TITLE: Interesting mathematical topics arising from biology
QUESTION [36 upvotes]: I've heard that there's a relatively new field of science called mathematical biology.
It will certainly apply well known and less known mathematical techniques to the understanding of some biological phenomena such as strings of DNA knotting together, proteins bending, cell membranes, population dynamics,...


Which interesting advances from the point of view of a mathematician are there that have been inspired by biology and related areas?


For example, I heard of "membrane computation", but I don't know if it's genuinely inspired by biology in some nontrivial way or if it just bears that name by a loose analogy...


Which fields of mathematics are currently used in the discipline called mathematical biology?


If I were asked about economy and mathematical Finance I would loosely quote probability theory, stochastic differential equations, Ito integrals, ...  So, what about biology?

REPLY [2 votes]: I think this is quite relevant,
https://liorpachter.wordpress.com/2014/12/30/the-two-cultures-of-mathematics-and-biology/
especially the references to Haussler's work,
[Mapping to a Reference Genome Structure][https://arxiv.org/ftp/arxiv/papers/1404/1404.5010.pdf] and
[Efficient haplotype matching and storage using the positional Burrows–Wheeler transform (PBWT)][http://bioinformatics.oxfordjournals.org/content/30/9/1266.short].
(Incidentally, I'd say "David Haussler ... studied mathematics" is quite an understatement, as he's made seminal contributions to computational geometry and combinatorics.)