I am the first to admit that I'm not sure how much mathematics and theory has contributed to biology. Certainly the buzz is there. With the reams of data generated by the human genome project, biologists are begining to realize that they could use some help to understand all of this new data. The result has been a surge of available grant money and a flood of physicists, computer scientists and mathematicians into the field. (For the record, I made the jump over ten years ago when it was less fashionable.) I think it's safe to say that the jury is still out on whether or not the hype has been justified.
However, there has been one instance where mathematics has made a major difference and that is in the development of the triple cocktail treatment for HIV-AIDS. HIV is a particularly insidious virus because it attacks CD4 T cells of the immune system. However, it is rather slow acting. So often, when a person is infected with HIV, their virus load will remain low and CD4 counts will remain relatively high for a long period of time. Then, suddenly, the CD4 count will plummet and they will lapse into fully developed AIDS. It was first assumed that the virus replicated slowly and then accelerated at some point.
In the early 90's, David Ho and his group were testing treatments for HIV infection and decided that mathematically modeling the virus dynamics may give clues as to what was really happening. So they called in Los Alamos biological physicists Alan Perelson and Avidan Neumann (who is currently visiting our lab at NIH) to see if anything could be inferred about the virus. They used simple models of just a few ordinary differential equations to fit to the virus load during perturbation experiments where a potent protease inhibitor was administered.
Their simple model showed that the virus was far more active than previously believed. During the quiet phase where virus loads were low, the virus was actually replicating very rapidly but the immune system was running at high speed to compensate. Full blown AIDS developed when the immune system wore out and could no longer keep up with the virus. The implication was that any anti-viral treatment that targeted a single specific mechanism would fail because the virus would quickly evolve a defense. Thus the triple cocktail was invented. The virus would then need to evolve three separate defenses and this was difficult enough to keep it at bay. The results were published in two deservedly celebrated papers - the first in Nature in 1995 and the second in Science in 1996. I think their achievement represents the best example of how theoretical ideas can be useful in biology.