Fable "whipping up" SymPy like a "calculator app" is one such interaction that seems very plausible (in addition to SymPy providing feedback when training models). The scale of compute available to an Anthropic employee for such SymPy calls when using Fable is likely one of multiple factors for this counterexample being found in 2026. Unfortunately, we aren't going to be able to really know the various factors that best explain why an Anthropic employee was able to announce a counterexample this past weekend. For all we know, the counterexample was found by Anthropic employees months ago and used for training the Fable model used this past weekend.
I love this. Anthropic employees just randomly have solutions to Smale's open problems in their back pockets, waiting for the right moment to sprinkle them into the training set.
I can't tell what your point is, but it sounds like a straw man. A more likely scenario (than your strawman) is that Anthropic employees could be using models under development to try and crack math conjectures that have PR value and insights from those internal efforts help train future models that can crack such conjectures. We don't know because sharing of such explanatory factors are not part of the business effort.
Was Anthropic doing this earlier this year? with some of Smale's open problems? Did those improvement go into training the LLM that was used a week ago? Seems like a plausible factor.
