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What does it mean when a thesis supervisor says "You can use GenAI to polish the text, but not for anything else". What are the limits of polishing?

I am highly sceptical of generative AI and don't use it myself, but I know there's a general impression among students that it 'knows everything'. The discussions I have seen have focused on text (logical enough for 'large language models'), and images (many of which are disastrous), but I cannot see how LLMs can reliably do (complex) mathematics where there are many steps to a derivation, some of which are nuanced or require particular systematic techniques, and the final result should be as general as possible. How can I convince students that they will (probably) waste more time using generative AI than working through the difficulties themselves? Or do I have to resign myself to allowing an extra week or more for students to learn for themselves that there really isn't an alternative to putting in the effort and doing the derivation oneself with pen and paper, no matter how hard it is?

I've seen a lot of discussion, mostly in social media and teaching fora, about students using generative AI instead of doing the reading and writing assignments that have been central to university learning. But I've seen little discussion of generative AI in physics or other natural sciences. How worried should I be that some of my students will put their effort into learning to use generative AI rather than learning physics? How good are large language models at physics? And how are things changing as the models are improving?

There are great AI tools out there these days that generate podcasts from any document you upload or link to. I am considering doing that for my course, since students aren’t reading textbooks anymore (let alone scientific articles), so I was thinking that if I gave them a podcast, that might get them to engage with the ideas and concepts. What are the pros and cons?