Does LLM Dream of Differential Equation Discovery?

Discovering a governing equation from data means choosing its terms and estimating their coefficients. We ask whether a general-purpose multimodal model, given no feedback, can do both itself, with no library of candidate terms and no optimiser fitting the coefficients. Four such models are shown ten dynamical systems in twelve ways, each run returning five candidate equations, and a run discovers the equation when a screened candidate has exactly the true terms and every coefficient within 10% of its value. Each model is also run with the data withheld, so that what it reads from the data can be told from what it recalls. In its strongest configuration GLM discovers ten laws, Qwen and DeepSeek eight and Gemma four, including laws none of the models writes without data, with coefficients they estimate themselves, and their reasoning shows how: they read values where competing terms vanish, and GLM tests what it reads. Under added noise the models seldom say that the data are noisy, yet on several systems they keep writing the true law. The hardest laws are missed because one of their less common terms is never written.