Another sister, Margaret (1876–1951), was an authority on the history of fine English home-furnishings, and the life-long companion of the novelist Ivy Compton-Burnett.

[2] He corresponded with Ludwig Wittgenstein, meeting with him in Cambridge to discuss Frege's book Grundgesetze der Arithmetik, parts of which Jourdain had prepared a translation.

He also worked on algebraic logic, and the history of science with Isaac Newton as a particular study.

Near the end of his life Jourdain became increasingly obsessed by trying to prove the axiom of choice, and published several incorrect proofs of it.

Littlewood (1986, p.129) describes Jourdain on his deathbed still arguing with him about his (incorrect) proof of the axiom of choice.