Google Internal Math AI Targeted an Unsolved Number Theory Problem, Leak Reveals

On September 15, 2026 — one week after OpenAI announced it had used roughly 10,000 AI agents to claim a Navier-Stokes Millennium Prize breakthrough — a leaker named lyra posted two screenshots on X that told a quieter but structurally related story. Google, inside its own walls, had pointed a math-specialized AI at an open problem in number theory that professional mathematicians and distributed computing projects have failed to solve since 2019.

The screenshots showed an internal Google API descriptor and an unfiltered chain-of-thought trace from a build called models/deepthink-mathematica-tf-raw-thoughts. The trace, which accumulated more than a million views on lyra's account within days, went viral for the most superficially entertaining reason: while working through a polynomial Diophantine equation, the model erupted into all-caps exclamations. "HOLY MOTHER OF MATHEMATICS!!!" it wrote, followed shortly by "Let's admire the absolute beauty of this equation," and, after spotting a key algebraic cancellation, "OH MY GOD!!!"

The viral reaction was immediate and largely missed the point. The model's behavior was a predictable artifact of how it was trained. The mathematical problem it was handed was not. The two screenshots together make a more substantive argument about where Google's AI research is heading than the exclamation marks suggest.

Google has not confirmed the build's existence, issued a model card, or provided any benchmark results for it. Everything that follows comes from the leaked screenshots and what can be independently verified about the surrounding context.

What the API Descriptor Actually Says About Deep Think Mathematica

The first screenshot is a JSON object of the kind Google's Gemini API returns from a model listing endpoint. It is a machine-readable record with a version string, a model stage, supported methods, sampling defaults, and token limits. Read carefully, it answers several questions that the coverage has gotten wrong.

The model's internal identifier is models/deepthink-mathematica-tf-raw-thoughts. Each segment carries information. The deepthink prefix places it in the Deep Think family — Google's parallel-reasoning mode built on top of Gemini Pro, not a separate model family. mathematica is an internal codename, not a reference to Wolfram's Mathematica software; nothing in the descriptor connects the two. tf is an abbreviation for "Teamfood," Google's internal designation for the second stage of its testing ladder, where a model moves from the small team that built it to a wider population of internal employees. raw-thoughts signals that this endpoint exposes the model's unfiltered reasoning tokens rather than the post-processed summary that appears on public APIs.

The model stage field reads UNSTABLE_EXPERIMENTAL, which is the earliest classification Google uses in its descriptors. Models at this stage are rebuilt, renamed, and retired without notice. The version string gdm-eval-model-u looks like a sequential evaluation slot identifier rather than a numbered release, suggesting the model is being scored against a capability battery rather than prepared for a launch.

Two other fields define what the model can and cannot do. The descriptor lists only generateContent and countTokens as supported generation methods. There is no streamGenerateContent and no bidiGenerateContent. That combination is the technical profile of a batch evaluation endpoint — something you submit a problem to and wait on, not something you have a conversation with. If the model regularly spends many minutes working through a hard mathematical problem before producing an output, streaming would be close to useless in any case.

The token budget is 1,048,576 tokens of context input and 65,536 output tokens. The input figure is exactly 2^20 and is standard across the Gemini Pro family; it does not distinguish this build from existing public models. The output limit of 65,536 (2^16) tokens is large enough to hold a complete mathematical paper with full lemma proofs, which suggests the build is designed for extended derivation rather than conversational exchange.

The Temperature Claim the Coverage Got Wrong

One field in the descriptor generated a persistent error across the reporting. TestingCatalog's write-up described Deep Think Mathematica as featuring "high-temperature generation." Several aggregators repeated this. It is not accurate.

The descriptor sets temperature to 1.0. That is the standard default for the Gemini API. The field maxTemperature is set to 2.0, which is a ceiling the model can reach, not the value it runs at. Temperature 1.0 means the model samples in proportion to the probability distribution its weights produce — a neutral starting point, not a dial turned toward randomness.

What does distinguish the sampling configuration is the combination of temperature 1.0 with extended thinking time and parallel solution branches. The Deep Think architecture was designed to explore multiple proof hypotheses simultaneously rather than committing to a single chain of reasoning. A model that runs many parallel chains and synthesizes the most promising ones does not need high temperature to explore; it does it structurally.

Why the Model Screams, and What That Actually Reveals

The second screenshot is the chain-of-thought trace, and it deserves closer reading than the exclamation marks alone suggest.

