in progress January-April 2026
By dumb luck bob went to Princeton at exactly the right moment to be swept up in the renewed interest in Einstein's theory of relativity world wide with a strong group at Princeton University led by John Wheeler, and also by chance bob connected up with Wheeler's then collaborator Remo Ruffini in exploring the physics of the then still unseen black holes in our universe, and then randomly was suggested to help translate an important article by the Italian mathematician Luigi Bianchi from the turn of the 19th to 20th centuries. This was his gateway to a lifetime of part-time life in Italy centered at the Physics Dept of the University of Rome la Sapienza, but which in so many ways reconnected with Princeton and two other Italian mathematicians (Ricci and Levi-Civita) whose deveolopment of tensor calculus provided Einstein the tools to formulate his theory of gravitation, and a third intermediary (Marcel Grossmann) who helped Einstein use those tools, with further invaluable help from Levi-Civita in the final few years of finding his way to the 1915 theory that changed the world (eventually!).
In the early twentieth century Princeton was the common thread of the culmination of Italy's mathematicians work on differential geometry and tensor calculus, group theory and its application then and later to general relativity and cosmology.
Gregorio Ricci and his younger protoge Tullio Levi-Civita had developed what is now known as tensor calculus, which Einstein's friend Marcel Grossmann transmitted to him exactly when needed to develop the general theory of relativity as a field theory describing the gravitational field. Luigi Bianchi was a contemporary who contributed his identities earlier found by Ricci, whose tensor was crucial for the Einstein field equations, but also laid the fundations of group theory and his take on differential geometry which contemporary Luther Eisenhart introduced to the English speaking world at Princeton, which later attracted Einstein to Princeton due to a combination of circumstances. Levi-Civita actively engaged with Einstein during his search for the correct field equations, and immediately afterward himself introduced the fundamental idea of parallel transport that gave a physical interpretation to the curvature considerations embodied in the field equations. Godel followed Einstein to Princeton where they were close friends, and Godel's fascination with rotating universes led to the first application of some of Bianchi's work to cosmology. Abe Taub got his PhD in Math-Physics (?) under H.P.Robertson (of the Friedmann-Robertson-Walker cosmological models during the early part of the 1930s Princeton, a decade which later became to topic of an oral history project "The Princeton Mathematics Community of the 1930s". Abe was at the IAS when Godel presented his results to his friend Einstein, and a few years later abe published a complete analysis of the vacuum Bianchi cosmologies which led to a playground for mathematical cosmology in the 1970s. bob was happy to engage in this pursuit.
As a naive physics undergraduate at Princeton University 1970-1974, I found myself in the height of Princeton's relativity community led by John Wheeler who was my sophomore Modern Physics professor just as the proofs to the ground breaking MTW Gravitation textbook were appearing (MTW = Misner Thorne Wheeler). Another undergrad Jim Isenberg '73 was looking for enough students to satisfy some quorum for a student initiated seminar by Wheeler's collaborator on black hole theory research Remo Ruffini from the University of Rome La Sapienza where Levi-Civita had been in the Mathematics department earlier in the century. Noting that Wheeler often engaged students in projects, he set 5 of us undergraduates (in addition to grad students) on various topics, and having never understood the Bianchi classification of homogenous 3-spaces, got me started in "Bianchi cosmology" by attempting to translate Bianchi's original paper exploring the possible 3-dimensional homogeneous Riemannian manifolds based on 3 semesters of college Spanish and a dictionary. Decades later with the help of Andrej Krasinski this was published as a "Golden Oldie" in the journal General Relativity and Gravitation.
I did a junior independent paper on Bianchi cosmology, then a more sophisticated senior thesis learning group theory and after meeting Godel himself at the Institute for Advanced Study in 1973, who gave me some leads on current articles to study on the topic. Then off to UC Berkeley to work with Abe Taub until his retirement in 1978. While at Princeton I became aware of Eisenhart's two texts, one on Riemannian Geometry and the other on Continuous Groups of Transformations but was unaware of the confluence of Italian mathematicians underlying the personalities of his time.
After a year postdoc with another Princetonian James York, I spent a year in Rome at the Physics Department of the Unversity of Rome La Sapienza learning Italian and initiating a four decades long collaboration with Remo Ruffini's International Center for Astrophysics and his later International Center for Relativistic Astrophysics Network in Pescara.
When Abe Taub died in 1999, a Princeton librarian made me aware of the Princeton 1930s oral history project in which he had participated but it was inpe practice unavailable to the outside world. I met with famed Princeton historian of physics Charles Gillispie about this and he suggested I do something about it. I scanned typewritten pages and converted them to web pages for the university so anyone could view them.
After my own retirement in 2025 did I finally read the story which tied together so many of these famous names. For anyone interested in the history of general relativity and the mathematical context in which it all occurred, this is a must read book:
My local web pages associated with this story are:
Tullio Levi-Civita was a friend of Einstein and both were Jewish. The racial laws in Italy in 1938 took away Levi-Civita's position and work, ending a century of more enlightened treatment of Jews in civil society that marked Italy as somewhat exceptional. The story of this century is told by