What are applications of mathematics in cancer research?
Unfortunately, I heard quite little about applications of mathematics, but I heard something about applications of physics, and let me put this story here, as it might be useful to be aware of it. Radiation therapy is well-known, but less well-known is proton therapy, which is much more rare and based on proton accelerators used in particle physics.
The chief advantage of proton therapy is the ability to more precisely localize the radiation dosage when compared with other types of external beam radiotherapy.
As far as I know, it is only practiced in physics research centers that have proton accelerators. It is highly useful for cancer of sensitive tissues when it is dangerous to use other radiation therapy because it will destroy everything surrounding the malignancy.
A colleague of mine told me this really helped his father with eye cancer.
Moreover, proton therapy is so rare that the leading cancer experts were not aware of it and he become aware of it only through friends.
Best Answer
A variety of medical image reconstruction methods are very relevant to cancer research and diagnosis.
Prime examples are: Positron Emission Tomography (PET), CT, MRI, etc.; In particular, all of these famous and successful technologies depend on solutions to inverse problems where one must reconstruct an image from a set of noisy measurements.