I happen to share GJDS lack of fondness for the scarcity of mathematics in biology, and have railed and ranted about this for decades. Here is a quote from a recent two part post from my blog:
“On the face of it, it does seem strange (at least to me) that no universal law has been stated for the process of evolution. ….With good theoretical laws, certain doubts about evolution as the central basis for biological science might be laid to rest, and hopefully a good deal of disparate and confusing information could be integrated into a unified context. And biology would become another of the sciences governed by the rule of law.”
I would also argue Chris, that your comment about the deep complexity of biology being a problem for the formulation of mathematical laws, which is often cited by biologists, is not really valid. Quantum theory, general relativity and particle physics are pretty complex as well, and that is exactly why mathematical models and laws are so vital to them. I think the problem is more that biologists (like myself) are poorly trained or just really bad in math, and dont know how to proceed.
I also think that just as happened for relativity, we will probably need a non traditional mathematics to deal with biological laws. For example it seems likely to me that inequalities and probability theory will be far more useful than standard math.
I am not much of a mathematician myself, unfortunately, though I have made some not very effective attempts to apply math to some biological issues. What is needed are well trained biologists who are also well trained in math, and willing to work creatively to find the laws we are lacking. Mathematicians who learn a little bit of biology tend to do interesting mathematical work, that doesnt really help much, and biologists just dont seem interested. So, if anyone reading this is a student wondering what to do with their talent in math and their interests in biology, my advice is: go for it.