Chemistry is an enormous field too, you would have to concentrate on a much smaller section, I have been self studying for about 8 years now, (+ I have 20 years software development experience) and I think I'm getting to the point where I have complete understanding of the current SOTA and am pushing at the boundaries -- most of the ideas I am implementing are coming out in papers weeks or months later, so I feel like I'm at the edge.
Self study requires an enormous amount of discipline though, which is partially why universities exist - because most people do not have the discipline to stick at something for 3-8 years, and I am doing it 7 days a week, almost every day of the year - because I just love this stuff, it's not tiring, it's exhilarating!