By Mathematical realism I think you mean the belief that mathematical structures are independently real of their instantiation inside human thoughts. In which case the relevant mathematical structures underlying Life, as we know it, are akin to computer programs - that's how genes, cells and neurones seem to be organised - and cellular automata. But it's an imperfect analogy as a lot of chemistry and electromagnetism is involved and so the patterns of activity occur in 3-D structures quite differently to how programs are followed in the electron flows of our computers. Reducing biological information processing to something closer to our codes and programs isn't straight-forward and there's lots of pitfalls. The most common is assuming that the "genetic code" is somehow independent of its substrate, but the specific nucleotide and amino-acid interactions are an integral part of the processing, so it's not an isomorphism, more of a metaphor.