What makes math different from other subjects?

One significant way that maths are different from other subjects is that maths teach abstract concepts using the abstract symbols of numbers.

While it can be said that all language is communicated through the abstract symbols of words and letters, it is also true that these abstract symbols are part of our daily communication experience from the time that we're one-and-a-half or two years old (or even younger if we're read to). It can also be said that, as much as we love maths, we never use the abstract symbols of numbers in our daily communications of trivia, joys, sorrows, loves and irritations. This is because numbers are abstract symbols of a specialized set.

We are all so familiar with the opening gambit of math learning, "2 + 2 is the same as 4," that we forget these abstract symbols are conveying an abstract concept. True, "2 + 2 is the same as 4" originates in a concrete concept, often involving apples (or perhaps pomegranates): "If you have two apples and someone gives you two more apples, then you have four apples." Apples are very concrete: "two apples and two apples is four apples" is a very concrete concept, so concrete that you can eat those four apples. [It is fair to also say that for the literalist, not innately versed in metaphor, "2 + 2 is the same as or is equal to 4" is clearly an untruth for "2 + 2" and "4" are clearly not the same nor equal.]

The abstract concept behind the two and two is four apples is that things manipulated by rules in a non-spatial context, represented by abstract symbols, produce identical results that can affect the spatial world. To illustrate the abstract nature of maths, think of 10 apples raised to an exponent of 20. You do not want a concrete demonstration of the correct calculation for how many apples that results in (as you might want for 2 + 2 = 4 apples). You want to leave those apples on the abstract plane where they can be manipulated by rules. Ten apples raised to an exponential power of 20 yields 100000000000000000000 apples. To reiterate my opening point: maths are different form other subjects because maths teach abstract concepts using the abstract symbols of numbers (in combination with other abstract symbols: + = < ^ - ( ) and so on).