Iteris

Iteris: Agentic Research Loops for Computational Mathematics

Iteris is an agentic AI research system designed to tackle open problems in computational mathematics, combining numerical experimentation, adversarial construction, and algorithm design within an automated loop. Applied to two open problems from a Simons Workshop collection, Iteris produced numerical evidence, constructions, and proof drafts that—after expert review—yielded verified results: a phase diagram comparing conjugate gradient vs. randomized coordinate descent, and a counterexample to QR factorization with column pivoting under low coherence. The paper argues that agentic AI can meaningfully participate in mathematical research workflows while human validation remains essential.