Neel Somani Investigates How Artificial Intelligence May Help Verify Mathematical Research

Technology founder and quantitative researcher Neel Somani has spent his career grappling with a deceptively simple question: How can researchers prove that complex systems behave the way they are designed to?

From early research in differential privacy at the University of California, Berkeley, to founding Eclipse, a technology platform that has raised $65 million in funding, Somani has focused on narrowing the gap between theoretical reliability and real-world performance. Now, he is applying that same analytical discipline to artificial intelligence and its potential to solve unsolved mathematical problems.

His latest project, GPT-Erdos, explores what researchers call autoformalization, the process of converting traditional mathematical proofs into formats machines can verify using tools such as Lean and Coq.

In late January, Somani assembled a group of undergraduate researchers to test advanced AI systems against open mathematical problems drawn from the work of prolific mathematician Paul Erdős. The team evaluated multiple platforms, including GPT-5.2 Pro, Deep Research and Harmonic’s Aristotle system, producing several accepted solutions, partial findings and previously undocumented rediscoveries that were later released publicly.

“What I found is that the value of autoformalization goes beyond the raw technology,” Somani said. “By formalizing our work, we expose underspecified concepts that implicitly guide research, including novelty, progress and correctness.”

From Privacy Research To Critical Infrastructure

Somani’s introduction to formal methods began in the computer science lab at UC Berkeley. There, he worked on proving that a machine learning system satisfied differential privacy, a mathematical framework designed to protect individual data within large data sets.

“That was the first serious project I worked on in formal methods,” Somani said. “Instead of assuming a computation was private, the system could demonstrate that privacy mathematically.”

After graduating with degrees in computer science, mathematics and business administration, Somani found that U.S. power markets depend on complex optimization problems that require the use of sophisticated solvers. Math proofs are another extremely hard problem that handwritten algorithms cannot typically solve alone.

The GPT-Erdos project pushed that principle further. Somani said the project’s most valuable insights came from its failures.

“The most common failure is underspecification,” he said. “By formalizing research, you expose assumptions researchers don’t realize they’re making, including how they define novelty, progress and correctness.”

Why Formal Verification Matters

Autoformalization tools force researchers to translate complex reasoning into machine-verifiable steps, reducing ambiguity in the research process.

For the GPT-Erdos project, researchers fed original LaTeX problem statements directly into AI systems and independently reviewed each result using predefined evaluation criteria. The approach eliminated human influence during generation, allowing researchers to better evaluate how AI systems approached unfamiliar problems.

The findings reflected broader trends in artificial intelligence research. Current systems excel at identifying patterns similar to their training data but often struggle when confronting entirely new reasoning challenges.

For Somani, who researches reliability, interpretability, and safety issues in artificial intelligence, understanding those limitations is critical as AI tools expand into high-stakes applications.

Recently, other researchers have taken interest in the same approach. A group of mathematicians has assembled a collection of problems called First Proof, intended to evaluate the capabilities of frontier large language models.

The Broader Reliability Challenge

Across industries ranging from financial markets to data privacy and energy infrastructure, Somani said organizations are grappling with the same fundamental issue: ensuring that increasingly complex automated systems behave as intended.

Formal methods offer one solution by requiring systems to mathematically prove their behavior across all possible scenarios rather than relying solely on testing.

“That approach is becoming increasingly important as artificial intelligence takes on larger decision-making roles,” Somani said. “Verification allows us to understand not just when systems work, but why they work.”

Somani’s earlier research in differential privacy demonstrated this principle. Instead of running repeated tests to determine whether data remained private, formal verification could mathematically guarantee privacy regardless of input.

The GPT-Erdos project applies that same philosophy to mathematical discovery. If artificial intelligence can generate formally verified proofs, Somani said, it could allow machines to serve as more dependable collaborators in scientific and mathematical research.

Beyond his research work, Somani also mentors students and supports scholarship programs aimed at encouraging careers in mathematics and technology.

“Powerful systems are becoming easier to build,” Somani said. “The real challenge is proving they are safe, reliable and worthy of the trust people place in them.”