Not sure what mathematically interests you, but you should probably check out Vanessa Kosoy’s learning-theoretic research agenda (she is hiring mathematicians!). Also, the Topos Institute are doing many interesting things in AI safety and other things (I’m personally particularly interested in their compositionality/modeling work, which seems very cool to me).
A couple of unasked-for pieces of advice that may be relevant (would be for my past self who was sort of in a similar position):
Sadly, many times we should expect tradeoffs between impact and interest, where to actually implement innovations requires doing hard manual work. Especially in academic fields, where the impactful uninteresting work is more neglected.
Our interests change quite a bit over time, and it’s usually hard to predict how it might change. That said, for many people they find stuff more interesting the more competence they feel at it and the more they care about the problem they try to solve or about the product they intend to deliver.
Your points (1) and (2) are ones I know all too well, though it was quite reasonable to point them out in case I didn’t, and they may yet prove helpful to other readers of this post.
Regarding Vanessa Kosoy’s work, I think I need to know more math to follow it (specifically learning theory, says Ben; for the benefit of those unlucky readers who are not married to him, he wrote his answer in more detail below). I did find myself enjoying reading what parts of the post I could follow, at least.
Regarding the Topos Institute, someone I trust has a low opinion of them; epistemic status secondhand and I don’t know the details (though I intend to ask about it).
Not sure what mathematically interests you, but you should probably check out Vanessa Kosoy’s learning-theoretic research agenda (she is hiring mathematicians!). Also, the Topos Institute are doing many interesting things in AI safety and other things (I’m personally particularly interested in their compositionality/modeling work, which seems very cool to me).
A couple of unasked-for pieces of advice that may be relevant (would be for my past self who was sort of in a similar position):
Sadly, many times we should expect tradeoffs between impact and interest, where to actually implement innovations requires doing hard manual work. Especially in academic fields, where the impactful uninteresting work is more neglected.
Our interests change quite a bit over time, and it’s usually hard to predict how it might change. That said, for many people they find stuff more interesting the more competence they feel at it and the more they care about the problem they try to solve or about the product they intend to deliver.
Your points (1) and (2) are ones I know all too well, though it was quite reasonable to point them out in case I didn’t, and they may yet prove helpful to other readers of this post.
Regarding Vanessa Kosoy’s work, I think I need to know more math to follow it (specifically learning theory, says Ben; for the benefit of those unlucky readers who are not married to him, he wrote his answer in more detail below). I did find myself enjoying reading what parts of the post I could follow, at least.
Regarding the Topos Institute, someone I trust has a low opinion of them; epistemic status secondhand and I don’t know the details (though I intend to ask about it).
Thanks very much for the suggestions!