Real Face of János Bolyai Tamás Dénes

I n Vol. 56, No. 11, of Notices, I saw a fascinating article with the title: Changing Faces—The Mistaken Portrait of Legendre. The author, Peter Duren, writes with understandable bewilderment: “It seems incredible that such egregious error could have gone undetected for somany years.” This encouraged me to publish, in the same journal, the story—no less fascinating—of the real face of János Bolyai. It should be explained that in the case of János Bolyai two different interpretations of the word “face” are justified: the “face” in terms of the portrait (painting, drawing), and the “face” as an abstract concept. The first part of the article introduces the surprising story of his only portrait, which, although universally accepted, turns out not to be of him at all. The second part explores his intellectual or “mind-face” (it is my own word formation) and outlines a new approach to Bolyai’s creative life and work. The town of Marosvásárhely—which lies in the heartof theCentral EuropeanTransylvania—fulfills an important role in the history of the Bolyai family: János lived most of his life there, and the local library holds most of his manuscripts. The reader might find it strange that while János Bolyai is well known around the world as an eminent Hungarian, Transylvania (and so Marosvásárhely) can be found within the borders of Romania. This can be explained by the unsettled history of Transylvania. If we look back only to the nineteenth century, the part of Transylvania that was populated mainly by Hungarians was autonomous at times, whereas at other times it belonged to Hungary. In 1947, following World War II, the Treaty of Paris gave this area to Romania, so that is where it is found on today’s maps.