Figure 1: The author at the Brougham Bridge in Dublin.

Remember the Brougham Bridge, where Hamilton carved the quaternionic multiplication table in 1843? Well, on 21 July 2004, as the author walked along that very same canal in Dublin… (See Figure 1.)

No, that's not how the octonions were discovered. Hamilton sent a letter to his good friend John T. Graves the day after his discovery in October 1843. On 26 December 1843, Graves wrote back describing the octonions, which he called octaves, a name that is still sometimes used. However, Graves didn't publish this work until 1845, shortly after (and in response to) Arthur Cayley's publication of his own discovery of the octonions. For this reason, the octonions are also known as Cayley numbers. Although Hamilton later vouched for Graves' priority, Cayley did publish first; both are given credit for independently discovering the octonions.