You need sensor feedback to learn new math and talk to other mathematicians.

To learn new math, a professional mathematician foremostly just thinks further (it's its job); to discuss with other entities (and acquire new material), textual input and outputs suffice.

Hmm, the ones I know do a fair amount of multimodal discussion. (Shapes for instance.)

Which you can still acquire as compact data (like SVG)

Which to machines is direct information, as opposed to noisy data requiring complex processing to extract the relevant content.