I have been chosen by my university to give a 1 hour public research lecture. Every year a researcher is chosen for this honour. Traditionally people explain their own research about designing improved airplanes or the life of a peasant in the middle ages or whatever. I don't feel that I can explain my research in an hour to the general public in any sort of intellectually honest way.
I have decided that it would be more interesting and more useful for me to try to say some things about math research in general. I hope to explain what math research is like, why it is important to society and how it differs from research in other scientific fields.
I think 3 or 4 really good examples of advances arising from recent mathematical research would go a long way to making my points in an interesting manner. I am thinking of examples like the page rank algorithm used by Google. Or perhaps modern cryptography techniques such as the RSA algorithm.
Question: What are some other examples that help show the public why math research is important?
I think it is important that these be relatively recent examples and that they relate directly to things people experience themselves.
I would be grateful for any suggestions which might improve my talk.