Does Programming Help You Understand Complexity?

I got the following question in an email. My nephew is currently in high school in China and has developed a strong interest in computer science and mathematics. Recently, we've been talking about how computers can solve incredibly complex problems, yet there are still some problems that even the most powerful computers struggle to handle efficiently. I work in backend data maintenance myself, so I often think about how much a system's performance depends on the way a problem is approached, rather than simply how powerful the technology is. From your experience, what do you think is the most important thing a young student should understand about the limits of what computers can do? Would you encourage someone like my nephew to begin exploring these questions through mathematics and logical reasoning, or to start by writing programs and discovering the challenges through practice? A great question with no perfect answer. For me, I did considerable programming in high school and…