Two things: 1. Needless complexity 2. Needed complexity 1.: Think how programming in assembler requires you to mentally keep track of registers, and how highe

Two things: 1. Needless complexity 2. Needed complexity 1.: Think how programming in assembler requires you to mentally keep track of registers, and how higher level programming languages did away with that by enabling variable names. The resulting program is still mostly the same thing underneath. You can get the same logical results but the former is much harder. There is a question here though: why is it easier for most humans to program in C rather than in assembler? Sure, there's more housekeeping in assembler. But I think it's mostly because there's one less layer of representation. a=5; b=10; c=a+b; Vs "load 5 into register A1", "load 10 into register A2", "calculate sum from registers A1 and A2 and store it to register A3". So here in "less layered math", instead of saying: Let alpha represent the angle, a the closer cathete and b the further cathete and c the hypotenuse, then sin(alpha) = b/c You instead say: sin is the relation of the further cathete to the hypotenuse. Again, a large portion of people can get the former way of explaining sin, perhaps when they see it all at once on the blackboard or book and go back and forth... (what was b again?) but the latter way of explaining does away with the whole exercise of variables. (Note that I picked a subject of convention, not something that can be deduced from more basic principles, I think those again can be taught somewhat differently.) The problem is, many math teacher love variables and think how beautiful all that symphony of x:s and y:s is. But for the average school student math is just one subject among others. They just want the essentials with the least amount of extra crap and layers on top. Lots of caveats here. I think people need to learn basic algebra, but it makes me sad that so few people can't use it for problems they are trying to solve. I think these would make interesting psychology research subjects. It's a very important field. 2.: Yet you can't go beyond some point in simplification.