Description: Craig G. Fraser, Ph.D., Institute for the History and Philosophy of Science and Technology, U of T Leonhard Euler (1707-1783) was the greatest mathematician of the eighteenth century, occupying a position in mathematics analogous to that of Bach in music or Goethe in literature. Some fifty years after his death the French scientist François Arago wrote “Euler calculated without apparent effort, as men breathe, or the eagles sustain themselves in the wind.” The 300th anniversary of Euler’s birth has been marked by a resurgence of interest in Euler studies, with scholarly conferences held throughout the world to commemorate and to document his extensive contributions to mathematical science. We examine Euler’s career at the academies of Berlin and St. Petersburg and describe some of the innovations for which he is best known. Among these was his introduction of the function concept to formalize the diverse range of geometric forms employed by earlier mathematicians to represent relations among variables and constants. Euler’s vast labours in calculus-related parts of mathematics earned for him the historical title of “analysis incarnate.” **Co-sponsor The Fields Institute for Research in Mathematical Sciences