My way involves a lot more risk that nothing useful will be produced.

I basically want a higher risk / reward than what working in this field as an employee would provide. I wouldn’t be able to try far out ideas if I wanted to keep my job, because it may be the case that one avenue of research never goes anywhere for years.

Peter Higgs has some interesting thoughts on how he would probably not have produced anything valuable if his work had occurred in the current academic environment that prioritizes frequent publications in high impact factor journals (https://www.theguardian.com/science/2013/dec/06/peter-higgs-...)

I share your goals.

I'd put it this way: your way involves a lot more risk of dead ends, but also offers a lot more of focused, productive deep work.

In general sense, companies are set up to derisk work. It's a trade-off - we get consistency, but also mediocrity.

In my case I just want to follow the rabbit hole to wherever it takes me without worrying about showing results to anybody.

Why can't you do that now?

It generally leads to being fired for not completing milestones, which leads to not having income to support yourself.

How much monthly income would a person need to support themselves and work on what they want to work on?

Depends on the location but living without a job is not really feasible without government assistance of some sort which is usually tied to stress and extra work proving you need the money. For example in many US states you have to prove that you are constantly looking for a new job and are willing to accept any kind of job offered in order to receive unemployment assistance. This is a far cry from being relaxed enough to work on projects in peace.

Have you heard of the 4% rule? That basically means if you save up X amount, you can spend 4% of X every year, in perpetuity, given some reasonable return like 7%. So if you can live on $80k/year, save and invest $2 million.

I can live on much less than $80k and I actually currently do. But $2 million actually sounds like a reasonable goal. If I can get it down to $1 million then that will be achievable.

Yes, if you can get your expenses under 40K a year, you'll be good. I read a lot of financial independence / FIRE forums. Some people are much more conservative and think 4% is too high. They prefer the 3.5% or even 3% rule. For a very early, longer retirement, they are probably right. The 4% rule was based on a "normal" 30 year retirement.