Today, for many students, the logarithm is a bogeyman: a strange word, a $\log$ that appears out of nowhere and rules to memorise. In the seventeenth century it was the opposite. It was Europe’s calculator, the tool that saved astronomers, navigators and accountants months of work. The old texts on this site said the logarithm was the purest example of mirabilis abbreviatio, the marvellous abbreviation. And its inventor agreed: the title of his book begins with the word marvellous.