What are the recent and new applications of Mathematics in other Sciences ?
Let me try to be more precise about the question:
- By "recent" I mean the last 15 years.
- By "new" I want to exclude the standard answers like cryptography or finance
- By "applications" I mean a mathematical concept (or even a trick) successfully used in another field (preferably not Theoretical Physics) to solve a problem or to shed a new light on a phenomenon.
- I would prefer to see recent applications of modern Mathematics, but new applications of classical results should be considered as a valid answer too.
- the answer should not simply be "XXX was successfully applied to YYY". it should contain a short explanation of the mathematical concept involve, and a description of the problem/phenomenon it solved/enlightened.
The typical example I have in mind does not strictly answer the question (first it is an application of Theoretical Physics to condensed matter, and then I am not giving the required details): it seems that some 2d quantum field theories which had a priori no physical meaning were successfully used to understand properties of graphene (I think this was really unexpected: 2d conformal field theory was considered as a toy model to approach the understanding of more relevant field theories in higher dimension).
v2: I hope this version is better than the previous one.
Best Answer
Statistics applied to microarray data in biology. And Bernd Sturmfels and his students have been applying algebraic geometry to this. He wrote a book titled Algebraic statistics for computational biology. Biology is a field that will explode in coming decades. Advances in that field will probably capture the public imagination the way physics did in the 20th century. The next Einstein could be a biologist.
(Does any of the empirical data used in any research papers published in that field have any validity? That's something that could bear inspection. People put vast numbers of large data sets on the internet, and others base research papers on them. But before they do that they transform raw numbers by, for example, raising everything to the power 3/2. If you later ask them specifically how they transformed it, they may be blindsided by the question and think you're making a strange unusual request that they'd never have expected in a million years. People don't normally ask such weird things. At least such has been my impression.)