I disagree with you. Many of the careers that get a lot of prestige - law, medicine, business management, etc - all require that you understand a variety of fi

I disagree with you. Many of the careers that get a lot of prestige - law, medicine, business management, etc - all require that you understand a variety of fields, or are at least greatly aided by understanding a second field in depth in addition to the one primarily related to your career. Similarly, if you're not competent in a few fields (math, reading, writing, basic computer operation), you're simply going to lose out to more competent peers in the workplace. Finally, your annotation makes an extremely important point: people we see making breakthroughs in fields - the truly top tier academics for instance - are well known for working in multiple fields and having wide interests. You cite an example yourself when you mention Neumann, who made contributions to a wide variety of math, led the team that invented the first computer, worked on several military projects, and contributed to a few tangential fields occasionally, for example applying game theory (which he invented) to economics. In reality, the truly dominant people tend to be polymaths, and the middle to middle-top tier tend to be highly specialized.