[1][2][3] Due to the situation in Uruguay in the 70s, he emigrated to Spain to study the bachelor of mathematics at the University of Barcelona,[2][3] which he completed in 1983.

[3] In 1993 he organized the workshop Continuous Algorithms and Complexity at the Centre de Recerca Matemàtica in Barcelona[5][6] where he started his long-term collaboration with Lenore Blum, Michael Shub, and Steve Smale.

[3] In 1996 he moved with them to the City University of Hong Kong to write the book Complexity and Real Computation.

[1] Cucker was one of the founders of the nonprofit association Foundations of Computational Mathematics, of which he has been a member of the board of directors since its creation in 1995 until 2017.

In 1998, he co-authored one of the fundamental books in this topic, Complexity and Real Computation, together with Lenore Blum, Michael Shub, and Steve Smale.