In 1637 Pierre de Fermat, a French lawyer and mathematician, scribbled a short note in the margin of his copy of Arithmetica, a 3rd century AD treatise by the Greek mathematician, Diophantus. He wrote that he had found a marvellous proof of the following statement:

a^{n} + b^{n} = c^{n} has no solution for any integer value n greater than 2

His comment that the margin was too small to contain his reasoning intrigued mathematicians and started a search for the proof that was, presumably, only a little too long to fit into the blank space at the side of the page. But a simple proof proved to be elusive. Many eminent mathematicians chipped away at the problem for the next 358 years until Andrew Wiles found the key in 1993 and published the first complete proof in 1995.

The proof, when it came, relied on modern mathematical techniques that would have been unknown to Fermat. And it certainly wouldn’t fit into the margin of Arithmetica; it was far too long and complicated for that. Fermat was very probably mistaken but perhaps he only missed his target by the tiniest of margins. He never published his proof, so we will never know.

Half Moon Run think they narrowly missed their objective, too. In Narrow Margins they tell of the rules they must live by, rules that misdirected their hands when they reached out to catch their heart’s desire.

I swear I almost touched it
Yet it slipped between my fingers

Half Moon Run is a Canadian indie rock band with strong folk and subtle country influences. Their single, Full Circle, was featured in one of the very early Crotchety Man blog posts in February 2015. At the time, my partner and I were busy preparing to move house and that post did little more than provide a link to the song on Spotify. If I was writing that post today I would say that it’s a delightfully catchy song.

Narrow Margins is equally delightful and, for my money, is the stand-out track on the band’s second album, Sun Leads Me On. Why it was never released as a single baffles me almost as much as Fermat’s marginal note perplexed three and a half centuries of mathematicians. Perhaps it had something to do with the rules and narrow margins of the record publishing companies.

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