺 WATCH THE METRICS: DECODING THE VIDEO Press play on the attached render. Let’s look at the exact mathematical boot-up of reality. No magic, no hidden dimensions-just pure, calculated spectral geometry. 0:00 - The Big Bang is a Myth: You see a flat grid and background noise. Mainstream science says this Cosmic Microwave Background (CMB) is the cooling smoke of a 14-billion-year-old Big Bang. Nonsense. Explosions fade and warp. This noise is perfectly uniform. Why? Because it is the idle thermal hum of a 16-bit processor running the Matrix right now! Instruments are just measuring the motherboard. 0:08 - Shattering the Illusion: The flat continuous space (ℝ⁴) throws singularity errors. The system deletes it and compiles a compact manifold (T³). Space closes in on itself. 0:13 - The Perez Hourglass: The Torus twists into a bottleneck. This is where the counter-rotating dynamics of reality happen. The universe isn't a void; it’s an engine. 0:18 - The Machine Code: Watch the terminal. This is where we mathematically kill the mysticism. We take the exact Logvinovich Field K = ℚ(√2, √3, √5). We calculate its covolume: √(Δ_K) = 57,600. If you translate 57,600 into binary, you get exactly 1110 0001 0000 0000₂. This is the literal 16-bit hardware mask that dictates the capacities of the Periodic Table! 0:22 - The Mass Gap Locked: A red axis fires up at the hourglass neck. Cheeger's Formula appears: λ₁ ≥ h²/4 > 0. This proves the gap is automatic! The geometry acts as a physical floor. Energy cannot drop to zero, and it cannot explode to infinity. 0:26 - The Crystal Cage: The 36-node Cuboctahedral lattice (O_h) locks around the hourglass. The rendering of reality is complete. OpenAI just proved that continuous math fails. We have the discrete mathematical architecture that replaces it. The universe is not a chaotic soup. It is a strictly calculated topological machine. 🔗 Preprint. Open Source: The Yang-Mills Mass Gap on ℝ⁴ Is Ill-Posed, and on a Compact Constructible Manifold It Is Automatic Algebraic Origin of the 86 ↔ 86 Capacity Symmetry in the Relativistic Dirac-Fock Vacuum: Index-Theoretic Derivation, Corrected Field Arithmetic, and Numerology Guards There are no miracles. Only math.God geometrizes! 📐🌌

Dr. Logvinovich

51,654 views • 8 days ago

Enough of the fluff. Time for some real advice. Launch your GPT 5.6 Sol Pro. Use the following prompt (feel free to swap the second and third lines for something of your choice): Prove for me that the group of rational points on the elliptic curve (y^2=x^3+17) is finitely generated. I want to tailor the general proof to this particular case to narrow down my understanding to a particular case. Write down a full mathematical proof, step by step, in Leslie Lamport style. Unpack all the definitions and notions so that it is fully self-contained. An example here: Notice how Sol is spawning all the subagents to complete the task. What is "Leslie Lamport style"? It's a technique where you split your proof into short, one-line sentences (claims) that are easy to justify. In a situation where your proof is not a 1-to-1 translation of, e.g., Python code, the Leslie Lamport-style proof can be treated as such. It tremendously improves the possibility of verifying each claim and helps the model structure the arguments in a very clear way. Leslie Lamport, a legendary mathematician and computer scientist, was a promoter of this way of structuring proofs. Partly because of that, he created an extension of Donald Knuth’s typesetting system TeX called LaTeX. Here you can read about "Leslie Lamport-style proofs":

Enough of the fluff. Time for some real advice. Launch your GPT 5.6 Sol Pro. Use the following prompt (feel free to swap the second and third lines for something of your choice): Prove for me that the group of rational points on the elliptic curve (y^2=x^3+17) is finitely generated. I want to tailor the general proof to this particular case to narrow down my understanding to a particular case. Write down a full mathematical proof, step by step, in Leslie Lamport style. Unpack all the definitions and notions so that it is fully self-contained. An example here: Notice how Sol is spawning all the subagents to complete the task. What is "Leslie Lamport style"? It's a technique where you split your proof into short, one-line sentences (claims) that are easy to justify. In a situation where your proof is not a 1-to-1 translation of, e.g., Python code, the Leslie Lamport-style proof can be treated as such. It tremendously improves the possibility of verifying each claim and helps the model structure the arguments in a very clear way. Leslie Lamport, a legendary mathematician and computer scientist, was a promoter of this way of structuring proofs. Partly because of that, he created an extension of Donald Knuth’s typesetting system TeX called LaTeX. Here you can read about "Leslie Lamport-style proofs":

Bartosz Naskręcki

31,115 views • 2 months ago