Today is the 204th birthday of the Irish polymath Sir William Rowan Hamilton. Although he made major contributions to various branches of physics, astronomy and mathematics he is most famous for his discovery of Quaternions in 1843. This is considered to be the first non-standard algebra of which many were to be developed in the following decades of the nineteenth century. In his algebraic work Hamilton was very much part of a group of contemporary mathematicians centred around the two Trinities, Trinity College Dublin and Trinity College Cambridge. Two other prominent members of this group were the logic pioneers George Boole and Augustus De Morgan, both of whom published important new works on symbolic logic in 1847, Boole’s Mathematical Analysis of Logic and De Morgan’s Formal Logic. Boole’s work was the second non-standard algebra. Now Boole’s work was, according to his own account, inspired by the very public dispute between De Morgan and the Scottish philosopher Sir William Hamilton over the quantification of the predicate (if you don’t know what that is don’t worry it’s not relevant to the story!). As the Scottish philosopher and the Irish mathematician were contemporaries and are both called William Hamilton writers on the history of logic go out of their way to tell their readers not to confuse them, which in fact does happen in books about the history of logic!
Now I worked for many years in a research project into the external history of formal logic that amongst other things built up data banks on the logicians and their publication as well as secondary literature about those logicians. One of our side projects was a collection of portraits of all of the logicians we were researching. This meant that we were also trying to acquire portraits of both William Hamiltons. Just for information, this was of course pre-internet. Now one of my colleagues had managed to find a portrait of an early nineteenth century Sir William Hamilton in the collection of the National Portrait Gallery in London. He wrote them a letter requesting a photographic copy of said portrait and offering to defray any costs that might occur. In due course he received the desired photo and was now faced with a new problem, he didn’t know which William Hamilton was represented in the picture. I got the job of finding out! My researches led to a very interesting result, the gentleman portrayed in the photo was neither Sir William Hamilton the Scottish philosopher nor Sir William Hamilton the Irish mathematician but Sir William Hamilton Scottish diplomat and archaeologist and most notoriously the husband of Emma Hamilton the legendary mistress of Admiral Lord Nelson.
Sometimes being a historian of science can lead down some very strange paths.