The origins of modern computing are dispersed over centuries, often in the work of pure mathematicians, who invented methods in order to understand mathematical objects and prove theorems. A typical example is the famous Schwarz method for parallel computing, whose origins lie in a problem in Riemann's audacious proof of the Riemann mapping theorem. Another example is the finite element method, which has its origins in the variational calculus of Euler-Lagrange and in the thesis of Walther Ritz, who died just over 100 years ago at the age of 31 from tuberculosis. We will see in this talk that the path leading to modern computational methods and theory was a long struggle over three centuries requiring the efforts of many great mathematicians.