Working through the equation, the model writes the all-caps outburst, then "Let's admire the absolute beauty of this equation," then, after detecting a remarkable algebraic cancellation, another cascade of "OH MY GOD!!!" followed immediately by "WAIT!!! LET'S CHECK IF THIS IS JUST THE IDENTITY WE STARTED WITH!!!"

That last line matters more than the shouting. It shows the model doing something the Deep Think architecture was specifically designed to encourage: self-checking. After identifying what looks like a dramatic simplification, the model stops to verify that it has not simply looped back to where it started. That verify-then-doubt behavior is precisely what makes advanced mathematical reasoning hard for humans and for AI, and the raw trace makes it visible in a way that no summarized output ever would.

The emotional language itself is a training artifact, not evidence of experience. Models learn from the text humans write, and when human mathematicians — on MathOverflow, arXiv, research blogs — encounter an elegant identity after hours or days of failed approaches, they write things like "Holy cow, look at this" and "Oh my god, it works." During pretraining, the model's parameters absorb the statistical relationship between those expressive phrases and the mathematical conditions that preceded them. During reinforcement learning on intermediate-step reward signals, the training further amplifies tokens that historically correlate with successful derivation steps. The exclamation marks are, in a technical sense, mathematical confidence indicators wearing punctuation.

On public APIs, this behavior is invisible. Google's production endpoints post-process the reasoning tokens into a calmer, shorter summary before returning them. The -raw-thoughts suffix on the Mathematica build's name strips that processing away, which is why the trace reads as it does. The same behavior exists in every reasoning model that uses extended thinking; it is normally hidden by design. Deep Think Mathematica's visibility is a diagnostic tool artifact, not a feature intended for end users.

The Math Problem Was Not a Toy Exercise

The equation the model was handed is one of number theory's genuinely open cases.

The sum-of-three-cubes problem asks which integers can be expressed as the sum of three integer cubes — that is, for which values of n does x³ + y³ + z³ = n have a solution when x, y, and z can be any integers, including negative ones. The problem is simple to state and extraordinarily hard to resolve in full. Numbers equal to 4 or 5 modulo 9 are provably impossible. For all other integers, the conjecture is that a solution exists, but proving or disproving it for any specific case requires finding three integers that satisfy the equation, and those integers can be astronomically large.

For decades, the smallest cases without known solutions were 33 and 42. In 2019, Andrew Booker at the University of Bristol found the solution for 33 using a new search algorithm and weeks on a university supercomputer. Booker and Andrew Sutherland of MIT solved 42 later that year using volunteer computing power from more than 400,000 personal computers organized by the Charity Engine distributed computing project. Their solution for 42 involved three numbers each in the range of 10^16 — a 16-to-17-digit scale that makes intuitive search practically impossible.

After those two solutions were found, 114 became the smallest open case below 1,000. It has resisted computational search ever since. A solution, if one exists, would require discovering three integers — potentially with tens or hundreds of digits — satisfying the equation. No such discovery has been announced.

The Deep Think Mathematica trace shows the model setting substitutions, computing symmetric identities involving a + b + c = 3m, and reaching the line "We know 114 = a³ + b³ + c³ = (a+b+c)³ – 3(a+b+c)(ab+bc+ca) + 3abc." That is the standard algebraic identity for expanding a cube sum, and applying it to the 114 case is a legitimate line of attack rather than random symbol manipulation. The screenshot ends mid-derivation. The model did not claim a solution, and no solution to the 114 case has since been announced. What the trace demonstrates is that whoever configured the test deliberately chose a problem from the frontier of unsolved mathematics, not from a problem set with known answers.

Deep Think Mathematica Inside the Broader Race to Aim AI at Open Problems

The leak arrived on September 15, exactly one week after OpenAI announced on September 8 that it had claimed a resolution to the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems established by the Clay Mathematics Institute in 2000. OpenAI's result used roughly 10,000 AI agents working in parallel over approximately 88 hours, with Lean-verified formal proof. The company said the internal model involved was more capable than its publicly available GPT-6 Astra. The Clay Institute listed the problem as "active" pending mathematical community review — and the result remains subject to ongoing expert scrutiny.

Read more: OpenAI's Navier-Stokes claim and the race toward the next Millennium Prize

Separately, Levent Alpöge, a mathematician at Anthropic, and Tristan Buckmaster, a professor at NYU's Courant Institute, published proofs on September 7 showing forced blowup for the three-dimensional Euler equations and two related fluid systems — work OpenAI acknowledged in its own announcement. Neither the Euler results nor the Navier-Stokes result used systems available to the public.

