Mathematics and the Arts: What Does Geometry and Calculus Have to Do with Salvador Dali and War and Peace?

On Tuesday 31st March 2015, Piergiorgio Odifreddi, Professor of Mathematical Logics at the University of Turin, will give a public lecture at HSE titled ‘Mathematics and the Arts’. The lecture is held in cooperation with Istituto Italiano di Cultura, and will examine the deep and close relationships between the objects of Mathematics and of the Arts.Professor Odifreddi, who is also a well-known journalist will talk about ‘a mathematical reading of the arts’, and will present a short history of the visual arts from a mathematical perspective. He talked to the HSE English News service about the surprising connections his unusual approach reveals.

— How did you start working on the issue of mathematics and the arts? What inspired you? Was it some masterpiece or the result of scientific reasoning?

— I was always interested in the arts, and as a mathematician I started noticing the mathematical and scientific aspects of paintings early on. Through the years I gave some talks about them, but some years ago I decided to write a popular history of geometry, and to illustrate the concepts and the results through artistic works. This eventually became a trilogy (There's Space for Everybody, A Way Out and Down with Euclid), with hundreds of pictures in each volume, which has been quite successful in Italy.  

— You include the works of world famous artists such as Michelangelo, Severini, Malevich and others in your research and presentation. It must be a real aesthetic pleasure working with such material. What is your method for a mathematical reading of the arts?

— I always try to choose works that have a mathematical point to illustrate. Often these aspects have been conscious in the artists' mind, and sometimes they have talked and theorized about it. Severini, for example, wrote an explanation of how he had used a theorem of Euclid on similarities to automatically induce an artistic balance in one of his paintings, called Maternity, which of course I used to illustrate that very same theorem.

The visual arts should be used to make mathematics visible to the body's eye, not to keep it confined to the mind's eye as they usually are

— How would you formulate the main goal of your research matching visual arts with a mathematical perspective?

— I think that the visual arts should be used to make mathematics visible to the body's eye, not to keep it confined to the mind's eye as they usually are. This is very natural to do in geometry, that naturally lends itself to this treatment, being a study of space. It would be more difficult to do it for arithmetic, and even more so for logic or other highly abstract fields.

— Did you ever use any visual images, besides Malevich, from Russian and Soviet arts?

— Sure. Among the moderns, Kandinsky and Chagall. And among the classics, Andrei Rublev: his work is very interesting from the perspective point of view, since the Byzantines used a "reverse perspective" in which parallel lines did not converge on the canvas, but rather diverged. This corresponds to having the vanishing point not in front of the observer, but on his back. And I will talk about this in my presentation.

— What's next on your research plate now?

— I have now started an illustrated trilogy on arithmetic and numbers, which will complement the geometrical one. And I'm experiencing the difficulties I've hinted at above, in trying to visually illustrate numbers and numerical concepts. The first volume is already out: it's called A Museum of Numbers, and is presented as a catalogue of "numerical pictures at an exhibition", as Mussorgsky would have said.

If you don't see the geometrical transformations of a score that the baroque composers used in their music, you would certainly lose a lot of what they put it in

— Could you name your favorite painters or is the list too long?

— I'm very fond of Salvador Dalì, a surrealist whose work at first sight should have no mathematical content. Instead, he was very interested in mathematics, and liked to talk about it with the mathematician Thomas Banchoff, who suggested to him concepts that he later used in some of his paintings, such as Corpus Hypercubus, or The Last Supper.

— Who could understand your ideas better, mathematicians or art lovers?

— Their two views are not opposite, but complementary. It's the same as with music: if you don't see the geometrical transformations of a score (reflections, rotations, translations, etcetera) that the baroque composers used in their music, you would certainly lose a lot of what they put it in. But if you stop at that, you then lose the rest of their inspiration, which was also, but not only mathematical.

— Do you have any special plans to visit the Tretyakov Gallery or Pushkin Museum of Fine Arts in Moscow?

— I lived in the Soviet Union for two years, in 1982 and 1983, and at the time I travelled through it extensively, from Leningrad to Novosibirsk (where I stayed), from Tbilisi to Yerevan, from Samarkand to Tashkent. And everywhere I always tried to see as much as possible, including the museums.

At the time, I spent a couple of weeks in Moscow, and I came back for the first time this last New Year's holiday. Three months ago I did go back to the Tretyakov Gallery, where I saw Rublev's Holy Trinity: a wonderful example of the "reverse perspective" I was talking about. This time I hope to have time to go back to the Pushkin Museum.

But I also have a plan to visit Yasnaya Polyana, where I've never been before. And, having just finished reading War and Peace, a work with an unexpected use of mathematics (calculus, in particular) as a theory of history, this will be one of my top priorities.

Incidentally, in the second book of the geometric trilogy I quoted a famous page of Dostoevsky on non euclidean geometry, and illustrated it with a portrait of him that is indeed in the Tretyakov Gallery.

Anna Chernyakhovskaya, specially for HSE News service