Jean Bourgain’s Coat of Arms

In hope against hope

Jean Bourgain, IBM von Neumann Professor in the School of Mathematics, was bestowed the title of Baron by the Belgian government in July 2015. In association with the honor, Bourgain designed a coat of arms inscribed “In hope against hope.” Bourgain explains elements of the design:

The essential part is the center where you see four mutually tangent circles that generate a so-called Apollonian circle packing (named after Apollonius of Perga, 2nd century B.C.). Such a packing is a fractal set in the plane, which one obtains if one keeps removing from the curvilinear triangles the tangent discs. In the Renaissance, these configurations were a subject of study for the French philosopher and mathematician René Descartes and later, in the twentieth century, for Frederick Soddy, who won the 1921 Nobel Prize in Chemistry. Soddy discovered the integral Apollonian packings (IACP) where the reciprocals of the radii are integers, for all circles in the packing. The theory of these IACP is today a rich mathematical research area, at the interface of hyperbolic geometry, dynamics, and number theory.