# Iteris: Agentic Research Loops for Computational Mathematics

arXiv: https://arxiv.org/abs/2606.02484 · HTML: https://mlsanity.com/paper/2606.02484/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Educational agents and math problem solving, one of 16 directions in LLM agents and tool use.
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Placed in

- LLM agents and tool use / [Educational agents and math problem solving](https://mlsanity.com/agents/educational-agents-and-math-problem-solving/)

## Builds on (most cited first, 8 of 8)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Towards End-to-End Automation of AI Research](https://mlsanity.com/paper/2606.15497/) (2026)
- [Automated Conjecture Resolution with Formal Verification](https://mlsanity.com/paper/2604.03789/) (2026)
- [Sharp Analysis of Sketch-and-Project Methods via a Connection to Randomized Singular Value Decomposition](https://mlsanity.com/paper/2208.09585/) (2022)
- [Subspace-constrained randomized coordinate descent for linear systems with good low-rank matrix approximations](https://mlsanity.com/paper/2506.09394/) (2025)

## Built on by (most cited first, 3 of 3)

- [VALG: An Agentic System for ML Theory Research](https://mlsanity.com/paper/2608.13060/) (2026)
- [VGPT-RSI for RH-Adjacent Formal Progress: Boundary Certificates, Verified Finite Lagarias Inequalities, and Explicit Failure Localization](https://mlsanity.com/paper/2606.15096/) (2026)
- [Mathematical Discovery in the Wild: AI-Guided Proofs in Banach Space Theory](https://mlsanity.com/paper/2607.17388/) (2026)

## Abstract (arXiv)

Recent advances in large language models and agentic AI systems have enabled significant progress in mathematical discovery, from solving competition problems to tackling research-level conjectures. However, open problems in computational mathematics have received comparatively less attention: research in this area often requires not only proofs but also numerical experimentation, adversarial constructions, and algorithm design. In this paper, we introduce an agentic research system, Iteris, designed for open problems in computational mathematics. We apply Iteris to two open problems from a recent Simons Workshop collection (arXiv:2602.05394). In these case studies, Iteris generated numerical evidence, constructions, and proof drafts that led, after expert review and correction, to verified results. The first result is a phase diagram for the asymptotic comparison between conjugate gradient and randomized coordinate descent on power-law spectra; the second is a counterexample showing that QR factorization with column pivoting can fail to select well-conditioned submatrices even under low coherence. These case studies suggest that agentic AI systems can participate meaningfully in research workflows for open problems in computational mathematics, while human validation remains essential.