Living organisms are composed of cells. Often, Biology studies life building on (molecular) chemistry of cells and their multi-cellular (or even inter organelle) collective interactions. On the other hand, Condensed Matter Physics has made great progresses in highlighting the role of similar collective effects in matter, probably far beyond any other scientific discipline studying complexity. As an example, already Einstein concluded that superconductivity has quantum mechanical origins, showing the failure of the initial reductionism approach. Since a few years, it has been widely accepted that it is not possible explaining and predicting superconductivity with chemistry. Today, we know that superconductivity is well captured by the universal, symmetry-based Ginzburg-Landau theory. It’s a matter of universality classes (i.e. categories) describing collecting behaviors that manifest under certain conditions: for example superconductivity is from symmetry breaking of the global U(1) gauge symmetry in the field theory.
The point is, do we need a new physics (and mathematics) of evolving living systems as well, which is capable of reflecting allowable dynamical symmetries? What is sure it that the laws governing dynamics far from equilibrium (which typical of life) are still unknown: I wouldn’t be so surprised in learning that these laws (and the related mathematics) are behind brain functioning as well. Nature has jumped ahead of us: once we discover these laws, then we can probably make use of them to make a breakthrough in our technologies.