EmbeddingGemma 2: an open, lightweight multimodal embedding model
deepmind.google·6d ago
AI Engineering
Hacker News·Sep 10·5 min read
The part of Navier-Stokes no one is talking about
TL;DR
OpenAI has announced a proof resolving a long-standing question about the Navier-Stokes equations, accompanied by a formal proof in Lean 4. This marks a significant advancement in the use of AI for formalizing complex mathematical proofs.
✦ Why It Matters
Explore Lean 4 for formal proof verification in your mathematical projects today.
Key Takeaways
- Consider using Lean 4 for formal proofs in your work.
- Evaluate the feasibility of formal verification for your algorithms.
- Stay updated on AI advancements in mathematical proofs.
- Explore applications of formal verification in security and contracts.
Full Summary
OpenAI recently announced a formal proof for the Navier-Stokes equations, a fundamental topic in fluid dynamics, using Lean 4, a proof assistant. Traditionally, formalizing mathematical proofs has been a labor-intensive process, estimated to take around 40 hours for a single page of undergraduate material.
Given the complexity of research papers, this could mean over 132,000 hours for a typical 166-page paper. However, OpenAI managed to verify their proof in just 17 hours, representing a four-order-of-magnitude reduction in effort.
This breakthrough not only simplifies the process of formal verification in mathematics but also opens doors for applications in verifying security policies, smart contracts, and mission-critical algorithms. The implications of this work could lead to more reliable systems across various domains.