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Today's quote is by Raoul Bott who said "There are two ways to do great mathematics. The first is to be smarter than everyone else. The second way is to be stupider than than everybody else - but persistent."
I am of the belief that mathematics and written language are more similar than different. Each has its structure and its form of creativity. I have touted this belief to my English teaching colleagues using author, John Greene, and his views on the education continuum as a supportive example. I often hear from some of these colleagues that they do not possess the "math gene". I am not a believer in a math gene. I am not any more a genetic math mutant than I am a lobster fisherman. Keith Devlin states in the prologue of his book, The Math Gene, How Mathematical Thinking Evolved and Why Numbers Are Like Gossip, "One of my aims in this book is to convince you of just how remarkable and powerful - and uniquely human - language and mathematics are. Let me once again quote Neil Armstrong. When the lunar module broke free from the command ship that would remain in orbit above the moon during the course of the moon walk, Armstrong declared that "The Eagle has wings." The acquisition of language and mathematics gave humanity the wings to soar above our fellow creatures. My other aim is to argue that these two faculties are not separate: both are made possible by the same feature of the human brain."
My first educational love was books. Each day as a youth I visited the library and each day my imagination soared with the descriptive voice of the author. I was transported from my sleepy hometown to bustling cities and exotic locales snuggled in a world that were filled with intrigue and adventure that I was sure did not exist in my community and most definitely, in my life. During my high school years, I took classes that were titled Short Stories and Novels which were taught by Bill Nems and with his facilitation, my perception of what I read deepened.
As my formal education continued, I gained a mistress. Her name was Mathematics, the queen of sciences. She offered me structure, organization, predictability, and the allure of a right answer. She eventually introduced me to my drug of choice, solving complex mathematics problems. I had my first initial rush from this drug in my 8th grade algebra class. I do not recall the problem but I do remember solving it in my sleep. This was my first dream in which I awoke with the solution in hand. I was ecstatic. The thrill was overwhelming and I have been addicted ever since. I have continued to solve math problems in varied states of consciousness.
Language is not complete without the written word. I started to appreciate writing as I was completing my master's degree. Within the composition of papers that detailed the educational practices of teaching mathematics and examinations of mathematical curriculum, I discovered my voice. I could be insightful and humorous, sarcastic and tactful, gregarious and prudent. I became a logophile, a lover of words. Writing has offered me creativity in structure and the tantalizing mystism of solving the problem of organizing my thoughts and voicing my passion.
As I stated earlier, I constantly discuss with the English teachers in my school, the parallels that exist in mathematics and English. Recently, an English teacher stopped me in the hallway, approached me resolutely, and stated "Where is the voice in mathematics?" I was delivered a knock out punch. I stood speechless and wandered away muttering to myself, "Where is the voice of in mathematics?"
My first question to address is what is meant by voice in writing. I found two sites that offered descriptions of an author's voice. Understanding Voice and Tone in Writing by Julie Wildhaber and Voice in Writing: Developing a Unique Writing Voice by Cris Freese. Freese states "A writer's voice is something uniquely their own. It makes their work pop, plus readers recognize the familiarity." Wildhaber defines voice as "the distinct personality, style, or point of view of a piece of writing or any other creative work." She elaborates, "Many musicians have played the 'Star-Spangle Banner,' for instance, but there's a world of difference between the Boston Pop's performance and Jimi Hendrix's, even though the basic melody is the same."
I asked my English colleagues their opinions of voice.
Beth Gadola: "In writing, voice can be expressed when a writer puts him or herself 'into' the words, providing a sense that a real person is speaking and cares about the message. When a writer is personally engaged with the topic, he/she imparts a personality to the piece that unmistakably his/hers alone. And it is that individual personality - different from the personalities of all others - that we call voice. Voice is the distinct personality of a piece of writing."
Stan Berg: "For me, it's a sense of authenticity, the idea that a real person is letting his/her real self come through in the writing so that it doesn't sound like a canned response that could have been written by anyone."
