Artist Statement
“Topics in Math by Danielle Sabey”

“Topics in Math by Danielle Sabey” is an artistic expression of how math feels. I am
addressing mathematical themes such as infinity and the enormity of it, how to work with
infinity in order to understand it better. I am also looking at how the topic of intricacy and
even chaos that is so prevalent in math is the same thing that leads to simplicity. The
rigor and the extreme formality required for proofs is another theme within the book.
Through out the book I deal with the different traits and emotions attached to the study of
mathematics. The elegance of a theorem that intertwines concepts from different areas,
the satisfaction of finally discovering the key to proving something you knew must be
true, the chaotic path that must be tread to reach an understanding, and the silliness of the
formal nature of math.
The whole concept of doing a book for this project already embodies my themes. While
studying different topics in math you become so well acquainted with the textbook that
you can visualize certain pages and you know right were all the important theorems are
and probably their page numbers. When looking back on these books each page full of
symbols and theorems, strikes an image or understanding, correlations and nostalgia. This
intimacy with the text while learning math is already embodied in my art by being in the
same format. By altering the pages artistically it is like going through the learning
process which alters the pages full of unknown symbols and concepts into understanding
and knowledge.
In the section about proofs I used a formal step by step card on how to bow properly at a
social setting to relate the formality and hoops you have to go through to write a proof. In
proving things, to know something is true is not near enough, you have to be able to show
why it could not possibly, under any circumstances, be false and then express that to
others. This is quite a difficult and necessary thing, and it feel a little like a dance or a
chase. This is why I have a boy and a girl who at one stage in the page sequence are
apart, just like logically the knowledge you have and the conclusion you have will not be
aligned, yet want to be so badly, just like the crushing pair. On the next page they come
together and the proof is done and satisfaction is great. Then when you turn the page it is
a mostly white page with a heart shaped Band-Aid painted gold. This embodies this
emotion of satisfaction to me. The Band-Aid is a sort of symbolic thing of recovery or
fixing of something that was not whole as well as relief from a struggle. The contrast of
the collaged pages of marked errors and comments on formal math language to the stark
white of a wall, is how I feel after finishing a proof. It is a clarity. It has been said that
understanding comes only through the proof. Your mind clears from the chaos of trying
to understand the concept and trying to understand all possible cases to finally
understanding to key that clears it all up and you are left enlightened, even if only to a
tiny degree.
While in the section about Galois Theory and Elliptic Curves I am discussing the concept
of the need for intense pre-requisite knowledge to come to such simple and elegant
conclusions. It is the same idea as chaos leads to simplicity. It is almost necessary to get
something so elegant. I have a whole bunch of equations and theorems in the paint tubes
and with the paint tubes I have painted the picture. I feel like many concepts in math are
like this. You receive a lot of knowledge that you keep putting in your knowledge bag
and then eventually it all comes together and it becomes one piece of knowledge, or one
picture painted with the different parts you have learned.
In the section called “Chaos: the Adolescence of Simplicity” I am continuing this theme.
I have a sort of graph with paths and vertices as the hole-punch holes connected to the
fuscia thread. The thread intertwines and curves and is disorganized and yet the holepunch
dots, as perfect circles, glued down gives a sense of possible underlying order. I
also have complicated procedures that lead you to one answer. While looking at the
computations there is a definite sense that something is in control but it is still incoherent,
and in the end it spits out something coherent, and surprisingly simple. I have the positive
integers all written out because they feel the same way to me. They are massive, even
infinite, and yet they are so accessible when broken down.
Modular Arithmetic defines a way to collapse infinity. It takes all the numbers and
collapses them into categories which then allows for us to realize certain like properties
in each category. Counting on the clock and starting over at 12 every time is an example
of modular arithmetic (24:00 = 12:00 and 13:00 = 1:00…). Each number, while just one
number, represents an infinite set of numbers. In cutting the squares over each little box,
which each represents a number in modular arithmetic, gives a sense of massiveness to
each box. Each layer of paper helps to define the box. The boxes have different things
inside of them which represent the unique characteristics that each number has. This is
also an expression of the relationship that intricacy and simplicity has. While each box is
uniquely loaded and incased in a square of hundreds of pages, they are still just whole
numbers, the things you learn about in elementary school, and in-fact behave the same for
the most part. The cut squares and boxes also give a feeling of discovery and intrigue,
which is part of the fun of mathematics. It is fun to learn about the categories that give
characteristics to what seem like just numbers but there is actually a bigger world out
there. I wanted to express this aspect of math that often eludes many high school and
intro math courses.
The little books are the same thing, they show that although they are just one simple
polynomial, there are and many more complicated polynomials that it represents. The
little books imply this depth and categorization. They are organizing a form of infinity.
I want people to see the other side of math than what they generally experience as a dry,
uninspired and uncreative process. I have found it to be quite the contrary and think it one
of the most elegant areas of study. The concepts of math can be seen as abstracted forms
of things we experience everyday, even to the extent of social order and anthropological
systems, but that is for another art project. For this reason, I find it relevant to express
math to other people besides just to math people.