Not simply the converse of trivial that it sounds like, nontrivial (or non-trivial) implies exceptionally difficult. Use of this word is perhaps the most pervasive example of geek powers of understatement. There are probably three categories of problems: trivial, nontrivial, and tasty.

nontrivial adj.

Requiring real thought or significant computing power. Often used as an understated way of saying that a problem is quite difficult or impractical, or even entirely unsolvable ("Proving P=NP is nontrivial"). The preferred emphatic form is `decidedly nontrivial'. See trivial, uninteresting, interesting.

--The Jargon File version 4.3.1, ed. ESR, autonoded by rescdsk.