Oscar Zariski - forgot about his own wedding

I am always excited when I stumble upon a biography of a mathematician I wasn’t previously aware of. It’s strange (or perhaps not, given we’re talking about mathematics) how many brilliant minds in the field lack the biographical treatment they deserve. Consider just a few luminaries from the first half of the 20th century: André Weil (opens new window), Hermann Weyl (opens new window), Carl Ludwig Siegel (opens new window), Emil Artin (opens new window), Edmund Landau (opens new window), Helmut Hasse (opens new window).

For physicists, it’s a bit different. I think they are much better covered. The reason might be that their work is more directly connected to everyday life. Just think of nuclear energy or the theory of relativity, which is crucial for GPS (opens new window) to work properly.

So, recently I came across the biography of Oscar Zariski (opens new window). Zariski (1899-1986) was one of the founders of modern algebraic geometry.

My wish is that one day I will be able to read Zariski’s book Algebraic Surfaces from 1935, as well as the 1971 version, which includes notes from his students—remarkable mathematicians like Robin Hartshorne (opens new window) and David Mumford (opens new window). Zariski mentioned that with this book, he began doing real mathematics, real algebraic geometry. In it, he reconstructed the algebraic geometry developed by the Italian school using the modern algebra introduced by Emmy Noether (opens new window) and Wolfgang Krull (opens new window).

But what about his life? Let’s consider the following paragraph from the book: “I spent hours and hours doing math problems without a teacher forcing me. Whole books of algebra problems – I did them one after another. I was only seven or eight, but I always wanted mathematics.”

That might be something you’d find in many biographies of world-renowned mathematicians, right? However, Carol Parikh notes: “Although Zariski was by all accounts an exceptionally quick and eager math student, the full extent of his gifts became apparent relatively late in life. He was almost twenty-five before he published his first paper and almost fifty when he did his great work on holomorphic functions...”

In fact, Zariski remained active and productive even into his eighties.

But how did Zariski’s story begin? It seems his older brother Moses played a significant role in shaping young Oscar. He taught him elementary algebra, and even when Oscar began surpassing him, he never resented it. While Oscar was in gymnasium, Moses would buy math and philosophy books for him during his business trips to Moscow and Petrograd. Oscar was especially interested in Hegel and Marx.

I think it’s difficult for us today to fully grasp the hope that the Russian Revolution brought to the working people. There’s the following paragraph in the biography that illustrates this well: “He crossed the border into Italy in the late winter of 1921, having decided to enroll at the University of Pisa. On the platform at Udine, where he had stopped to change trains, he was recognized as Russian. Before he could even step into the waiting room, he found himself surrounded by a crowd of railway workers eager to hear about the revolution.”

Of course, Italy was a turbulent country at that time, and Parikh continues: “Had there been a Fascist among the workers, the warmth of his welcome might have been quite otherwise...”

But back to mathematics. I was quite surprised when I read the following paragraph: “In the fall of 1921 the University of Rome was the most important center of algebraic geometry in the world. What is now known as 'the Italian School' had been started by Luigi Cremona (opens new window)... It was only after 1900, however, as a result of the combined efforts of three great Italian mathematicians – Guido Castelnuovo (opens new window), Federigo Enriques (opens new window), and Francesco Severi (opens new window) – that the Italians had carried algebraic geometry off in a startling new direction.”

In many history books on mathematics, you read so much about Göttingen mathematicians that you might easily get the impression that most of the important work was done there. Of course, that was not the case. I was surprised to learn that algebraic geometry actually began in Rome.

However, Zariski later regretted not engaging with Göttingen mathematics earlier: “It was a pity that my Italian teachers never told me there was such a tremendous development of algebra connected with algebraic geometry.”

The leader of the algebra revolution in Göttingen was, of course, Emmy Noether. Emmy Noether is one of my favorite mathematicians, and I’m always happy when I discover something new about her. Her lectures were legendary, but there are two anecdotes from Zariski’s biography that I hadn’t heard before: “Once, for example, when she was lecturing, her slip came down. She bent down, pulled off the slip, threw it into the corridor, and kept on lecturing.” And another: “Noether would be so eager to get her thoughts down that she would write across a wet blackboard, leaving her students to wait patiently for it to dry so they could read it.”

There was at least some interaction with Göttingen, though. It is mentioned that Edmund Landau visited Rome at some point, and when he heard that the young Zariski liked to play chess, he invited him to a game. “But how can we play with all these people around?” asked Zariski, as they were in the middle of a party. “Easily,” Landau replied. “Blank. You know, without a board.”

Zariski and other mathematicians and physicists regularly gathered at Caffè Greco to gossip and play chess. It’s interesting how important cafés were at that time. A recurring theme in the biographies of European mathematicians from the first half of the 20th century is their role in cafés. Just think of the Vienna circle (opens new window) or the Scottish Café (opens new window).

What also surprised me in the biography was the striking difference between Jews in Italy and in Poland. Last year, I read Leopold Infeld’s autobiography, where he describes the Jewish ghettos in Poland as being almost completely isolated from the general population. In contrast, Zariski’s wife, Yole, who was an Italian Jew, was raised as an Italian and was largely unfamiliar with Jewish traditions. She was utterly surprised when she first saw the Jewish quarter in Warsaw, remarking: “The Jews in side curls and kaftans made me feel that I was living in two different nations.”

But the story in the book that I liked the most is this one: Zariski was, of course, very much obsessed with mathematics. On the day he and his fiancée Yole were getting married, with Yole already dressed in white and veiled and the rabbi standing by, the bridegroom was nowhere to be found. It turned out he was working on a mathematical problem. Luckily, Yole was neither angry nor surprised; she was amused. Ha! I need to tell this to my wife.