When speaking of a problem that has no solution, do the words insolvable, insoluble, and unsolvable have different shades of meaning? How do you decide which to use?

  • Any particular class of problem? Technical jargon will have different usage patterns for example.
    – terdon
    Commented Mar 28, 2014 at 16:59
  • I'm thinking of formal and scholarly writing in the humanities.
    – user53907
    Commented Mar 28, 2014 at 17:08
  • it should be unsolvable, not insolvable which is listed as extremely rare and I've never heard of.
    – Oldcat
    Commented Mar 28, 2014 at 17:34
  • @Oldcat: That's helpful. Can you tell me where insolvable is listed as rare? My Merriam-Webster doesn't mention this.
    – user53907
    Commented Mar 28, 2014 at 17:52
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    Many non-native speakers, especially Germans, get their 'uns' and their 'ins' mixed up. I had a German colleague who used to say things like 'it is unpossible', and 'we must not use the 'inofficial method'. Our mutual American colleague was amused by this, until I pointed out that Thomas Jefferson had the same problem. The American Declaration of Independence talks about 'unalienable rights'. For such a faux pas to exist in a nation's first document, the German thought it hilarious.
    – WS2
    Commented Mar 28, 2014 at 22:37

4 Answers 4


I don't think there's any possibility of a semantic distinction in the context of problems. The only difference worth pointing out is that insoluble is far more common...

This isn't to say that either of the alternatives are "incorrect", though I personally don't like insolvable (it's just a relatively uncommon/dated negated form). And in fact there's some justification for preferring unsolvable simply because insoluble has another well-known sense...

insoluble [of a substance] - that cannot be dissolved [often, in water]

...but since that sense can't possibly apply to problems, there can be no ambiguity here.

  • 7
    I'm surprised that "insoluble" is more common when it has a precise alternative meaning in chemistry and related contexts. Based on the information you've given here, I'm inclined to use "unsolvable" for problems, "insoluble" for substances, and "insolvable" for nothing at all. Thanks.
    – user53907
    Commented Mar 28, 2014 at 18:15
  • @Rebecca: That would be my inclination too. If we extrapolate the trends on the chart, it seems highly likely the majority will fall into line with our preference within a generation or two. They already have for unsolvable equations Commented Mar 28, 2014 at 18:33
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    You'll be using 'pugilist' for 'boxer' next. Commented Mar 28, 2014 at 20:42
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    @Edwin: Hardly! The whole point of my comment was to underline the fact that my preference is in line with what one could reasonably expect to be the most common usage in a few decades time (even though it certainly isn't yet). But since pugilist was supplanted by boxer over a century ago, I'd have no reason to use it except in a deliberately dated/facetious context. Commented Mar 28, 2014 at 22:16
  • We might all be speaking Chinese in a few decades time (I think the apostrophe can be left out). If they can sort out my 370-year-old telomeres. Commented Mar 28, 2014 at 22:31

A pedant will of course tell you that "insoluble" relates to "solubility", and talking about an "insoluble problem" is... bizarre at best. Alas, this seems to be one of those words that has been co-opted from its original meaning. Still, I wouldn't use it.

I recall seeing once, but can no longer find, that the difference between "insolvable" and "unsolvable" is whether a problem cannot be solved due to insufficient information or resources, or whether it cannot be solved because no solution is possible. I think "insolvable" had the latter meaning, but without being able to find the original source, I'm not sure.

  • 3
    And a real pedant will tell you that it’s the other way around: using ‘insoluble’ to refer to problems predates the dissolution-related meaning by centuries. It is the liquid sense that has been co-opted from the original meaning. The original sense was ‘unloosenable’ (referring to knots, bonds, etc.), which was then quickly transferred figuratively to problems (which are also knots). Personally, I agree that ‘insoluble problem’ sounds odd, and I too would say ‘unsolvable problem’; but that’s current usage—nothing to do with which came first in which sense. Commented Jan 20, 2017 at 16:32

I think the problem is that "solve" is not the opposite of "dissolve"; a solution may be either a liquid or an answer. The negative form should depend on the meaning of the positive form, so a substance would be insoluble, but a problem would be unsolvable. However, "insoluble" sounds more erudite and is easier to say, making it doubly attractive to most of us.


I would think "un" would link to the person applying the word, and that "in" would be applied in universal terms, that would link to all persons. So 'unsolvable' is with respect to my frame of experience, and insolvable with respect to all. So it's "can I, or can I not solve it," or "can it, or can it not be solved?" (But that's guessing--I've been called an idiot). Curious

  • Hi Cordell! This is an interesting guess, however it would be mich better if you found some sources to support your answer.
    – as4s4hetic
    Commented Oct 28, 2017 at 22:41