In less than 100 seconds, Carola-Bibiane Schönlieb of the University of Cambridge in the UK provides a basic definition of a Fourier transform. She explains how this mathematical tool was introduced in the early 19th century by Joseph Fourier while he was searching for solutions to the heat equation. It is a way of taking a signal or a function and deconstructing it into a series of sines and cosines.

Today, Fourier transforms are prevalent in many areas of science and engineering. They are used in processing many of the signals we encounter in our everyday lives, such as phone and TV signals, and even in the evolution of the Stock Market. Schönlieb gives an example of how Fourier transforms are used in her own area of mathematics, a field called inverse problems. She explains how images generated using magnetic resonance tomography are derived from a partial knowledge of a Fourier transform.

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