Eduard Cech collaborates with Guido Fubini

Eduard Cech was a student of Guido Fubini and the two collaborated on the two-volume treatise Geometria proiettiva differenziale (1926-7). In a letter to Beniamino Segre written in 1954, Cech explains how the collaboration came about:

I personally met Fubini in 1921, that is, two years after I began dealing with questions that now belong to the field of differential projective geometry, and the printing of my first scientific work dates from that year, in whose Autumn I began to study in Turin.

At the beginning of my stay in Turin, Fubini helped me a lot listening patiently to every detail of the descriptions of the research I had just begun and following nearly daily the development of my ideas. Although he himself was rather analytic, he strongly encouraged me to develop the faculty of synthetically reasoning; on the other side, he never stopped encouraging me to deal with questions that required long and complex calculations. There is no doubt that, when later I analytically solved very complex questions in some memoirs, without Fubini's encouragement I would not even have dared to think about solving them.

The idea of collaborating in writing a broad summary of differential projective geometry goes back to Fubini, and was suggested by him towards the end of my stay in Turin. I did not think of myself as being able to do it and only with great effort did Fubini manage to convince me. During the preparation of our treatise on differential projective geometry and later, we exchanged hundreds of letters, sometimes really voluminous ones. Maybe there are not many examples of so close a collaboration supported only by letter exchange. And then, even if there are many books written by an expert scientist in cooperation with a young pupil, it is rare that there is a case such as ours in which the master fully allows the pupil to add to the mutual work the detailed description of developments sometimes distant from the master's interests. I also consider this point to be remarkable, and significant evidence of Fubini's greatness.

JOC/EFR May 2013

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