We show how mathematics can help in the complex process of drug discovery. We give an example of modification of a common cancer drug that reduces unwanted side effects. The mathematical model used to do this relates to the hydrophobic effect, something not yet fully understood. The hydrophobic effect modulates the dielectric behavior of water, and this has dramatic effects on how we process drugs. Future mathematical advances in this area promise to make drug discovery more rational, and thus more rapid and predictable, and less costly.