Mathematical research

An organic chemist devises synthetic routes to newly discovered molecules.

A particle physicist tries to elucidate sub atomic matter. Recently there was the discovery of magnetic electricty, for example.

A human biologist discovers how the body works.

What exactly is the nature of mathematical research?

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[quote]Functional Analysis:

Take some well-known function (say Fourier Series) and find some convoluted example when it breaks.

Write a paper

still broke, but at least now you have a PhD[/quote]

fix'd