9 papers
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…
Polynomial towers and inverse Gowers theory for bounded-exponent groups
Asgar Jamneshan, Or Shalom, Terence Tao
In this paper we develop Host--Kra and inverse Gowers theory for abelian groups of bounded exponent. We show that the Host--Kra factors associated with act…
The maximal length of the ErdÅs--Herzog--Piranian lemniscate in high degree
Terence Tao
Let , and let be a monic polynomial of degree . It was conjectured by ErdÅs, Herzog, and Piranian that the maximal length of lemniscate $\{z…
Mathematical exploration and discovery at scale
Bogdan Georgiev, Javier Gómez-Serrano, Terence Tao +1
AlphaEvolve (Novikov et al., 2025) is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary f…
Sum-difference exponents for boundedly many slopes, and rational complexity
Terence Tao
The dimension of Kakeya sets can be bounded using sum-difference exponents $\SD(R;s)$ for various sets of rational slopes and output slope ; the arithmetic Kakeya conjecture…
Dense sets of natural numbers with unusually large least common multiples
Terence Tao
For any constant , we construct a set such that one has $$ \sum_{n \in A: n \leq x} \frac{1}{n} = \exp\left(\left(\frac{C_0}{2}+o(1)\right) (\log\log…