Detailed Analysis
A developer's Show HN post describes an inventive workaround for one of Anthropic's more debated product decisions: the hiding of Claude's extended reasoning ("Chain of Thought") from users. The context is a claimed refutation of the Jacobian Conjecture, a famous open problem in algebraic geometry concerning polynomial maps and their invertibility, which was reportedly produced with Claude's help. When the mathematical community asked for the reasoning trace that led to the counterexample so they could understand the underlying intuition, none was available—Anthropic's Fable model (an internal or specialized variant referenced here) does not expose its CoT to end users. Rather than accept this as a dead end, the author devised a "clean room reverse engineering" technique: feed one instance of Claude the final result and ask it to construct a plausible derivation path without giving away the answer, then have a second instance attempt to follow that derivation, iteratively tuning the difficulty by adding or removing hints until the second model could reliably reconstruct the reasoning. This is a clever, almost adversarial use of two model instances to approximate a hidden process—essentially treating the model's own generative capabilities as a proxy for introspection it isn't permitted to share.
The significance here extends beyond one quirky math puzzle. It highlights a real tension in how AI labs deploy reasoning models: hiding CoT is a common practice at Anthropic, OpenAI, and others, often justified by safety concerns (preventing models from learning to game or obfuscate their reasoning), competitive protection of proprietary techniques, or the risk that raw scratchpad reasoning can be misleading or contain content the company doesn't want to expose to users directly. But this opacity has real costs when the model is being used as a discovery tool for genuine intellectual work, as in mathematics research, where the *path* to an insight is often as valuable as the result itself—teaching mathematicians new proof strategies, intuitions, and search heuristics. The author's technique represents a grassroots response to that opacity, essentially reverse-engineering a teaching narrative from an AI system that has been deliberately configured not to reveal its own scratchpad.
The specific mathematical content also reflects a broader emerging trend: AI models being used not just to verify or assist with existing mathematical proofs, but reportedly to help generate genuinely novel counterexamples to long-standing conjectures. The Jacobian Conjecture has resisted proof or disproof for decades, and if a Claude-assisted refutation holds up to scrutiny, it would be a notable milestone in AI-assisted mathematics, alongside other recent instances of large language models contributing to proofs, olympiad problems, and research-level mathematics. The author's post includes a distilled set of intuitions extracted from the reconstructed reasoning: avoiding certain standard normal-form reparametrizations that increase complexity, working in three complex dimensions rather than two, searching for a 3:1 rather than 2:1 covering map, and constructing a composition of functions with specific Jacobian determinant properties. These are the kinds of heuristic, exploratory judgments that constitute real mathematical intuition rather than mechanical proof-checking, suggesting the underlying model engaged in something resembling genuine mathematical search.
Finally, this episode illustrates how AI users are increasingly building informal infrastructure around commercial models to extract capabilities the providers didn't explicitly design for—essentially community-driven interpretability research conducted from the outside, using prompting and multi-instance protocols rather than access to internals. As reasoning models become more central to serious technical and scientific work, pressure will likely grow on labs like Anthropic to reconsider blanket CoT-hiding policies, or at minimum to provide sanctioned mechanisms for extracting pedagogically useful reasoning traces in domains like mathematics, where transparency has clear scientific value and lower misuse risk than in other contexts.
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