12 papers
Long-Horizon AI Research for Grothendieck Constant: A Case Study in Human-AI Mathematical Collaboration
Alan Li, Rahul Saha, Anton Xue +4
AI agents are increasingly used in mathematics research, but it is often unclear how to use them effectively. Towards this, we present an extensive case study of how AI was used to…
New Lower and Upper Bounds for the Grothendieck Constant
Rahul Saha, Alan Li, Anton Xue +4
We establish new bounds on the Grothendieck constant : \[ \frac{6π}{11} \le K_G \le \fracπ{2\log(1+\sqrt2)} - 10^{-4}. \] Methodologically, our lower bound approach differs fr…
A Matrix Factorization Approach in Turnstile Streaming
Jan Bulanek, Ravi Kumar, Raghu Meka +2
We define the -point query problem in data streams. Given a fixed matrix , the goal is to maintain a vector under turnstile updates and answer each query with an esti…
Optimal Sparsifiers for Abelian Cayley Graphs
Arpon Basu, Pravesh K. Kothari, Raghu Meka +1
We prove that for every Cayley graph over any finite abelian group , there is a weighted Cayley graph with generators that is a spectral sparsifier f…
From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier
Eric Jiang, Xiao Liang, Yikai Zhang +16
Recent developments in AI for Mathematics (AI4Math), especially Large Language Model (LLM)-driven theorem provers, has achieved remarkable success in formal proof generation for we…
The Grothendieck Constant is Less Than
Alan Li, Rahul Saha, Anton Xue +4
We prove that the Grothendieck constant . This improves on the work of Braverman, Makarychev, Makarychev, and Naor (2011), who proved…