I am a 31 years old software engineer at a big technology company in Silicon Valley. I have a master's degree in computer science and moved into working full time right at the time of my graduation. During those ~6 years in industry, I always tried to work a few hours during the day on my personal passion which is studying mathematics. Ultimately, every time I want to study a specific topic, I made so little progress because of my full-time job that I got frustrated. I figured just a few weeks ago that something needed to change and I should pursue my passion, which is research, and then got into my head that I must do a PhD. Now, the principal reason of doing a PhD for me is to be able to work full-time on maths. Something I am dreaming about, just thinking about it makes me very happy. On the other hand, at the same time, I know that I am taking a major pay cut (from 6 to 5 figures), and my lifestyle will dramatically change.
EDIT : Question has been put on hold so I will try to narrow down my questioning to a specific concern.
Considering that I have no demonstrable research experience, no real recommendations by academia people ( 7 years out of college, my teachers will likely had forgot about me ), no good grades in my masters ( average ), and a degree in computer science vs a math one, is it really possible to get accepted in a pure math phD program ?
Note : the only math experience I had is high school ( grade 18/20 ) and my personal experience ( which is not demonstrable )