Eclipse Research Explores Autoformalization and the Future of Mathematical Discovery Inspired by Work from Founder Neel Somani

SAN FRANCISCO, March 5, 2026 /PRNewswire/ -- Eclipse, a blockchain infrastructure platform founded by computer scientist Neel Somani, has released new insights into the growing role of artificial intelligence in mathematical discovery. The research initiative examines how advanced AI systems can assist mathematicians in solving complex problems through a process known as autoformalization, the conversion of human-readable proofs into machine-verifiable mathematical formats.

According to Eclipse, the exploration builds on an experimental initiative inspired by Somani's work in artificial intelligence and mathematical reasoning. The project, known internally as GPT-Erdos, involved a team of undergraduate researchers applying advanced AI models to open mathematical problems originally posed by the prolific mathematician Paul Erdős.

The experiment utilized cutting-edge AI tools, including large language models and research-focused reasoning systems, to analyze unsolved conjectures. Eclipse reports that the initiative produced several notable outcomes, including partial solutions, rediscoveries of previously undocumented results, and new perspectives on existing mathematical techniques.

Beyond the mathematical results themselves, Eclipse says the initiative revealed important insights into how human researchers define discovery and novelty. As AI systems increasingly generate mathematical proofs and reasoning chains, the traditional boundaries between rediscovery, incremental improvement, and genuine innovation are becoming less clear.

One of the key observations highlighted by Eclipse researchers involves the concept of underspecification in mathematical problems. AI-generated proofs frequently satisfy formal requirements while diverging from human expectations about what constitutes a meaningful solution.

During the GPT-Erdos experiment, Eclipse researchers observed instances where AI systems produced valid solutions using known methods or rediscovered approaches that had been informally explored but not formally documented. These outcomes illustrate how AI can expose ambiguities in how mathematicians define success, novelty, and originality.

According to Eclipse, these findings suggest that many apparent "failures" of AI reasoning systems are actually failures of specification, where a model technically solves a problem but does not align with human interpretations of significance or novelty.

The research also highlights a broader debate within the mathematical community: how to determine whether a proof represents a genuine advance.

Eclipse notes that mathematicians have historically relied on intuition and consensus to judge novelty. However, as AI-generated proofs become more common, the need for clearer definitions may grow. One potential approach discussed by Eclipse researchers involves measuring the complexity required to express a proof. Under such a framework, results that merely recombine existing theorems might be considered derivative, while those requiring new theoretical structures could qualify as true discoveries.

Another insight emerging from the research concerns the human concept of "interestingness." Human mathematicians often select problems based on intuition about their potential significance, difficulty, or aesthetic value.

According to Eclipse, large language models currently lack this type of intuition. While AI systems can generate solutions or explore large search spaces, they cannot independently determine which problems may unlock broader scientific breakthroughs.

Eclipse researchers suggest that this limitation reveals how deeply human judgment influences scientific progress. Concepts such as importance, curiosity, and intellectual beauty—while rarely formalized—serve as essential guides in research.

Eclipse also highlights the practical implications of autoformalization beyond theoretical mathematics. In fields such as blockchain infrastructure, quantitative finance, and distributed systems, provably correct software is essential.

The rapid growth of AI-assisted software development has increased the volume of generated code, creating challenges for traditional human review processes. Eclipse notes that autoformalization techniques could enable formal verification systems capable of mathematically proving the reliability of software at scale.

By combining AI-generated reasoning with formal verification frameworks, developers may eventually be able to guarantee properties such as memory safety, security constraints, and protocol correctness.

Looking ahead, Eclipse researchers say one of the most promising directions involves developing tools that measure how close a mathematical proof is to completion.

Current formal verification systems operate in binary terms—a proof either verifies or it does not. However, scientific discovery often unfolds gradually, with partial insights guiding future breakthroughs.

Eclipse is exploring approaches that could introduce new metrics for "closeness," allowing AI systems to identify promising proof paths even when a fully formalized result has not yet been achieved.

According to Eclipse, the intersection of artificial intelligence and formal mathematics may fundamentally reshape how research is conducted. Rather than replacing human mathematicians, AI systems may act as collaborators capable of exploring vast conceptual spaces and rapidly verifying complex reasoning.

The company notes that initiatives inspired by founder Neel Somani's work highlight how emerging technologies can transform both decentralized systems and academic research. As AI-assisted proof generation and autoformalization mature, the practice of mathematics may increasingly shift toward conceptual exploration supported by machine verification.

About Eclipse

Eclipse is a blockchain infrastructure platform focused on advancing decentralized technology through high-performance architecture, cryptographic research, and scalable systems design. Founded by computer scientist Neel Somani, the company explores the intersection of distributed systems, artificial intelligence, and formal verification to develop secure and reliable digital infrastructure.

Media Contact
Neel Somani, Eclipse Layer 2 Founder
Berkley, California
email: neeljaysomani@gmail.com

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