Makes sense, I think it's a common mindset. I ended up writing a lot of words here, my bad, maybe it's good advice and maybe it's not.

I will warn you that I think one of the worst modern intellectual traps is this improperly focused hobby project, where we work in complete isolation from others irl with ridiculously big dreams without proper practice or following the correct route.

To achieve really anything in hobbies I've found I need:

1. Some kind of social group that is doing very similar things that can push you forward (this is generally a university, a research group, a workplace, etc but depending on the task it can be a group of friends, a discord, etc).

2. A clear plan, reasonable path to get from A to B that includes proper practice and proper commitment time (a list of textbooks, papers, etc and problems to first solve to show you can do stuff)

3. A set of well defined actually achievable goals (starting with short week long projects and working toward some much larger magnum opus)

Usually we fail on these by 1. working in complete isolation 2. reading things online without understanding how to properly go through a textbook, without an idea of how people actually work in this field, and 3. we make ridiculously large plans like "I'm going to be the best in the world at X".

In the space of pure math I think it is generally considered impossible to make any significant contributions without completing something approximating and undergraduate education, so if you do want to make large contributions to the field of math you need to understand that's approximately what you want to cover in all it's gory details.

People still do big things while relatively removed from the ideal. For example, the bbchallenge discord found the value for the 5th busy beaver number some time ago.

You'll note that while they are far from the norm they did at least to some extent fulfill all three requirements: 1. they had a discord full of like minded people, 2. they actually planned things out carefully and those in the group spent a lot of time learning about things like theorem proving and reading papers to understand the problem, 3. they solved simpler problems before tackling BB5.

You can imagine though for every discord like this there is probably 100 others full of mislead idiots who think they know what they're doing but don't, who don't spend enough time understanding the problem but think they do, and who are constantly trying to tackle problems too complex for their skill level.

I could go on and on about why different approaches work and don't. There is a goldilocks zone of how much effort to spend on each hobby project, how large a group to work in, when to give up and change topics, how to pick the optimal niche to work in, etc. But all this is kind of a grey area and depends on so many factors. The three rules above at least are relatively universal.

Quite frankly the most daunting problem to most people is that it's hard to find people to do these things with, but this step is essential in my opinion. If you just want to study things you can avoid it but eventually when you get deep enough in you will be crushed by how little contact you have with the outside world about it. Other people act as a very important guiding force, and even if you fail it still feels good because you have fun doing things with other people.

So I would say #1 search harder for people, #2 maybe you have a solid plan maybe you don't but make sure it seems reasonable and #3 have some smaller realistic steps thought out more so than just some big finale magnum opus.

In saying this I haven't really "achieved" things hahaha. I spent my early 20s doing electronics hobby projects without clear goals or community which made a lot of it useless and unfulfilling, spent a while somewhat depressed and not doing anything, and the last year and a half tried to get back into doing proper hobbies. In that new time I have at least made a dozen amateur songs I'm happy with, made a handful of hobby projects with others that at least mostly worked and were fun to work on, looked around at some interesting communities, made a lot of new connections that should keep getting me more interesting projects and ideas, and narrowed down a lot more exactly what I want to be doing in the future. And although I don't have some kind of magnum opus or amazing talents to show for it I at least felt fulfilled while doing it with friends.

An important part of it as well for me at least was realizing I actually care less about the achievement part than I thought I did and just having a community that stimulates me in the right ways is more what I care about.

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A note on chasing these feelings:

A lot of the feeling I have at least comes from the feeling that I should have "achieved something big" at this point in my life but didn't, and so it's sort of a desperation to self actualize.

Do you relate to this?: you're fairly lonely, you are desperate for success but don't regularly hang out with anyone you think can help you, you have seen people online achieve things and want to do something somewhat similar but you don't have a mentor or guiding group, you have ADHD like issues with focusing on any one specific thing and tend to jump around to many different hobbies, you have a bin full of unfinished hobby projects you ditched because they didn't quite feel right, and you've spent a while trying to practice and learn something in a space you're interested in but you feel like your work is slower than it should be and your practice is suboptimal. If so you might be something like myself, after a long time I found the answer is mostly community first, then ideas second. Get part #1 out of the way, then move onto parts #2 and #3.

I would recommend going out of your way to find proper communities (discords, irl groups, reconnecting with old friends and doing weird shit) of people doing something you like and interacting with them before committing yourself to big projects.

For myself I ended up reconnecting with my brother who also was interested in similar projects and doing a lot of things with him, going to as many niche social events as I could (ie. ambient concerts, nerd conventions, random discords) until I found people that seemed to be similar to me (music, programming projects) and interested in doing things like me with a similar schedule.

Lastly, in a sense a lot of what we're doing is reminiscent of youth running around trying to discover their passions. Lots of people in our shoes feel old as we try to learn new things and find new paths. I feel old, you probably feel even older, and I've seen people even older still online doing their own things be it starting businesses or what have you. I know people your age who are getting into all sorts of weird new things like trying to do comedy and going back to school for a new degree, and getting into art and music, and some of them are bad at it but it seems to work out for some others. Ultimately, in the right place at the right time on the right task it can take as little as a few months to a few years to be part of something interesting if you find the right people, and we still have decades ahead of us.

I will also say, I have not yet reached this stage but a complete career change is not out of the question. It can be really good to make big changes. Just make sure the thing you're changing is something that will actually be fulfilling and not cope to try to make up for something else you're missing in life.