California, US, 4th February 2026, ZEX PR WIRE, For decades, the “Erdős problems”, a collection of over 1,000 mathematical conjectures posed by the legendary Hungarian mathematician Paul Erdős, have served as a rigorous proving ground for the world’s brightest human minds. They range from deceptively simple number theory puzzles to complex combinatorial nightmares.

For a long time, the consensus was that Artificial Intelligence could handle calculation, but not creation. It could crunch numbers, but it couldn’t reason through abstract proofs.

That consensus just shattered.

Over a single weekend, Neel Somani, a software engineer and founder of the blockchain platform Eclipse, utilized OpenAI’s GPT 5.2 Pro to crack open Erdos problems that had remained unsolved for years. This wasn’t a case of a computer searching a database faster than a human; it was a case of an AI generating novel mathematical logic, formalized by a human expert.

We are witnessing a fundamental shift in the epistemological hierarchy of mathematics. The barrier between “human reasoning” and “machine processing” is dissolving, and Somani’s work provides the data to prove it.

The Weekend Win: Cracking Problem #397

Neel Somani, a former quantitative researcher at Citadel with a triple major from UC Berkeley, was stress-testing the reasoning capabilities of the new GPT 5.2 Pro model. He wasn’t looking for a calculator; he was looking for a co-author.

He fed the model Erdos Problem #397. After approximately 15 minutes of “thinking,” the model returned a full solution.

The problem asks for integer solutions to a specific binomial identity. To the layman, it looks like a jumble of variables. To a mathematician, it represents a precise relationship between numbers. The AI proposed that since $a$ can be chosen arbitrarily large, there are infinitely many distinct-index solutions.

Specifically, for an example where $a = 2$, the AI derived that $c = 49$, and the identity becomes:

$$ binom{2}{1} binom{49}{6} = binom{98}{3} binom{1}{1} $$

Somani reviewed the output. It wasn’t just hallucinated gibberish; it was sound logic. He formalized the proof using a tool called Harmonic and submitted it. The result? Accepted by Terence Tao, one of the most respected mathematicians alive today.

The AI had not only identified a solution but had effectively “reasoned” its way through a path that differed from previous partial attempts. While the model found a 2013 Math Overflow post by Harvard mathematician Noam Elkies regarding a similar problem, GPT 5.2 Pro’s final proof offered a more complete solution to the specific version posed by Erdős.

The “Unambiguous Instance”: Problem #281

If Problem #397 was a fluke, Problem #281 was the confirmation.

Neel Somani turned the model toward a covering system problem in number theory. The problem posits:

Let $n_1 < n_2 < dots$ be an infinite sequence such that, for any choice of congruence classes $a_i pmod{n_i}$, the set of integers not satisfying any of the congruences $a_i pmod{n_i}$ has density 0.

The question was whether for every $epsilon > 0$ there exists some $k$ such that the density of integers not satisfying the congruences is less than $epsilon$.

GPT 5.2 Pro generated a new proof. When Somani published the results, Terence Tao referred to it as “perhaps the most unambiguous instance” of AI solving an open problem.

This distinction is critical. In the past, AI “solutions” were often just efficient retrievals of existing literature. In this case, no prior solution was found. The AI bridged the gap between the known and the unknown.

The Data: Separating Genius from Hallucination

Skeptics often point to LLM hallucinations as a reason to dismiss their utility in rigorous fields. Somani, approaching this with the mindset of a quant and a computer scientist, decided to quantify the model’s actual efficacy.

He recruited a team of undergraduates to construct a dataset of ChatGPT responses to every open Erdos problem, 675 in total. The results provide a fascinating map of the current AI frontier:

• Recited known literature: 618 (The AI acted as a search engine)

• Incorrect: 17 (The AI hallucinated or failed)

• Correct, known results: 12

• New solutions to Erdos problems: 3

While 3 out of 675 might seem statistically small, in the world of high-level mathematics, it is monumental. It implies that for a specific subset of problems, the AI is already operating at the level of a published mathematician.

The “Long Tail” of Mathematics

Why is this happening now? Terence Tao, observing Somani’s progress, conjectured on Mastodon that AI systems are uniquely suited for the “long tail” of obscure Erdos problems.

Many of these problems are not “unsolvable” in the sense that they require a new branch of mathematics to be invented (like Fermat’s Last Theorem). Rather, they are tricky, labor-intensive, and obscure. They require connecting disparate axioms, Legendre’s formula, Bertrand’s postulate, the Star of David theorem, in novel ways.

This is where the scalable nature of AI shines. A human mathematician might spend a lifetime solving a dozen such problems. An AI, directed by a human operator like Somani, can attempt thousands in a day, clearing out the “clutter” of the mathematical landscape and leaving humans to focus on the deepest, most structural conjectures.

The Role of the Human Operator

It is important to note that GPT 5.2 Pro did not do this alone. It required Neel Somani.

Neel Somani’s background is pivotal here. As the founder of Eclipse, a Layer 2 blockchain platform that raised $65 million, and a former researcher at Citadel, he understands complex systems. His triple major from Berkeley in CS, Math, and Business gave him the vocabulary to prompt the model effectively and, more importantly, the expertise to verify the output.

The future of mathematics, and enterprise problem solving, looks exactly like this workflow:

1. The Architect (Human): Identifies the problem and frames the prompt.

2. The Engine (AI): Generates potential proofs, leveraging vast databases of axioms.

3. The Verifier (Human/Formalization Tools): Tools like Lean or Harmonic are used to formally check the logic, ensuring the AI hasn’t made a subtle error.

The Future of Discovery

We are moving toward an era of “Formalization,” where labor-intensive verification is automated by tools like Harmonic’s Aristotle, and creative reasoning is augmented by models like GPT 5.2.

Neel Somani’s work with the Erdos problems is not just a “weekend win” for a crypto founder. It is a signal to every industry. If AI can reason through unsolved number theory, what can it do for supply chain logistics? For cryptographic security? For protein folding?

The tools are here. The frontier is open. The only question remaining is: what problem will you prompt next?