What does a mathematician do?

During our discussions with non-mathematician communities, questions were often raised about mathematics that at first appeared naïve. Here, we would like to remind readers what mathematics is and what it does, basing our observations on the important work of learned societies and the initiative entitled “Mathematics of Planet Earth 2013”.

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Mathematics in the real world

Acting as an aid to understanding, forecasting or decision-making, mathematics is like a very practical toolbox. However, it does have some shortcomings: a few mis- or poorly-understood tools lie at the bottom of the box, some are still new because they are unusable, while others still have to be invented. It is therefore important to take particular care in maintaining the links between the real world, theory and computational science.

Emerging mathematics

New environmental and societal issues call for a better understanding of numerous complex and highly heterogeneous behaviour patterns. Inspired by these challenges, mathematicians are formalising new questions and attempting to provide answers (see Mathematics in the Real World) by digging deep into their mathematical culture. These answers sometimes require the development of new mathematics.

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Numerical mathematics

Numerical mathematics maintains close links with theory. Going from one to the other is a daily sport for some mathematicians. Such mathematicians often focus on problems arising from applications: coupling of processes, model validation, parameterizations, high-performance computing (supercomputing) ... Forming a bridge between the abstract and the concrete, numerical mathematics has difficulties in finding its place in the world of research in France.

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