For instance, in my life, I went all the way up to PhD level courses in mathematics. This translated into me being able to go into my start-up and solve all sorts of problems. I was also solving problems that were already solved because I was ignorant of what was considered good programming practice.
Like source control. Because I could, I wrote my own source control. Like an IDE. Because I could, I wrote my own.
I attribute my fantastic problem solving skills to my mathematics back-ground. After all, when dealing with proofs in abstract algebra and the creative process of making up strange sets that exhibit strange behaviors... Most things seem trivial at some level.
The fundamental problem of mathematics is that you spend a lot of time solving fake or stupid problems to build up the ability to solve real problems. If you are going to go into the cutting edge of research, then you will need those skills. Otherwise, you will be very good at solving artificial problems.
I want to say that it will make you a better engineer, but I'm very biased. I feel like it has helped me compared to my peers in terms of raw engineering power.