[cconroy]

Alan Kay had a good answer on quora for this.

Let me confess that I’ve not read every answer. But the ones that I did read were all very concerned with “squaring” etc.

The simplest answer — and I think the reason many people have difficulty with both arithmetic and especially algebra — is that you need to deeply internalize just what the “=” sign symbolizes and asserts: that there is the very same number on each side.

In other words don’t be distracted by the symbols and operations. One way to think about this is that “a number is all the ways you can make it” (i.e. it can be thought of as “processes” (an infinite number of them) as well as a “value”).

This means whatever you can do to any number can be done on both sides of the “=” because there is just the same number underneath the gobblydegook on both sides.

This is what “=” actually means. And it’s why algebra is actually quite easy rather than mysterious or difficult. [0]

[0] http://qr.ae/TU1SxJ

[cconroy]

I also think prolog has the most advanced sense of this concept with equalities and unification operators.