Is Mathematics Art or Science?”

Mathematical formula on black-board.

Image from The beauty of mathematics comes from the vision and creativity of the mathematician.

By Scott Hamilton

Over the last three weeks I have been making various links between Mathematics and various arts. This week I want to make an unexpected argument. So many people make a link between Mathematics and Science that the assumption quickly becomes that Mathematics is a science. It is very true that every science uses mathematics to explain theories and describe properties, but I would argue that mathematics falls closer to art than it does to science.

So why do I make the argument that math is an art rather than a science? The first has to do with the subject area being studied in math versus the sciences. A typical high-school graduate already knows the basics of science. They know Physics is the study of things in motion and focuses on forces, mass, friction, and even subatomic particles. They know Chemistry is the study of atoms and molecules. They know that Biology studies living things. They also know that psychology is the study of the mind. They know, at least at a basic level, what someone with a career in a given science does and have experienced some of it at a very basic level. However, most of us don’t truly know what mathematics is about, or what mathematicians do.

There is a reason for this and it is related to how mathematics is taught. In high-school science classes students do simple experiments that mimic what a professional in the field would be doing on a daily basis, but we never act like a mathematician in high-school, or even in college, unless we choose to move forward to obtain a doctorate in mathematics. We are taught the basic facts of math and how to use them as a tool. We may even be taught a little of the history about the discovery of certain facts, but we never really experience the world of the mathematician.

Scientists study real things, tangible objects, with which we can touch, feel and interact, but a mathematician studies numbers. Guess what? Numbers are not real things. Mathematicians created the number systems to explain phenomena in the real world; for example, even the simple act of counting is a creation by mathematicians to describe the quantity of objects. We can see two newspapers, or six pages in a newspaper, but we cannot actually see the number six or two. We all know the symbols that represent six (6) and two (2), but we can never experience the number itself. Numbers are an abstract concept, not a tangible thing with which we can interact. It is often said of the wind, that you can feel the effects of the wind, but not see the wind itself. Numbers are even more abstract than wind, you cannot even feel the effects of numbers.

The goals of mathematics are also quite different from the goals of science. Scientists seek explanations of known facts; they call these explanations, theories, and theories are considered “good enough” even if they are not 100 percent proven. Scientific theories are always adapting as new facts are gathered to either support or modify the theory. Mathematicians, on the other hand, come up with conjectures and seek to prove those conjectures. A mathematical conjecture can only become a mathematical fact when it is 100 percent proven, and it is very rare for a mathematical fact to be disproven once the proof is provided.

Mathematicians are always seeking more beautiful ways to prove existing facts as well as seeking new beauty.

Mathematician G. H. Harding said, “Beauty is the first test. There is no permanent place in the world for ugly mathematics.”

Mathematicians seek the beauty in the proofs just like a musician wants to compose beautiful music and an artist wants to create beautiful works. The mathematician studies the old art of mathematics in much the same way an artist studies the classic artists. The scientist however, is only seeking out better explanations of the facts and rarely focuses on the past works. For these reasons I argue that mathematics is far more like art than science. Until next week, stay safe and learn something new.

Scott Hamilton is an Expert in Emerging Technologies at ATOS and can be reached with questions and comments via email to or through his website at

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