Euler and the modern mathematician

It is remarkable that Euler, who preceded Gauss and Riemann, is still very much with us. The ramifications of his work are still not exhausted, three hundred years after his birth. In number theory,in algebraic geometry,in topology,in the calculus of variations, and in analysis, both conceptual and numerical, not to mention mechanics of particles and solid bodies, astronomy, hydrodynamics, and other applied areas, the ideas that he generated are still motivating mathematicians. In this talk, which will require no specialized background, I shall focus on his pioneering work in the theory of summability of divergent series, which was the precursor to the entire modern theory of divergent series and integrals.