Maths Makes Waves!

Waves are everywhere, from the smallest scales to the largest, from waves which oscillate in a pico second, to ones which change over may years, and from waves with length scales smaller than the size of the atom, to waves which stress across the galaxy. Waves lie at the heart of much of modern technology, physics, chemistry, biology, medical imaging, music, popular culture and are all around us. The study of waves also led to major advances in mathematics (both pure and applied), connecting such seemingly diverse subjects as trigonometry, geometry, differential equations (both partial and ordinary), functional analysis, harmonic analysis, fluid mechanics, quantum theory, electromagnetism, integrable systems and thermodynamics, to name just a few. Calculating problems involving waves led to the 19th Century development of the analogue computer, and the problems posed by studying waves remain some of the biggest challenges that we face.