  We are beginning to see progress in language model assisted scientific
discovery. Motivated by the use of LLMs as a general scientific assistant, this
paper assesses the domain knowledge of LLMs through its understanding of
different mathematical skills required to solve problems. In particular, we
look at not just what the pre-trained model already knows, but how it learned
to learn from information during in-context learning or instruction-tuning
through exploiting the complex knowledge structure within mathematics.
Motivated by the Neural Tangent Kernel (NTK), we propose \textit{NTKEval} to
assess changes in LLM's probability distribution via training on different
kinds of math data. Our systematic analysis finds evidence of domain
understanding during in-context learning. By contrast, certain
instruction-tuning leads to similar performance changes irrespective of
training on different data, suggesting a lack of domain understanding across
different skills.
