In any case, the evening began with Frenkel comparing the lack of appreciation for mathematics in society at large to a fictitious scenario in which painting is studied without any reference to the great masters such as van Gogh and Picasso. As one can imagine, the subject of painting in such a world would be devoid of lineage and it may very well be reduced to the art of repetitive brush strokes. This, unfortunately, quite accurately describes how mathematics is commonly taught in schools, where rules and formulas are introduced rather mechanically and without reference to their origins.
From this starting point, Frenkel goes on to argue how mathematics and art contain many elements in common. One of these is the central role that abstraction plays. To illustrate, Frenkel described the concurrent introduction of higher dimensions into mathematics and physics as well as art in the early twentieth century. In the former scenario, we have figures such as Poincaré and Einstein who developed the mathematics of special and general relativity, and in doing so, revolutionized our conception of the universe in which we live. Indeed, whereas Euclidean geometry had been the model for reality for over two millennia, and its absoluteness was even regarded in Kant’s philosophy as being fundamental to our ability to perceive the world, the new vista of a curved spacetime was now provided solely by the powerful abstraction of mathematics. In the world of art, we have in the same period, the workNude Descending a Staircase, No. 2 by Marchel Duchamp in 1912, in which Duchamp departs from traditional painting and attempts to incorporate the dimension of time into a static, two-dimensional canvas. Frenkel, via this example and others, suggests that it is through such novel and powerful ways of introducing abstraction that we soar to higher levels in mathematics and art.
Frenkel goes on to explain briefly the relationship between love and math. Despite tattooing a mathematical formula on his lover in his film Rite of Love and Death (a formula discovered by Frenkel by the way), Frenkel explains that it is not that the case that he thinks there is a formula for love (thankfully). But rather, he believes (if I understood him correctly) that math and love can share aspects in common, namely, its ability to infuse passion and desire. On this point however, I do not recall if Frenkel explained what is unique about mathematics’s intersection with love (in contrast to any other creative pursuit), something I personally would have liked to be clarified…..
absolutely fascinating. I am always reminded of the quote from Bertrand Russell in his magnum opus, A History of Western Philosophy, on this matter
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.”