There are two great points in favor of this plan:
You don't mention, however, what your next-best option is. It's possible that you can get FASTER iteration of your cycle while working directly for someone who'll pay you. Success outside academia is a credential that gets you influence and respect, differently than a PhD, but not necessarily less.
It is rarely wrong to follow what you are passionate about. Go for it. But do think hard before discarding your placement in industry. Obtaining a diverse set of career relevant experiences early on is valuable. Industrial placements look good on a resumé as well.
Don't overthink this! Go with the feelz!
My simple answer is: Go for it! I have done a PhD in mathematics myself (also in the UK), and although I have since changed career in a direction where it has not been that useful, I have never regretted it! And I’m sure I would have regretted it if I hadn’t done it.
Thinking a bit more about the question, I wonder if “Should I do it?” was really the question you wanted to ask? It seems not quite well-defined, when you are not stating any alternatives. Were you hoping to answers to “What other options do I have?”, “How do I get started on this path?”, “Will the change from CS to maths be too big?” or something else?
I’m not the right person to answer what other options you have. About the two other questions, I think you should focus on who you want as a supervisor, rather than whether it will be in mathematics or in computer science (I actually thought my PhD was in both maths and CS while I was doing my PhD, and only learned that it was only in maths when my diploma arrived! One of the examiners who awarded my PhD later told me he thought he had awarded me a PhD in CS!). If you find the right supervisor, it is not important if they are in CS or maths or something else.
Thanks for the answer!
Out of curiosity, what career did you transition to?
I think you should focus on who you want as a supervisor, rather than whether it will be in mathematics or in computer science
...
If you find the right supervisor, it is not important if they are in CS or maths or something else.
I'll be keeping this in mind.
That said computational/biological anchors are a good reason for longer timelines absent foundational breakthroughs in our understanding of intelligence.
Furthermore, I suspect that intelligence is hard, that incremental progress will become harder as systems become more capable, that returns to cumulative investment in cognitive capabilities are sublinear/marginal returns to cognitive investment decay at a superlinear rate, etc.)
Introduction
I'm currently flirting with the idea of trying for a math PhD 2 - 3 years down the line.
I'm currently on a Theoretical Computer Science Masters program at the University of [Redacted] in the United Kingdom.
(My program is 2 semesters of teaching (7 - 8 months) followed by a 9 - 12 month industrial placement starting in June 2023. [I might forego the 1 - year industrial placement if I can't get a suitable placement [I.E. theoretical research that feels like it would be valuable experience for the kind of career I want to pursue] and graduate after one year by completing a masters project over the summer instead.)
After graduation I'm considering taking a gap year to fill in the gaps in my maths knowledge/prepare for the PhD, maybe see if I can contribute to the research agendas I think are interesting/promising).
I might also pursue a PhD in Theoretical Computer Science instead of mathematics (maybe applications for a TCS PhD would be looked on more favourably with a TCS Masters/recommendations from my current lecturers).
Why A PhD?
I currently plan to learn a lot of (especially abstract) maths to (upper) graduate level for alignment theory (I want to do theoretical alignment work that is basically just applied maths), and I think I would benefit from the opportunity to study the relevant mathematics under a "guru"/the dedicated mentorship a PhD provides. I expect the first few years of my career in alignment research would be mostly spent on deconfusion/distillation, and I expect high levels of mathematical sophistication to be very valuable for that.
I find abstract maths and mathematical modelling "fun", and really enjoy being a student.
My Alignment Theory of Change
I am operating under/optimising for long timelines (transformative AI is decades away [20+ years]), and this influences what kind of research I believe to be most promising.
I expect theoretical (especially foundational [especially in our current pre paradigmatic stage to be the most promising]) and am persuaded by agent foundations agendas. The extant research agendas I'm most excited for and could see myself working on someday:
My basic plan for alignment is something like:
Of course, I don't expect to make it all the way to step 8. Mostly, I expect that deconfusion and distillation would be where most of the value from my "career" will come from.