This was Salvador Dali's last oil painting and is a representation of Dali’s understanding of mathematical theory based on the thinking of the Rene Thom. Thom, a highly respected French mathematician and Fields Medal winner proposed a catastrophe theory that, according to Dali, was “the most beautiful aesthetic theory in the world”. Thom’s theory suggests that in four-dimensional space there are seven equilibrium surfaces: swallowtail, butterfly, fold, cusp, elliptic umbilic, parabolic umbilic and hyperbolic umbilic, and Dali, perhaps because of his admiration for Thom’s work, undertook the not-inconsiderable challenge of successfully representing this relatively intangible four-dimensional theory on a two-dimensional canvas.

The shape of the swallow’s tail at the bottom of the painting for example, is copied from the mathematician’s graph of the same name, and the f-holes of the cello in the painting describe the integral symbol in calculus. Similarly, the S curve represents Thom’s second catastrophe graph. Given the often-considerable differences in thinking between artist and mathematician (although the lines purportedly blur the more theoretical the mathematics becomes) the relationship between Dali and Thom is remarkable.