Truly great read from Marcus Miller via Scientific American discussing the close relationship between math, music and creativity.
Let me explain. To improvise or compose one must learn the technique of the instrument and the harmonic and rhythmic language of music. All the while, the fun comes in imagining and experimenting with the technical and linguistic components one has incorporated, in order to invoke a sensation, express an emotion, or tell a story. As the mastery of both the instrument and the underlying language expand, the mind becomes more sensitive to different ideas while the body becomes more competent at putting those ideas in practice. The process thus expands naturally from creative absorption to transformation, and eventually to execution.
Math can work similarly. A student must become adept with numbers and other symbols, various rules of algebra and calculus to manipulate symbols, and several functions. This is the language of mathematics; its grammar, and its technique. Mathematical problems can be viewed as structured opportunities to play with what is already known in order to discover what is not.
Through this process, a mathematician begins to develop a sense of the nature of mathematical ideas and their logical interrelationships, thus becoming sensitive to new ideas while becoming better equipped to manipulate them internally. To think of math as just formulas memorized through rote learning and mechanical thoughtless symbol shunting tragically misses the point.
As with music, everyone incorporates the underlying language, grammar and technique in their senses differently, and thus comes to their own individual understanding that leads them to express ideas in their own unique way. Contrary to the trope of the socially dysfunctional lone genius, mathematicians collaborate for most of their work, which makes them in some sense much like musicians. Expressing our internal worlds through pictures, words, and symbols and sharing them with one another, riffing off of each other’s ideas is how much of modern mathematics is done.
What if the world understood math in this way? What if we educated with the idea of playing with numbers in order to master arithmetic the same way improvising musicians are taught to play with musical notes to learn their scales? What if we honored the unique way that people understand and taught from that space rather than by rote? What if we refined people’s logical aesthetics to the point that mathematics felt more personal, more artsy, and the profound experiences of mathematical “beauty,” “elegance” or “risk” weren’t reserved for an intellectual elite?
Math as self-discovery, math as play. These two ideas may seem foreign at first, but I am convinced this change in paradigm is exactly what’s needed in order to enlarge the tribe of creative problem solvers in mathematics and many other human disciplines—equipping them to “jam” on the world’s toughest challenges.