Albert Einstein and the Italian Mathematician Tullio Levi-Civita – Part I of II
The following is the first part of a two part essay by Richard Palumbo of New York, NY discussing Italian mathematician Tullio Levi-Civita and his influence on Albert Einstein.
A few years ago I remember reading, I no longer remember where, that the two things Albert Einstein cared for most in Italy were Tullio Levi-Civita, and somewhat jokingly, spaghetti. Never having heard of Levi-Civita, I decided to do some research to find out who he was and his connection to Einstein.
Only a few years older than Einstein, Levi-Civita, a beloved professor at the University of Rome, was a world renowned mathematician, the author of several books and hundreds of scholarly articles. He had received honorary degrees from foreign universities and had membership in many learned academies in Italy and abroad, including the prestigious British Royal Academy.
Both of these two great scientists were Jewish and both suffered because of Nazism. In 1933, when Hitler came to power, Einstein was lecturing in the United States. He had the foresight never to go back to Germany. Already a Nobel prize winner, a highly esteemed professor at the University of Berlin and head of the Kaiser Wilhelm Institute for Physics, he knew he was no longer welcome there. At the age of 54, he had to leave all of that and much more behind and uproot himself and his family to the United States. This was certainly a hardship, but luckily for him and the rest of humanity in the not-too-distant future he was to prosper magnificently in the United States.
Levi-Civita, on the other hand, was much less fortunate. In 1938, Fascist racial laws against Italian Jews went into effect. Like many others, he was cut off completely from Italian cultural and intellectual life. All Italian Jewish teachers at every level of education from primary to university were summarily dismissed from their jobs. Some, scientists like Enrico Fermi and Rita Levi-Montalcini, future Nobel Laureates managed to get out of Italy. But Levi-Civita was not one of them. Besides losing his teaching post at the University of Rome, he was stripped of his membership in all the scientific societies he belonged to in Germany and in Italy, such as the Royal Academy of the Lincei of which Galileo had been a member. Throughout the whole of Italy there was only one institution which did not revoke his membership: The Vatican’s Pontifical Academy of Science. He remained an honored member until his death.
Levi-Civita was especially interested in Einstein’s general theory of relativity. He and his teacher, Gregorio Ricci Curbastro, had formulated the absolute differential calculus, now known as tensor calculus. The major significance of tensor calculus was not seen until 1915, when it became known that Einstein had found it indispensable for the gravitational field equations part of his momentous theory of general relativity.
However, in 1915, in the months before Einstein announced to the world his theory of general relativity, he still had some serious flaws in his field equations. It was because of these flaws that Levi-Civita, began a correspondence with him, which lasted from March to May of that same year. During these months, Einstein wrote eleven letters to Levi-Civita, all of which have survived. Unfortunately only one of the Italian mathematician’s letters is extant.
Judging from Einstein’s letters to him, filled with highly complex mathematical equations, Levi-Civita offered serious, critical proofs to the flaws in Einstein's field equations. Einstein often smarted at these counterproofs and insisted on his own proofs. For example, in his very first letter, to Levi-Civita of March 5, there’s a hint of the controversial nature of their forthcoming correspondence:
By examining my paper so carefully, you are doing me a great favor. You can imagine how rarely someone delves independently and critically into this subject..... When I saw that you are directing your attack against the theory’s most important proof, which I had won by the sweat of my brow, I was not a little alarmed, especially since I know that you have a much better command of these mathematical matters than I. Nevertheless, upon thorough consideration I do believe I can uphold my proof.
And again in a letter of March 26, Einstein wrote: “You … do a very charming thing in your letters: First you flatter me nicely, [so as] to prevent me from making a sour face upon reading your objections.”