The muddle over vanishingly unlikely

Dot Wordsworth
issue 18 July 2026

When my husband asked me whether I knew any mathematics at all, I replied by telling him that I had been a properly brought-up girl. The cause of our little wrangle was the phrase vanishingly unlikely.

A newspaper article on scams pointed out that ‘only a tiny minority of oil workers are women, meaning it is vanishingly unlikely to meet a real one online’. Another said that ‘Britain is vanishingly unlikely to meet Nato’s target of spending 5 per cent of GDP on national security by 2035.’

In both those examples, vanishingly is used in the sense ‘infinitesimally’. But the meaning properly wanted here is ‘hugely’ or ‘almost infinitely’ unlikely. It is the likelihood that is vanishingly small. The unlikelihood is very great.

This is different from vanishingly small, which is just something so small as to vanish, or even vanishingly rare, which is something so rare as to become invisible to inspection.

My husband’s mathematical challenge was directed to what he saw as my weakness in not understanding calculus and allied trades. There are, for example, things called vanishing fractions. A vanishing fraction reduces to the form zero over zero for a particular value of the variable which enters it. But I don’t think this has any bearing on vanishing likelihood.

With vanishingly unlikely, I think we are caught in the same positive/negative muddle that makes people say not unsurprisingly when they mean ‘unsurprisingly’. Listen out to news programmes like Today and you’ll hear them do it, quite unaware.

It’s quite a boring thing to say that something is unsurprising in the first place. I’m afraid that the World Cup has brought it to a very florid state: ‘Argentina have unsurprisingly been unable to retain possession.’ The author might as well have written uninterestingly. But if he’d been delivering his opinions orally he’d have been likely to say not unsurprisingly.

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