Computational mathematics is the working arm of mathematics. In computational mathematics, rigorous mathematical reasoning is used to design robust and accurate algorithms that typically serve multiple fields of application.

In this talk, I will focus on the branch of computational mathematics that deals with the mathematical modeling and simulation of complex physical phenomena described by partial differential equations. This branch is foundational for digital twins and has a growing impact at the interface of mathematics and other sciences. Inspired by several applications my group and I have tackled recently, I will provide examples of the role of mathematics and mathematicians in developing reliable computational twins, ranging from personalised medicine to additive manufacturing and plasma physics.