This Quote Means: ‘Mathematics is the music of reason’

While it is not clear where the statement originates from, it is often attributed to the 19th century English mathematician James Joseph Sylvester. In the 1993 book ‘Comic Sections Plus: The Book of Mathematical Jokes, Humour, Wit and Wisdom’ by Des MacHale, the full quote is given as: “May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.”

A 1992 book by French mathematician Jean Dieudonné is titled ‘Mathematics: The Music of Reason’.

What it means

The quote can be looked at in two ways — math as the expression of what is harmonious and beautiful in the human ability of reason, and the overlaps between music and math.

For the first, let us take the example of architecture. All the great examples of architecture around the world, from the Konark Sun temple and Taj Mahal in India to the pyramids of Egypt to the St. Peter’s Basilica in Rome, have been created thanks to the use of the mathematic concepts of geometry, algebra, trigonometry, etc. Just like musical notes combine to produce a piece of art, here, the human ability for reasoning, the rules of x and y combining in a certain way to produce z, were used as the bedrock to create art of enduring beauty.

In a more literal sense, of course all music is linked to math. To take the example of the Indian classical dance form of Kathak, all dance pieces are performed on taals, which are broken down into specific numerical matras and chhands. These combine to produce the music on which dance is set.

The underpinning of music — rhythm and metre — have mathematical structures. As mathematicians David H Bailey and Jonathan Borwein wrote for Huffpost, “….there are well-known mathematical relationships between the pitch of various notes on the musical keyboard. An octave is separated by a factor of two; a fifth interval (say C to G) by the ratio 3/2, and two adjacent notes on the keyboard are separated by the twelfth root of two = 1.059463…”

The role of mathematics is apparent in many famous pieces of music. For example, The Art of Fugue, by the famous German composer Johann Sebastian Bach, is based on the Fibonacci series and the golden ratio. Bach, in fact, has often been regarded as a mathematician because of the use of math in his music. Another musician recognised as a genius, the Austrian Wolfgang Amadeus Mozart, is also known for the use of math in his works. On the other end is Albert Einstein, a scientist who was an accomplished pianist and violinist.

A more contemporary example is of the song ‘We will rock you’ by the British rock band ‘Queen’. Brian May, the lead guitarist of the band, has described the role of math in the iconic ‘stomp stomp clap’ section of the song. May, who has studied astrophysics at Imperial College in London, talked about how the band was looking for ways to incorporate audience’s reactions in their songs, and for this song, they were stamping on some wooden boards in a disused church.

NPR quotes him as saying, “And there were some old boards lying around, but they just seemed ideal to stamp on. So we piled them up and started stamping. And they sounded great anyway. But being a physicist, I said, ‘Suppose there were 1,000 people doing this; what would be happening?’ And I thought, ‘Well, you would be hearing them stamping. You would also be hearing a little bit of an effect, which is due to the distance that they are from you.’ So I put lots of individual repeats on them. Not an echo but a single repeat at various distances. And the distances were all prime numbers.”

However, some argue that there is a fundamental difference between music and math. Bram Duyx, a statistician with a PhD from Maastricht University, Netherlands, told The Indian Express, “If you analyse music, you discover patterns and consistencies. Having said that, music is perhaps best enjoyed without analysing, by just immersing oneself in it. In this, it is the opposite of mathematics, where the underlying logic and patterns are all-important. Reason is the natural habitat of math, whereas music is more about intuition and emotion.”