The Deep Think Mathematica leak is not at the scale of a Millennium Problem attempt. But the pattern is the same: internal AI systems being directed at open research problems that humans have not solved, rather than competition exercises with known answers. The 114 case of the sum-of-three-cubes problem carries no prize, but it has resisted professional effort and distributed computing since the 42 case was resolved in 2019. The decision to use it as a test problem rather than, say, an IMO exercise with a known solution suggests that Google's internal team is evaluating the model at research difficulty.

This is the context that the entertaining screaming trace mostly obscured. Google has published research showing that existing public Deep Think mode helped identify a logical flaw in a peer-reviewed mathematics paper that had passed human review, and contributed to progress on the Max-Cut and Steiner Tree problems in algorithms research. A dedicated math-specialist build would push that capability further, though neither the leaked descriptor nor the trace provides evidence that Mathematica has done so.

Read more: Anthropic's Claude formalizes Fermat's Last Theorem in Lean, opening a new era for AI-assisted proof

Where Deep Think Mathematica Stands Against Existing Gemini Math Capability

The appropriate comparison for Deep Think Mathematica is not against OpenAI's public models or Anthropic's Claude line. It is against the Deep Think that Gemini AI Ultra subscribers can already access.

Gemini 3.1 Deep Think is available publicly, gated behind a subscription tier. An advanced version of it earned a gold-medal standard at the 2025 International Mathematical Olympiad by solving five of six problems for 35 of 42 possible points, formally certified by the IMO President. By January 2026, an updated version scored 65.7 percent on the Advanced IMO-ProofBench evaluation per human expert grading, according to the IMO-Bench research paper. These figures are company-reported or derived from independent research; the full IMO-Bench evaluation also noted that all non-Gemini models scored below 25 percent on that Advanced subset.

The Epoch AI research group independently evaluated an earlier public Deep Think on genuinely novel mathematical problems not in its training data. Their assessment found the model impressive at deploying background knowledge and executing detailed calculations, but unable to solve either of the novel problems tested, even across ten attempts each. The distinction between applying learned mathematical technique and extending the frontier of known mathematics remains a significant one.

Deep Think Mathematica, as described by the descriptor, is a different kind of system from the subscriber-facing product. It has no streaming support, no tool calling listed in the descriptor, no consumer-facing interface, and a model stage designation that explicitly warns against expecting stability. If the IMO gold-medal Deep Think build was a research prototype that shipped as a narrow preview for trusted testers within weeks of its result, Mathematica is at least one stage earlier than that in Google's development pipeline.

The naming does not align cleanly with Google's public versioning: "DeepThink V3" appears in the descriptor's display name, while the public product is branded as Gemini 3.1 Deep Think. How Google reconciles its internal generation counter with the consumer naming convention will say more about the release plan than any benchmark rumor.

What Would Need to Change for This to Become a Product

Nothing in the leaked descriptor points toward a product launch, but there are specific signals that would indicate the build is heading somewhere.

The -raw-thoughts suffix implies a production sibling: a deepthink-mathematica endpoint without that suffix, with summarized rather than raw reasoning, designed for broader use. If that identifier appeared in any public API listing, it would be a significantly stronger signal than this leak. A movement from UNSTABLE_EXPERIMENTAL to a preview stage, or the appearance of streamGenerateContent in the supported methods, would mark the formal transition from evaluation to product. A Google DeepMind research paper crediting a math-specialized model — rather than the general Deep Think family — for contributing to a published result would surface the capability before any product page does.

The precedent from 2025 is relevant but imperfect. Google moved the IMO gold-medal Deep Think build from research to a narrow preview for trusted testers including mathematicians within weeks of announcing the competition result, before rolling it more broadly to AI Ultra subscribers. Deep Think Mathematica could follow a similar path if Google decides it has something worth releasing. It could equally be retired, renamed, or folded back into the general Deep Think line. At UNSTABLE_EXPERIMENTAL stage, none of those outcomes is unlikely.

The actual mathematical community interest in such a tool would not primarily center on whether the model can produce theatrical reasoning traces. It would center on whether the model can serve as a legitimate collaborator in mathematical research — holding an entire literature's worth of prior work in its context window, generating proof sketches that a mathematician can verify and extend, identifying non-obvious connections between subfields, and catching errors that passed human review. The IMO gold-medal system demonstrated those properties in a structured competition setting. Mathematica's test on the 114 problem, though incomplete, suggests the evaluation is now being run against open rather than solved targets.

Whether the model is capable of contributing to that problem is not knowable from one trace. What is knowable is that the question is now the one being asked.