A correspondent writes to say she had read the sentence 'She resigned after fewer than 14 months in the post', and she comments: 'I can see that, in theory, "fewer" is correct here because it refers to the number of months; but, in practice, it sounds completely wrong to me. My explanation, for what it's worth, is that what "fewer than 14 months" communicates is a number of months smaller than 14; whereas what the writer really meant was "just under 14 months" - i.e. an amount of time, not a number of months. Does "fewer than 14 months" sound wrong to you? And if so, why?'
It certainly does - but not for the numerical reason given. It's not so much the fact that there's a number but how we view the number which is important. '14 months' here isn't being viewed as a series of separate months but as a holistic period of time. It's really 'She resigned after a period of less than 14 months in the post'. The usage is therefore uncountable rather than countable, which is why 'fewer' sounds odd and 'less' would be the preferred option.
There are lots of alternations which depend upon how we view the noun. The standard examples are 'more cakes' vs 'more cake'. But virtually any noun can vary in countability, if the context is right. 'Tables' and 'chairs' are countable - but in a story about a hungry termite family, we might encounter someone asking for 'some more chair' for pudding, or one termite complaining that he had been given 'less chair' than another.