Need a suggestion regarding choosing PhD stream.

The question

I wanted to ask if I like pure mathematics, will there be something for me if I decided to pursue PhD in the field of AI? I don't want to disregard the option of PhD in AI/ML field due to my ignorace and predefined wrong notions.

Background

When I think of doing phd in mathematics, I feel the following:

1.) I like how every thing is rigorous, and it seems beautiful.

2.) It's tough and feels satisfying.

3.) It will equip me with sophisticated tool to study anything like theoretical physics, CS, theoretical CS etc.

But there is little incentive money wise. I will be living above average life sure, but not a very lavish life.

So , I decided to do phd in CS particularly in AI/ML, but I get the following idea:

1.) I feel I can go through it because it will involve me reading mathematics and will be easier for me.

2.) It will pay me well, I can become research scientist etc.

3.) I have BS-MS in mathematics so I feel I already have a little edge.

4.) I never get excited by the word "data" and feel heuristic and don't like. Even the concept of LLMs don't excite me much. But I do like the idea of "artificial Intelligence", conscious robot etc.

I do feel a little bit that if I study ML rigorously I might like that terminology but I ain't sure, I am not that much excited by the idea of LLMs, data etc.