TITLE: Mathematics and cancer research
QUESTION [27 upvotes]: 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.

REPLY [2 votes]: Ricci flow is an analytic surgery. Prediction and control of cancer invasion Can be done by Ricci flow theory see this paper
Ricci Flow and Entropy Model for Avascular Tumor Growth and Decay Control
Tijana T. Ivancevic
https://arxiv.org/abs/0806.0691
We can apply discrete Ricci flow like Ollivier Ricci flow, to study cancer and tumors
https://www.nature.com/articles/srep12323
There are a list of discrete Ricci curvatures which based on we can define Ricci flow. Just we need to know which discrete Ricci curvature on the graph network is suitable for the tumor.