First of all I explain my situation: On my University most of the careers are doing videos to explain what we do and try to atract more people to our careers.

I'm in a really bad position, because the people who are in charge of the video want me to explain what a pure mathematician do and how it help society (with practical examples and maybe naming some companies that work with pure mathematician and what they do in that companies) in only 5 or 10 mintues, so I think that the best that I can do is make a example.

Other reason that have me in a bad position: In my University we have the career "Mathematical engineering" and they do most applications and some research in numerical analysis, optimization. (*)

I know that pure mathematics are increasing its importance in society every year. Many people in my country think that mathematics has stagnated over time and now only engineers develop science. I think that the most practical thing I can do is give some examples of what we are doing with mathematics today (since 2000).

If some of you can help me I need the following:

  1. A topic in mathematic that not appear in (*). Preferably dinamical systems, logic, algebraic geometry, functional analysis, $p$-adic analysis or partial differential equations.

  2. A research in that topic.

  3. Practical applications of that research and the institution that make the application.

Extra 1. If you know a institution (not a University) that contract pure mathematicians and you know what they do there you can tell me too.

Extra 2. If you have a very good short phrase explaining "what a mathematician do" or "how mathematics help society" i will regard it too.

Thanks in advance.


A nice example would be Bayesian analysis. It works as an example on how mathematicians work could take decades or more into becoming useful tools. Bayesian algorithms are used everywhere today in both artificial intelligence and cognitive science, either to create smarter AI software or to understand how the brain processes information.


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