[teraflop]

"Elementary" is a somewhat subjective term that roughly means "from first principles", i.e. not relying on a bunch of advanced theorems and concepts. It doesn't necessarily mean the explanation is simple or concise.

[eru]

Often the advanced theorems and concepts make for a simpler and more concise explanation.

I guess the closest equivalent in programming is "implement X without using any external libraries (or perhaps only the standard library)".