I strongly believe they should. I've learned much more about math by looking at its history. Then again, I've simultaneously had to learn a lot of applied math

I strongly believe they should. I've learned much more about math by looking at its history. Then again, I've simultaneously had to learn a lot of applied math quickly, so I have skipped the historical perspective on many things too. I think the way I learn best is simply try to apply a concept first and struggle until I become deeply frustrated. Then I backtrack and try to learn the fundamentals that influence the most current tools and methods of application. Part of understanding these fundamentals is understanding the history of an idea and how it evolved.