AI Math Formalization Current Players

Claude Formalization Campaign

Claude produced 13 million lines of Lean code and proved 29,500 intermediate theorems while completing the proof in 11 days. The work consumed about six billion output tokens from a general-purpose internal research model roughly comparable to Claude Fable 5.1. Dozens of agents collaborated through the Prove2Me platform, which maintains a directed acyclic graph of theorem statements.

Anthropic's announcement includes the quote from Kevin Buzzard: “This extraordinary autoformalization achievement, which Anthropic researchers say only took 11 days, proves Fermat’s Last Theorem with no assumptions other than the axioms of mathematics. Along the way we see autoformalization of algebra, harmonic analysis, geometry and number theory, and we learn that AI autoformalization artefacts are now robust enough to be built upon; the proof is multi-layered.” The scale exceeds Mathlib by more than five times because every trivial inference step must appear explicitly in the code. The campaign marks the broadest single formalization completed to date by any model.

Claude followed a simplified version of the Darmon-Diamond-Taylor exposition of Wiles’s 1995 proof. Human input stayed limited to occasional high-level directives such as “Jacobian as a scheme sounds high priority.” Initial agent runs without the coordination platform lost project state and contributed roughly seven percent of the non-boilerplate lines that later required cleanup. The final artifact passes Lean’s verifier against only the system’s three standard axioms and matches Mathlib’s statement of the theorem exactly.

OpenAI Astra Erdos Work

SiliconANGLE reported that OpenAI applied its latest Astra model to solve several Erdos problems and narrow a number of open questions in theoretical computer science. The work focused on generating new results in narrower domains instead of re-encoding an existing 129-page historic proof. The approach trades breadth of formal coverage for speed on frontier questions. No token counts or line counts appear in the published record for the OpenAI effort. Astra therefore occupies a different niche from full historic proofs.

The Astra results target open problems rather than verification of century-old theorems. Published accounts give no indication that the model produced millions of lines of Lean or coordinated dozens of agents over multiple days. The effort demonstrates capability on smaller, previously unsolved questions but leaves the large-scale formalization task untouched. Astra’s reported activity stays narrower in scope and lighter in verification overhead than the 13-million-line campaign.

Mathlib Community Library

Mathlib is the principal community library of mathematical proofs this theorem builds on. The existing library is concise and well-reviewed, yet Claude's proof exceeded its size by more than five times because every trivial step must be explicit. A multi-year community effort kicked off in 2024 by Kevin Buzzard at Imperial College London to complete the formalization using the Lean proof assistant. Human-led progress supplies the verified base but lacks the parallel agent throughput that produced the full result in under two weeks. The library already encodes the statement of Fermat’s Last Theorem that the new proof matches exactly. Mathlib remains the required foundation for any larger campaign.

The library’s conciseness reflects decades of human review and minimal redundancy. Claude’s output, by contrast, repeats patterns that experienced Lean contributors would compress. The gap in size highlights both the strength of the existing verified base and the current cost of scaling formalization without additional human pruning. Any future large proof will still need to reference Mathlib entries for its core definitions.

Prove2Me Coordination Tool

Prove2Me separates theorem statements from proofs into different files while preserving links between them. The platform also supplies natural-language descriptions of each statement so agents can search and reuse prior work. Anthropic's initial attempts without the tool lost track of project state and their failed efforts contributed ~7% of the non-boilerplate lines in the final proof. The scaffold turned repeated agent failures into a working campaign that finished the proof checked against only Lean's three standard axioms. The same platform supported a smaller three-day formalization of Vinogradov’s Three Primes Theorem using three personal Claude Max plans. Prove2Me supplies the coordination layer that single-model runs have so far lacked.

The tool’s directed acyclic graph lets agents select the next unproven statement without central memory degradation. Separate files for statements and proofs reduce compilation time and token waste during parallel runs. The smaller Vinogradov experiment shows the same harness works on consumer subscriptions when the target stays modest. Larger campaigns still require the same external coordination layer that the 11-day FLT run used.

Consumer Subscription Gap

No current effort supplies working mathematicians with an interactive formalization session that runs on ordinary subscriptions without custom multi-agent harnesses or dedicated platforms. The Anthropic post notes that three personal Claude Max plans completed a smaller formalization of Vinogradov’s Three Primes Theorem in three days. The sources leave open whether consumer-grade accounts can sustain campaigns at the 13-million-line scale without additional coordination software. That missing combination of scale, low friction, and standard accounts defines the empty slot.