Eugene Wigner famously wrote, in 1960, about the “Unreasonable Effectiveness of Mathematics” — primarily focusing on the seemingly uncanny ability for mathematically precise theory to produce experimentally valid data.
Sixty-four years later — and only fifty seven years since the Beatle’s song “When I’m Sixty-Four” — human’s find themselves no less mystified by a seemingly uncanny ability for mathematically efficient machines to produce commercially competitive content.
Yet what it means for a theory to predict experiment, or for a machine to generate content, I believe, amount to the same thing. Successful real-world predictions and readymade content generation have their goals in satisfying certain human feelings. These feelings of awe, of curiosity, of fear, of hope, of concern, of amusement, et cetera, if we’re truly honest with ourselves about what we’re up to, drive us to write down ideas and implement tools to satisfy these emotions.
Homo habilis reside deep in our genetic history, and their chief tool — language — entwines with our every effort.
By writing, then, I mean a multitude of concepts.
First, there's concept of inscribing language in durable forms. Socrates’ worried about writing in this perspective, from the point-of-view that the human cultural activities revolving around spoken language would atrophy. As usual, Socrates’ had a strongly compelling argument, and good enough that Plato, in full awareness of the irony of the act, wrote the argument down on papyrus.
Second, Wigner felt awed by mathematical precision that, in essence, can only be captured completely by writing it down. Very many scientific efforts start by explicitly writing down either a model that predicts or a hypothesis that examines something occurring in the human experience. Even if the professional necessity to write papers for publication were abolished, the scientist would still need to write down her theories and experiments in a durable form to effectively communicate her results. If not for others, at least for herself later on in life!
More far afield, still, there’s a certain sense in which humans — among whom I consider myself a particular specimen — simply enjoy the writing and the reading processes. This enjoyment feels to me like the same enjoyment I imagine songbirds feel when singing. I’ve compared reading to playing an instrument in my mind as I move my eyes over the score. In this sense, reading mathematics feels much the same as music or poetry.
Allow me to write more precisely, still. I suggest there’s three senses to writing: durability of otherwise ad-hoc communications, formation of otherwise ungraspable thoughts, and recitation of factually true and pleasurable language. Beyond any material production that may be enabled through the written word, these qualitative possibilities for writing satisfy a variety of human emotional needs rather directly.
I consider calculus a form of writing. Writing calculus feels special to me in the same manner as writing poetry. Its uncanniness in helping build tools and shape the world around us does not add or subtract from the beauty of mathematics. Just as a letter, written, copied, and translated over thousands of years, helps us “see through a glass, darkly”, and brighten our ability to discuss and perceive human experience today, a conjecture written, proven as a theorem, and re-proven by generations of student hence enlivens our thinking, perceiving, and experiencing as well.