Lyndsy Schwantes: "I would say that a writer's voice is what makes the writing stand out to me. It's not only their word choice, but the way their words work together to tell a story and create characters the reader can connect with. When I read a story by an author I consider to have a good "voice" I don't think about the words or why their choosing their words, but I become lost in the story."
Maria Burnham: "Voice, simply put, is the thing that breathes life into writing. It's the formula of writing that tells my brain's inner voice how to read something. Is the writing factual and simply stated? There is voice in that style of writing. Is the writing full of vivid description and flowery language? There's voice in that style as well. Is the writing full of questions followed by answers? You've got it, there's voice in that, too.
For what it's worth, the reason I majored in English in college was that I fell in love with voice in writing. I loved that the choice in words and the way in which they were arranged changed how the writing sounded. In writing there's cadence, emotion, meaning, all because of an author's choice.
I find myself gravitating toward specific kinds of voices, particularly those of poets and essayists like Whitman and Thoreau. But I also love humor, sappy love, and even the simplicity of technical writing.
Letters and words in isolation have meaning but little depth unless put together by an artist, a wordsmith, a writer."
A common thread winds through these definitions. Voice, like beauty, is in the eye of the reader. Even a boring voice in one's mind may conjure up an image of Ben Stein lecturing in Ferris Bueller's Day Off . A voice that paints images, resonates emotion, and is layered with complexity may only be appreciated by a few experienced readers. I watched a rich and vivid dance performance recently. A strong female voice emanated from that performance but I knew that my perception only heard whispers of her messages.
Mathematics has beauty. "Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." Bertrand Russell, The Study of Mathematics
A February 2014 article by James Gallagher in the BBC News entitled Mathematics: Why the brain sees maths as beauty, discusses the brain activity of emotion that is triggered equally by a beautiful equation, a great painting, or a classical piece of music. The equation that is believed to be the most beautiful is e^(iπ) + 1 = 0. This equation is referred to as Euler's Identity. The proof of the identity resonates in me wonderment and awe.
Does beauty in a medium indicate a voice? I don't necessarily think so. A rose can be appreciated for its beauty but it remains silent.
I was at a loss in describing a voice in mathematics until a recent Math League practice. I sat and listened to my students work on various problems. I believe these three problems spoke to my students.
1.
I was asked my students where to start on this problem and told them to rationalize the denominator. As one student proceeded, she paused, "Oh, cool! This is a cute problem!"
2.
2.
As we worked on this problem, several students remarked how this was a "sneaky" problem. When I asked them to define "sneaky", they described problems that first appear to relatively direct to approach but as those problems are solved, they entail twists, turns, and surprises that require persistence and flexibility by the solver.
3.
In this problem, the graph is defined as the second derivative and students were asked to draw the first derivative and the original function from which the second and first derivative were formed. Students described this problem as a simply stated but multilayered in its complexity. I compare their description of this problem to a single stanza poem. A poem that offers new insight to a reality that surrounds us each time it is read.
As I contemplate what specific mathematical ideas speak to me, I have a few the quickly come to mind.
The proof that the square root of 2 is an irrational number has always evoked a voice of sarcasm. I can hear my son, Sam saying,"So you don't believe it to be true? Let's assume its not and see where that leads us!"
The Pythagorean Theorem speaks to me in a voice of security, loyalty, and strength. The Pythagorean Theorem is in algebra, geometry, trigonometry, and construction. When I am stuck on a problem, I can hear John Wayne lean in and say "Hey, little pilgrim have you tried the Pythagorean Theorem?"
I can hear the imaginary i screaming at mathematicians, "You thought that negative numbers were imaginary and you found application. You define me as the square root of a negative one and call me imaginary, yet you found application for me! What is it with you guys?!"
Finally, the controversial number 0, the number that apparently does nothing in addition but is the mighty destroyer in multiplication. The number that can be divided but is not allowed to the dividing. The number that was considered the null and void and repulsed by religions but without it we would not have calculus. The number that says, "Go ahead, make my day."
The voice in mathematics exists but it is different than the voice in writing, the voice in music, the voice in dance, and the voice in art. Mathematics is creative. Its voice may be more restrained and its voice may take more work to hear but the voice exists, nonetheless.
