Emmanuel observes in the comments to the last post that the use of “algorithm” in the Felix Klein lecture predates by a few decades the earliest OED cite for the modern sense of that word; but adds, correctly, that it’s not at all clear Klein has the modern sense in mind.
Fortunately, the Cornell collection is fully searchable, and sortable by date! So one instantly finds that the earliest mention of “algorithm” among the digitized monographs is from J.R. Young’s 1843 text “Theory and solution of algebraical equations of the higher orders”:
in what is clearly its contemporary usage. No scare quotes, either. What’s more, only a handful of texts in the Cornell collection predate this one; so this use of “algorithm” could well be a lot older.
I’ve written the OED, as Emmanuel suggested. Let’s remember to check back in twenty years and see if the entry is changed!