Seeing the Unseen – Mathematics, a hidden spectrum of beauty | Naomi W

Mathematics is intrinsically beautiful. It is an eye through which we can view the elegance in organic natural phenomena. Even the seemingly random motion of particles can be modelled as complex interactions of mechanical formulae. We can explore new worlds which don’t even exist in the physical such as the fourth and fifth dimensions; seeing the patterns formed by colours invisible to the human eye and even calculating with imaginary numbers. Classifying mathematics as a science has long been accepted as standard practice but I would argue that maths has much more in common with the arts than with the sciences. Interestingly, I would not be alone. Richard Brown, a Pure Mathematics Professor, in his Tedx talk entitled Why Mathematics? argued convincingly that Mathematics is “not a science at all” but “perhaps it is an art” instead.

Firstly, he dispelled the theory of maths as a science by stating simply that, unlike science, Mathematics does not try to describe or explain the real world, and it is not about experimentation. This in fact links to one of my favourite qualities of mathematics, which is that, although it is always growing and developing it is almost never contradictory and new discoveries do not displace ancient theorems. Cutting edge research is just as relevant to modern mathematics as the papers written hundreds of years ago by geniuses like Einstein and Newton. Maths never dies! This is the opposite of scientific progress which is all about forming new conclusions based on the observation of patterns and trends within experimental data. Often new scientific theories disprove previously accepted ideas. Maths is a tool used by science but it is not itself a scientific discipline.

Richard Brown then goes on to suggest that Mathematics is more comparable to an art form. Its paralleled most profoundly with music. In his talk Prof. Brown references Paul Locker, author of an essay entitled The Mathematician’s Lament who wrote passionately of the appalling way in which maths is taught within the education system of today. He claimed that if we taught music in the way in which currently teach mathematics then throughout primary and KS3 we would spend our days learning scales and we would not hear any music at all until GCSE/A-Level. It wouldn’t be until university and beyond that we would actually be encouraged to hum a tune or create any music for ourselves as this is akin to research.

“Mathematics is the music of reason”

Paul Locker

Richard Brown goes on to expand on this view, pointing out that both Mathematics and Music are governed by a rigid set of strict rules and conventions which have to be obeyed, but both disciplines also exhibit infinite creativity.

He continues to expand on his analogy by demonstrating that mathematical theorems, in the same way as compositions in music, have a “very well defined, very refined sense of value” an “aesthetic quality” from which they cannot be separated. This I know to be true, as a maths student it is not enough to simply understand how to apply mathematics, but instead I desire to understand where the equations come from and how they fit into the complex structure of mathematics.

Prof. Brown refers to the highly acclaimed eccentric mathematician Paul Erdos who had a unique yet beautiful view of mathematics’ value.

‘Paul Erdos has a theory that God has a book containing all the theorems of mathematics with their absolutely most beautiful proofs and when he wants to express particular appreciation of the proof, he exclaims “This is from the book!” ’

Ross Honsberger

Interestingly, in my own research I found that Paul Erdos also compares mathematics to music, when asked why numbers are beautiful he responded: “It’s like asking why Beethoven’s Ninth Symphony is beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is” However further on in Richard Brown’s talk he went on to explain that unlike music you have to be mathematically literate to appreciate maths, whereas anyone who can hear music can form an opinion about its value. Because as he puts it, unlike music, in mathematics “nothing we create is real … it only lives in the collective consciousness of everyone who has ever thought about mathematics”. It can only be communicated through a “brain to brain connection, imagination to imagination”.

I would like to conclude by comparing this to the electromagnetic spectrum. We live within the limitations of our visibility so we can only see a tiny fragment of the spectrum from red through to violet but either side of these colours is an invisible spectrum of beauty which we will never fully understand, but which, using UV and infrared cameras, we can translate this into something visible to the human eye. In the same way, we encounter just a small amount of mathematical phenomena in the real world but we can never truly represent mathematics in the physical. However we can use the language of mathematics to see the invisible beauty of the ever expanding spectrum that mathematicians dedicate their lives to exploring.

Image Link: https://www.theparisreview.org/blog/wp-content/uploads/2019/07/istock-512102071.jpg (16/04/21)