Mathematics is often described as exact and abstract, and labelled as austere, cold, and even boring. Perhaps most people regard mathematics as a purely scientific discipline that does not allow much room for creativity. Some may not even see it as a science, but rather as a discipline in its own right, an exercise in logic bridging philosophy to science, the language of science. Undoubtedly, few see it as an art, mostly because they never experienced research in mathematics but only instruction. However, mathematics is very much also a form of art.
Art is creative activity. Traditional definitions of art emphasise the visual, auditory, and literary aspects. Painting, sculpture, music, dancing, poetry, and prose are among the most common given examples. However, “creativity” remains the key word. Contrary to common perception, there is much creativity in mathematics. In his famous book A Mathematician’s Apology, G. H. Hardy said, “I am interested in mathematics only as a creative art” and “A mathematician, like a painter or a poet, is a maker of patterns”.
Every mathematical activity starts with a problem. In research, one has two options: attack an existing problem or pose a new one and investigate it. Georg Cantor said, “In mathematics, the art of asking questions is more valuable than solving problems”. With rapidly expanding knowledge boundaries, formulating a natural or appealing problem is becoming ever more challenging. Often a conjecture is suggested. This results from a creative process involving checking, observation, and guesswork. Generating ideas for a proof is normally the most creative and most revered part of the whole process. An idea could outdo the result. Sometimes a partial solution is obtained but the ideas produced are elegant and useful for other investigations. Certainly, articulating the ideas and results in writing for publication and communicating them effectively (particularly in education) are not devoid of creativity.
As in other art forms, the beauty of a mathematical accomplishment is subjective. However, mathematics has a distinctive feature: the final product is an objective truth that could be attained by anyone but bears the name/s of the one/s who unveil it first. Eureka!