Non-trivial. Engineers especially seem to love this expression. Why does it always take me out of the moment? Some of my favorite programmers use this, for example Rich Hickey, the designer of the Clojure language.

Use of the word may be justified, as you can read here. "Non-trivial" usually signifies the quality being difficult to accomplish (or prove). Possible alternatives like significant, important, and substantial don't carry this meaning. What about simply, difficult?

closed as unclear what you're asking by Drew, Mitch, James McLeod, Janus Bahs Jacquet, choster Jul 13 '15 at 4:10

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    There seems to be no real question here. It seems to be only a statement that the OP is irked, and of what irks. – Drew Jul 12 '15 at 17:25
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    Exactly why it irks you is a non-trivial question. – Spehro Pefhany Jul 12 '15 at 17:34
  • I guess you don't have a good background in mathematics to be familiar with the term. – Blessed Geek Jul 12 '15 at 21:07
  • I find the question legit. OP is asking for alternatives to "non-trivial". The personal take (why the alternative is sought) is secondary... Admittedly, a context would be a great help. – anemone Jul 12 '15 at 22:00
  • The term seems to have spread from strict math and engineering lexicons to the infection of regular conversation, esp start-up and California business speak, where instead of lending mathematical clarity the term obsfucates, using an air of precision without, well, without the precision. It reminds me of when speakers use "utilize" to puff up their language. – Mallory-Erik Jul 13 '15 at 1:57

The term trivial comes from mathematics, where it is essentially a technical term with a relatively precise meaning.

The etymology of the term is said to have started with the way university studies were organised in the Middle Ages.

trivium (taught first):

  • grammar
  • logic
  • rhetoric


  • arithmetic
  • geometry
  • music
  • astronomy.

So we can assume that trivial originally referred to what didn't have to be repeated in the study of mathematics (arithmetic and geometry), music or astronomy because it was already clear from what students had learned in the trivium.

The modern sense in which mathematicians use the term trivial is still pretty close to this (presumed) original one, though in some ways it has been generalised and extended to different contexts. I will try to illustrate this with non-mathematical examples that capture the essence of the term:

The question whether a platypus or a cangaroo is a mammal is a non-trivial one. This is not the kind of thing that was taught in the trivium or that can be resolved by simple logical thinking. It depends on deeper knowledge of these animals and the precise choice of words in the definition of mammals. The question whether a cow is a mammal is arguably trivial. (Remember I said above that mathematicians use the word in a relatively precise way. This is nothing unusual. Most words are a bit fuzzy like that.) The question whether all unicorns are mammals (note the formulation, which matters in this case) is trivial in the sense that we can assume it to be general knowledge that unicorns don't exist. So the claim follows by pure logic without any required further knowledge of unicorns or mammals. It is equally true, and equally trivial, that all unicorns are insects and that all pink dragons are pregnant.

A derived usage is to call a mathematical object trivial if it is as simple as possible, provided this means it's totally boring. Some examples of this should be generally accessible. (1) For example the set of all unicorns is empty, and we could call the empty set the trivial set. (2) Every group must contain at least a unit element, often called 1 or e. So there is no such thing as an empty group. But if 1 is the only element of a group, the group is called trivial because it's as simple as it could possibly be.

The term non-trivial also comes from mathematics. As many negated notions do, it has two related meanings. The more technical one is just the negation of trivial. In this sense, calling a question non-trivial is just a short way of saying it is not trivial. Also (1) a non-trivial set is a non-empty one, (2) a non-trivial group is one with more than one element (i.e. with other elements besides 1).

The other meaning of non-trivial could be described as far from trivial. This usage probably started as an understatement, and it's what people usually mean when they call a problem non-trivial. Though not defined precisely, it often means roughly that a mathematician of average skill working in a different field wouldn't be able to solve the problem in a short time just by examining the definitions.

The precise interpretation of non-trivial depends on context just like the interpretations of similar words such as non-technical or non-violent do.


There are plenty of synonyms: an algorithm could be involved or complex for example. Speaking explicitly of an implementation, you could call it difficult or tricky. You could also use subtle, not obvious, or hard, as in a hard problem.

Non-trivial almost always actually means "I don't know how to do it, but can probably figure it out."


The problem with difficult and easy are that they can be subjective or dependent upon the capabilities of the person making the statement. Marathon runners may declare that some city marathons are more difficult or easy; but they are all impossible to me.

Alternative worlds like hard and complex also suffer from the same problem of perspective.

In contrast trivial is less likely to be seen as a subjective statement. In day-to-day use something is trivial if it is straightforward to a journeyman else easily solvable by a group of novices. A genius may say something is trivial when it is only obvious to a handful of people yet such abuses of the term are rare.

The description of a technical problem being non-trivial very specifically says that the problem has a non-specific degree of complexity. This is well suited to discussions about the amount of resources and effort which may be required. It rules out that the effort to explain or solve the problem will be negligible.


Perhaps, knotty?

knotty adjective: knotty; comparative adjective: knottier; superlative adjective: knottiest

• (of a problem or matter) extremely difficult or intricate.

synonyms: complex, complicated, involved, intricate, convoluted, involuted. (Google)

  • It is not helpful to attempt to yank the field of computational complexity out of the field and terminologies of Mathematics, especially if you do not realise you might be embarking on such an endeavour, by introducing terminology that already has its own mathematical significance. – Blessed Geek Jul 12 '15 at 21:11
  • @Blessed Geek - I was unaware that 'knotty' was terminology that already has mathematical significance. – user98990 Jul 12 '15 at 21:41

Non-trivial is not used in the sense of a problem being difficult. Most non-trivial problems are difficult.

Non-trivial, in engineering and scientific parlance means important. Non-trivial problems highlight interesting features of a theory. The sometimes highlight what's lacking in a theory. Non-trivial problems may or may not be difficult.

Example: Long-division method is difficult, but is trivial. But proving square-root of 2 is irrational, is non-trivial [the proof is quite short though!].

  • Non-trivial problems aren't necessarily important. E.g., determining whether the number of humans alive in a specific given instant is a prime is a non-trivial problem, but definitely not important. However, the attempt to solve a highly non-trivial problem, no matter how intrinsically unimportant the problem is, can lead to significant break-throughs. – user86291 Jul 12 '15 at 20:03

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