Something that I think is important in math is the practical and theoretical going hand-in-hand. I'm still an undergrad student, but I have really enjoyed my ma

Something that I think is important in math is the practical and theoretical going hand-in-hand. I'm still an undergrad student, but I have really enjoyed my math education so far. I have always appreciated both the beauty of the abstraction of math, as well as the beauty of applying that abstraction to solve very real problems. That being said, I think something might be lost when you take away the abstraction of math. I think a lot of math -and math abstraction especially- is difficult because of the way variables are understood. Since the beginning of algebra one, we learn that we can have an unknown, say 'x', and we can solve for it trivially by manipulating an equation to set 'x' equal to some value. But people always seem to get caught up in the naming idea. I remember in high school math classes, many of my peers would get so hung up as soon as the 'x' was turned into a 'y'. I felt like it was hopeless trying to explain that 'x' and 'y' are just names for something. This same problem percolates into every bit of math. After enough time, functions in math become first class citizens as well. That throws even more people. The exact same problem is seen in the programming world when people move from functions as an idea of a subroutine to being treated like a first class citizen. And lets not even mention Haskell or another functional language, with currying and stuff like that. I guess that's the problem that I see in math; the idea of an abstraction is difficult. However, I'm not totally convinced that making complex math more concrete is the best way to do that. At some point, having linked numbers like in interface builder looses its usefulness. So much of math is proofs. How can you do proofs when you are constantly instantiating concepts, rather than dealing with an abstraction. At some point, "there exists" needs to become "for all," which I think might be difficult in this type of mathematical environment. Again, concrete and abstraction really go best hand-in-hand, in my opinion.