Breadth of knowledge increases your mental sharpness just as depth of knowledge though, they both do. If you only go for depth, you can do a PhD in a super nar

Breadth of knowledge increases your mental sharpness just as depth of knowledge though, they both do. If you only go for depth, you can do a PhD in a super narrow field and it will increase your mental sharpness significantly. However, it won't be easy for you to apply that sharpness in the real world, as it is very specific. If you want to go for breadth, the best thing for that is definitely a startup, as you have to become really, really good across all disciplines. Having done that for a while now, I start to miss the challenge of depth, such as mathematics and physics, which I would like to do more once that has stabilized. :) So that's that, hope I could give some insights.