If I am designing an algorithm, drawing a map to illustrate Evliya Çelebi’s travel route, or etching arrows to represent morphisms connecting homology groups in mathematics, I want to be able to efficiently give a visual presentation to my audience, whether it be myself or a peer. I need it to be as quick as I read, as quick as I think, and as quick as I speak. A piece of paper, however, limits me to a small 8.5”x11” cage, where ideas are hard-pressed to grow and come to fruition. I want to be able to teach or work with my body, use gestures, and employ breaks in speech for emphasis, as if I were one with my medium of communication. I want to be able to tune into the rare moments of streamlined drifts of my consciousness, connecting idea to idea. I want to simultaneously become the dancer of the dance, singer of the song, and artist of the art. It is the blackboard that allows me to perform a saut de chat, to syncopate, to use thick or thin brush strokes, to employ chiaroscuro, and most importantly to extemporize. For me, all these aspects of the blackboard provide my mathematical reasoning, creativity, and presentation a place to blossom.
Consider chalk waltzing atop a blackboard. I move my whole arm to the rhythm of my writing. I oscillate between reaching to the top-left of the board and pointing to the diagram etched at the bottom of the board. Having taken advanced courses in topology, I consider myself a “blackboard mathematician” and have noticed that writing in wide motions causes us, humans, to instinctually fit the cyclic pattern of the “ins” and “outs” of our breathing. As I teach, it is crucial that I transfer my knowledge to my audience in real time and in an interactive and concise manner. The clacking of the chalk against the hard plane deliberately controls the motions of the cycle and helps my peers understand the stressed and unstressed meters of my speech, allowing all the important details to fall in place, forming a perfect scheme.
Since the area of the blackboard is finite, sudden recorded flashes of thoughts eventually populate its newfound habitat. As I run out of thinking space, I must either jump to a new board or erase and start anew. In doing so, I take the leap-of-faith and hope that all my ideas are already firmly imprinted into my mind. Switching every so often helps me to recollect and compartmentalize my thoughts and to perform with more fluidity and order. It also provides the swiftest segue into another topic because new ideas from the second board can be directly juxtaposed with the thoughts from board one. My blackboard, my companion for thought, is the only person who can truly understand my underlying reasoning and logic from which all my mathematical proofs are built upon.
Perhaps the most apt way to describe the blackboard’s function is to compare teaching mathematics and even portraying thoughts in general with the performing arts. Ballet dancers need the right type of stage floor with just the correct amount of friction, support, and bounce to foster a better and smoother performance. An artist has to make a distinction between using wooden easels or cold, metallic surfaces so that the right sentiment is evoked. And as a mathematician in training, the quality of the presentation surface of the blackboard is deeply ingrained as the perfect medium for communication within the mathematical world.