Old mathematical challenges: Precedents to the millennium problems

The Millennium Problems stated by the Clay Mathematics Institute became a stimulus for mathematical research. The aim of this article is to show some previous challenges that were also a stimulus to prove interesting results. With this pretext, we present three moments in the history of mathematics that were important for the development of new lines of research. We briefly analyse the Tartaglia challenge, which allowed experts to discover a formula for third degree equations; Johan Bernoulli’s problem of the curve of fastest descent, which originated the calculus of variations; and the incidence of the problems posed by David Hilbert in 1900, focusing on the first problem in the list: the continuum hypothesis.