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In Shakespeare’s Othello, Iago is furious to find Michael Cassio, ‘a great arithmetician’, whose knowledge of warfare is all book-learning, has been promoted ahead of him.

It is arguably a more instructive puzzle for budding computer scientists than it is for budding arithmeticians.

Of Carlile’s family, I can gather little beyond this, that his father had some reputation as an arithmetician.

He is well up in logarithms, and a capital arithmetician, I won’t say mathematician, though he knows something of mathematics as well.

You are a clever arithmetician, mamma; you do your sums and get your totals nicely.