There are many ways to study life, and one that is particularly appealing to physicists is regarding it as self-organized active soft matter that is away from equilibrium ``just the right way’’. In this Colloquium, I will discuss this notion, and provide a number of examples of how we can begin to put together simple systems - from basic ingredients that we fully understand - that would exhibit the kind of active behaviour we find in living systems. I will address the question of stability of a living system made of active components and propose a fundamentally new mechanism in which a competition between chemical signalling and cell division can determine the homeostatic conditions at the systemic level.
In this talk, I shall review the mathematical formulation of the Born-Oppenheimer approximation and compare it to the traditional physical point of view. I shall point out some rigorous results and open questions.