From Grassmann complements to Hodge-duality

Hodge duality is a central concept of 20th century algebraic and analytic geometry and plays a non-negligible role also in recent mathematical physics. At first sight one might expect that its origins lie in the 1930s when its name-giving protagonist, William V.D. Hodge, started his mathematical research. On the other hand, a close link between Hodge’s theory and the Maxwell equation has been claimed not only from a systematic point of view but also historically by Hodge’s former student M. Atiyah in his talks on dualities in mathematics and physics.