Einstein and Projective Geometry

We discuss research notes by Albert Einstein that we identified with considerations on projective geometry and more precisely with involutions. We find that Einstein considered specific sketches on projective geometry at different time periods, namely around 1913 before formulating his theory of general relativity, between 1929 and 1932 and in 1938 when he and Peter Bergmann published “On a Generalization of Kaluza’s Theory of Electricity.” Interestingly, the sketches are strikingly similar to each other, although they were written some quarter century apart. Already the fact that Einstein as a theoretical physicist of the first half of the 20th century considered this mathematical subject is intriguing. In this chapter, we connect the respective subjects to his own education and discuss them also with respect to his collaboration with Marcel Grossmann, who was a good friend of Einstein and an expert on projective geometry. At the end of the chapter, we outline a possible conjecture on how Einstein might have used projective geometry for his own research.