This is an essay about the conceptual foundations of modern biology and the role that mathematics can play for biology. Traditionally, two aspects have been considered as fundamental for or constitutive of life, reproduction and metabolism. The concept of evolution puts the emphasis on the first of them, reproduction. Some modern versions, like the notion of the selfish gene, go well with the general public, but fall short of capturing the complexity of life. An important property of biological reproduction is the transmission of information, rather than of material structures. Other approaches, like autopoiesis or dynamics far from thermodynamical equilibrium, put more emphasis on the second aspect, metabolism, that is, maintaining a biological organism and preventing it from disintegrating. Metabolism needs a constant inflow of matter and energy, not just of information.