I am 15 now. If I quit high school now and start a BSc around age 35 and finish my PhD around age 45, is it possible to find a job in some university after being out of academia for so long?
In modern dynamic society it is next to impossible to predict what happens with education systems, universities, and job market in 20 years time. Also, the success in finding an academic job depends highly on the skill of a candidate, and we do not know what your skills are now, and will be after 20 years. It is unlikely that you find the precise answer to your question here.
However, it is very likely that a proper education, and a "badge" which confirms it, will be still of some value. Therefore, quitting the high school may really be not the wisest choice.
Of course, there are stories of prominent success of people without any degree, and it is tempting to revolt the system and prove yourself a hero. Just bear in mind that a great amount of people without any degree achieve nothing and remain unknown to most. A real genius may (and hopefully will) rise no matter what, but in the long run and on average people with the structured education and degrees are more successful in getting themselves high-skilled jobs.
I entered a computer science PhD program over 25 years after my last formal education. Although I retired after completing the PhD at age 60, I did get contacts from recruiters suggesting I would have been able to find research work in industry. The gap is not in itself a killer problem.
However, there were two differences from your scheme:
- The 25 year education gap started when I received my master's degree.
- I was working in an intellectually demanding job that produced both patents and references suggesting I was capable of research.
I know some young people who are trying to earn enough to support themselves, at a minimal level, after only just scraping through high school and with little or no college. It takes a lot of time and energy, because of the low wage rates and physical demands of the jobs, when they get a job. It tends to be a very high stress lifestyle, because the jobs are temporary or part time, low benefit, and drastically varying hours.
I can't imagine living that way and being able to concentrate, when not working or looking for work, on mathematics research.
In another question you wrote: "Solving exercises or studying the texts in self-study themselves can (although difficult) be stopped for the duration of university affairs (classes, ...) but I believe that research can't be frequently stopped by other irrelevant things ..., as to be creative requires to be much more engrossed (to put it simpler: 1 2-day is more efficient than 2 1-day for research)."
Given that, you may have trouble getting much research done mixed with the practical demands of supporting yourself with no qualifications. You may need to work early morning rush Monday through Friday at a coffee shop and late afternoons Thursday through Monday at a supermarket. If you can get the work.