The world is on the cusp of abundant autoformalization. This will empower anyone to verify their mathematical ideas more quickly and engage in co-discovery with computers backed by a large, growing foundation of formalized mathematics.
Excited to share that we’re doubling down on @mathematics_inc.
AI is generating more code than ever, but correctness isn’t guaranteed and failures can be catastrophic.
Their agent Gauss delivers a missing primitive for AI: provably correct code and knowledge.
Thrilled to keep working with @jessemhan, @jdlichtman, and the @mathematics_inc team!
It gives the maintainers of the Sphere Packing Project great pleasure to announce a major milestone in the formalization effort: we now have a sorry-free Lean proof of the theorem that the optimal sphere packing in ℝ⁸ is the E₈ lattice packing. (1/9)
@npparikh I haven't worked with either as directly, and my sense is that it still depends a lot on the specific thing you're trying to show -- though linear algebra is probably the most mature of these in general.
I'm excited to share de Finetti's theorem formalized in Lean: three different proofs that infinite exchangeable sequences are conditionally IID.
43k lines across 113 files with 600+ lemmas.
💻 code: https://t.co/thYmw3ANDj
📊 blueprint: https://t.co/GWX9vc9hCT
(1/3)
All three proofs from Kallenberg (2005), each filling different mathlib gaps:
• Reverse martingales
• Mean ergodic theorem machinery
• Elementary L² bounds
Built over 3 months with Claude + GPT with my Skill for Lean 4: https://t.co/TMYbI7zQUV
(2/3)
Computer scientists often look to natural phenomena like the cosmic background radiation in order to obtain truly random sequences — but randomness can only take you so far. Many real-world situations depend on weighted outcomes. https://t.co/WHl0wiBLcq
The fast and efficient generation of random numbers has long been an important challenge. For centuries, games of chance have relied on the roll of a die, the flip of a coin, or the shuffling of cards to bring some randomness into the proceedings @MITEECS https://t.co/kFenrsLBQ6