What is the link between Maths and Music?

Posted by ap507 at Oct 10, 2016 11:45 AM |
What is the link between Maths and Music? For World Maths Day, University of Leicester's Professor Ruslan Davidchack describes the passion mathematicians feel for their subject
  • World Maths Day, held on Saturday 15 October, aims to encourage global participation in problem solving
  • To mark the international event Professor Ruslan Davidchack draws parallels between mathematics and a piano, with mathematicians being both composers and performers

On the occasion of World Maths Day on October 15, Leicester mathematician Professor Ruslan Davidchack describes mathematics as “the highest form of intellectual art known to mankind”.

World Maths Day is an international online Maths competition which challenges youngsters to solve equations and problems against other schoolchildren from across the globe.

The event, sponsored by Samsung, and supported by UNICEF, reached 1,204,766 participants in 2010, setting a Guinness Worlds Record for the largest online Maths competition. Professor Davidchack, whose research is in Mathematical Modelling and Computation, has describes how mathematicians feel about their subject in the hope that this will inspire the youngsters to rise up to the challenge of becoming professional mathematicians.

On Maths and Music

Mathematics… It’s not just about numbers, it’s not just about intellectual challenge, it’s not just about usefulness.  It is so much more!  It is beauty, it is passion, it is raw emotions expressed in the clearest of forms, it is the highest form of intellectual art known to mankind!

All mathematicians feel this, know this, they are driven by this.  Unfortunately, we are not very good at communicating this to the rest of the world.  We try to tell the rest of the world what the rest of the world can understand.  The world understands economics - we explain Mathematics in terms of how useful it is for the economy.  The world understands and appreciates technology - we try to come up with mathematical techniques which are useful for solving technological problems.

But all these explanations give extremely limited, narrow, truncated (dare I say ‘castrated’?) view of Mathematics. This view is devoid of passion, of fire burning in the hearts and minds of mathematicians.  We need to find another language to communicate this to the rest of the world…

So, here’s an attempt, based on my belief that the rest of the world has an appreciation for the beauty and passion of music.

Mathematics is like a piano.  Pure Maths: white keys, Applied Maths: black. Each key is a specific area of Mathematics (algebra, geometry, …) .   If we understand this, we will understand that, first and foremost, there is no division in Mathematics into Pure an Applied.  If you only play white, or only black notes, you will get deficient music.  All notes are needed, both pure and applied, to create beautiful music!  If anyone tries to ‘specialise’ Mathematics, by only retaining ‘useful’ bits, they are putting a straightjacket on it. It will not be able to function as intended and, ultimately, it will not be able to deliver even the ‘useful’ things.

Mathematicians are like composers. Most of us, mortal mathematicians, only know how to make music using a few notes.  Some are better at playing white notes, some black. Only the top mathematical geniuses are able to use all the notes.  Gauss, Euler, Poincaré… Were they pure or applied mathematicians?...

Every theorem is like a musical piece.  Mathematicians can also play the piano. We can play music created by other composers – we can understand and appreciate their score.

But Mathematics is not just an ordinary piano.  It is a magical piano!  The best of the mathematicians don’t just compose music from the known notes.  They create new notes!  New fields of Mathematics – white notes.  New applications of existing fields – black notes.  The piano becomes bigger and bigger, it allows us to play more and more sophisticated tunes.

Also, unlike composers, mathematicians can create music together!  Individually, we (mortal mathematicians) might not be skilful and creative enough to use all the notes, but together we can create musical pieces which draw on many notes and are very beautiful!  If we are separated, ‘specialised’, we cannot create beautiful pieces of music and, ultimately, cannot be ‘useful’ to the rest of the world!

In June we had Jacob Lurie visiting Leicester and giving a talk as part of his LMS 2016 HardyLecture Tour.  Wow!!!  That was a virtuoso performance!  What a plethora of notes!  What exquisite sound!  It was like listening to Chopin, Liszt, Rachmaninoff!   Mathematicians in the audience could ‘hear’ it.  Their eyes were aglow, maybe even tearful.  It was raw passion!

How can we communicate our passion for Maths to the rest of the world?  Well, I’ve given it a try…

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