The real use is in actually seeing connections. Every field has their own maths and their own terminologies, their own assumptions for theorems, etc.

More often than not this is duplicated work (mathematically speaking) and there is a lot to be gained by sharing advances in either field by running it through a "translation". This has happened many times historically - a lot of the "we met at a cafe and worked it out on a napkin" inventions are exactly that.

Math proficiency helps a lot at that. The level of abstraction you deal with is naturally high.

Recently, the problem of actually knowing every field enough, just cursorily, to make connections is easier with AI. Modern LLMs do approximate retrieval and still need a planner + verifier, the mathematician can be that.

This is somewhat adjacent to what terry tao spoke about, and the setup is sort of what alpha evolve does.

You get that impression because such advances are high impact and rare (because they are difficult). Most advances come as a sequence of field-specific assumption, field-specific empirical observation, field-specific theorem, and so on. We only see the advances that are actually made, leading to an observation bias.