Recent developments in mathematical AI are focusing on enhancing the capabilities of models to tackle unsolved mathematical problems and formal reasoning tasks. The introduction of benchmarks like HorizonMath allows for the assessment of AI's ability to contribute novel insights in mathematics, with early results indicating that models can propose solutions that improve upon existing knowledge. Concurrently, the Numina-Lean-Agent showcases a shift toward more flexible, general-purpose reasoning systems that can autonomously engage with complex mathematical tasks, demonstrating success in formalizing significant theorems. Additionally, projects like the semi-autonomous formalization of the Vlasov-Maxwell-Landau equilibrium illustrate the efficiency of AI-assisted research, where minimal human intervention yields substantial results. These advancements suggest that AI is not only enhancing mathematical discovery but also streamlining the formal verification process, potentially addressing commercial needs in fields requiring rigorous mathematical proofs and insights, such as finance, engineering, and data science.
Can AI make progress on important, unsolved mathematical problems? Large language models are now capable of sophisticated mathematical and scientific reasoning, but whether they can perform novel rese...
Agentic systems have recently become the dominant paradigm for formal theorem proving, achieving strong performance by coordinating multiple models and tools. However, existing approaches often rely o...
We present a complete Lean 4 formalization of the equilibrium characterization in the Vlasov-Maxwell-Landau (VML) system, which describes the motion of charged plasma. The project demonstrates the ful...
A single two-input gate suffices for all of Boolean logic in digital hardware. No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, sqrt,...
Deep Operator Networks (DeepONets) provide a branch-trunk neural architecture for approximating nonlinear operators acting between function spaces. In the classical operator approximation framework, t...