about.

I'm a fourth year undergraduate at Carnegie Mellon University, double majoring in Mathematics and Computer Science with a concurrent master's degree in Mathematics.

My primary line of research is on machine learning for mathematics, and more generally, AI for science. I also study higher category theory, homotopical algebra, and type theory. I'm jointly advised by Prof. Jeremy Avigad, Prof. Sean Welleck, and Prof. Prasad Tetali, and am a researcher in the Hoskinson Center for Formal Mathematics, the Language Technologies Institute, the L3 Lab, and the Institute for Computer-Aided Reasoning in Mathematics. I am the cofounder of Stagira Labs, a research lab focused on using game theory and multi-agent RL to scale AI for scientific discovery. I am also part of the Homotopy Type Theory (HoTT) group and the Higher Category Theory reading group at CMU. Previously, I also worked with Prof. Po-Shen Loh on scaling AI-assisted theorem proving on math competition problems at Expii, and ran The Purple Hand, an anti human trafficking nonprofit.

Recently, I also won the Richard A. Moore Award and was named an ACS Scholar.

My Erdos number is 2.

breaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking news
[Nov 30, 2025]

cLean milestone report released

[Sep 23, 2025]

Named as an ACS Scholar

[Sep 10, 2025]

Public release of Agora v0.1

[Apr 24, 2025]

Won the Richard A. Moore Award in Mathematical Sciences

[Apr 24, 2025]

Presented ImProver at ICLR 2025 in Singapore

[Apr 7, 2025]

Attended the Simons Institute and SLMath joint workshop on AI for Mathematics

breaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking newsbreaking news

research.

My research focuses on automated theorem proving and machine learning for formal mathematics. I'm particularly interested in developing AI systems that can assist mathematicians in discovering and verifying theorems in interactive proof assistants like Lean 4.

My work spans reinforcement learning for proof search, proof optimization techniques, and building tools that make formal verification more accessible to researchers and practitioners. I believe that AI-assisted theorem proving can accelerate mathematical discovery and improve software verification.

ImProver: Agent-Based Automated Proof Optimization

Riyaz Ahuja, Jeremy Avigad, Prasad Tetali, Sean Welleck

ICLR 2025

Agentic proof optimization framework for Lean for the rewriting of undergraduate and competition-level theorems.

ImProver²: Iteratively Self-Improving SLM's for Neurosymbolic Proof Optimization

Riyaz Ahuja, Tate Rowney, Jeremy Avigad, Prasad Tetali, Sean Welleck

In Progress

Generalized RL Pipeline for training proof optimizers for the optimization of research-level Lean theorems at scale, across metrics, and at low cost.

cLean: Verifiable GPU Programming in Lean

Riyaz Ahuja

In Progress

Framework for writing, executing, and verifying the safety and correctness of GPU programs in Lean.

Agora: Market-Based Multi-Agent Automated Mathematical Discovery

Riyaz Ahuja, Alexander Heckett, Shivansh Gour, Alexander Willoughby, Tate Rowney, Ishin Shah, Chris Su

In Progress

Market-based multi-agent mathematical discovery platform for collaborative human-AI research in formal mathematics at scale.

projects.

CohesiveGalois

Proof and formalization that the Shape functor in Cohesive ∞-Topoi is not conservative in Lean

LeanM2

Type bridge and tactics to connect Macaulay2 to Lean for computational algebraic geometry

Whitney-Graustein Theorem

Formalization of the Whitney-Graustein theorem in Lean

Baire Category Theorem

Formalization of the Baire Category theorem and applications in Lean

Keraunos

Autonomous drone swarm navigation and targeting system

Orbisol

Orbital debris tracking and collision avoidance software

other.

talks.

L3

ImProver2

Categorical Logic group

Kripke-Joyal Semantics

Algebraic Geometry group

LeanM2

L3

How to build a (useful) theorem prover

L3

ImProver

Differential topology group

Sard's theorem

past work.

Expii

Edtech platform for gamifying interactive math learning

The Purple Hand

501(c)(3) nonprofit for using data to fight human trafficking