“A great many smart things have been said about the connection between mathematics and music, so I feel justified in keeping this half-a-page personal. That there is mathematics in music has been amply demonstrated, but equally important is the music that is in mathematics. For unfathomable reasons, the path to a practicing mathematician is long and laborious so most of us do not walk it and do not ever experience the beauty that mathematics exudes. It is very much like that of music, sometimes intoxicating and at other times hampered by dissonances. Indeed, at times it seems unclear why the two are not the same, and why we do not yet have a direct mapping between them that does not appeal to feelings and opinions. Pythagoras apparently claimed ‘there is geometry in the humming of the string, there is music in the spacing of the spheres’. Perhaps he wrote these words in a state in which music and sound took on geometric reality in his mind and he could hear the intricate rock formations on Greek islands.
There is a more concrete thought to be mentioned in this context: both mathematics and music are built on unforgiving rules whose violations imply embarrassment or worse. Paradoxically, this opposition helps in the creation of beauty and perfection. We learn faster if our mistakes are told right away and without ambiguity. Beyond these parallels, there are surely deeper connections between mathematics and music that are tied up in areas of the brain that are not yet accessible to scientific investigation.”
Herbert Edelsbrunner is professor at the Institute of Science and Technology Austria. The mathematician is world-wide considered a pioneer in the fields of Computational Geometry and of Computational Topology. In 2018, Edelsbrunner was honored with the Wittgenstein prize, Austria’s most prestigious scientific award.
Foto (c) Paul Pölleritzer