Computer-aided serendipity (Q1904098)

This is a transcript of an entertaining lecture, best summed up in the author's own words ``\dots that the theory of numbers is an experimental subject and that nowadays the sensible way to experiment is usually on a computer''. The topics used to illustrate this are (i) elliptic curves and the local- global principle, (ii) cubic surfaces, and (iii) finding polynomials \(f\), \(g\) such that \(f(X)- g(Y)\) has a factor in \(\mathbb{C} [X, Y]\).