Not Fit for Human Consumption
By Dr. Eugene Maier
A couple of things happened last month that were a thousand miles apart, literally and figuratively.
One was a half-page article in a neighborhood weekly that caught my eye while I was at a niece's home in a suburb of Phoenix. "Life as a Mathematics Teacher" proclaimed the headline. Since that was a topic I knew quite a bit about, I was curious what the author, a local community college teacher, had to say. He described a life far different from the one I lead, although, I must confess, it was a life I once embarked on. The author, explaining to all those who wonder why in the world anyone would want to be a math teacher, had this to say: "The reason I do what I do can probably be summed up by paraphrasing the Clinton campaign slogan of 1992: 'It's the logic, stupid!' Those of us whose lives revolves around mathematics," he goes on in a sweeping generalization that might lead one to question the logic involved, "are dedicated to seeing things through to the end.…we try to eliminate unsolved mysteries, and what better way to do that then with the unassailable laws of mathematics?" While doctors, artists and politicians are concerned with other things "we mathematicians blissfully conclude that x unquestionably equals 3. While the world searches in vain for heroes and role models, we have our ready-made icon at whose feet we bow. His name is Mr. Spock. Yes, we practitioners of the art of numbers are the True Believers."
Meanwhile, a thousand miles away back home in Portland, according to my daughter-in-law who witnessed the event, a member of the cast of a local improvisational theater company asked the audience to name the subject in school they hated the most. The chorus of "Mathematics" drowned out whatever other offerings there were.
So there you have it. The math teacher extolling his emotionless, calculating, humanoid version of mathematics. The math students--quirky, emotional, intuitive, human beings--yelling out, "We hate this stuff!" For all the communication that's going on, the teacher and the students might as well be on different planets. And yet, ironically, they are both saying the same thing: "Mathematics is not fit for human consumption."
I sympathize with the math teacher's point of view. It's close to the view of mathematics I held when I decided to become a math major. It was my freshman year in college. Life at my family home was in a turmoil and had been for several years. Not only had the Second World War been waging, which generally disrupted life, but for several years my father, a conservative Lutheran pastor, had been engaged in his own personal war, attempting to defend himself against clerical charges of heresy and civil charges of extortion. Whereas the latter turned out to be baseless, the former, although many thought baseless also, was upheld by the governing body of the church. As a result, shortly before I left for college, my father's position was terminated and we were evicted from the parsonage. For the moment, there was no income and no home. My whole world had unwound in a zany, irrational course of events.
Math was a refuge from all this. At least, math as I knew it from my high school days. It was a nice predictable world where things behaved in a sensible, logical fashion. And I was good at it. So I became a math major to put some sense and order into my life -- and I suspect many a math teacher has done the same.
Then, as I became involved in upper-division and graduate mathematics, I discovered that mathematics wasn't as sensible and orderly as I thought. I learned the distinction between truth and validity--that truth was an elusive quality, more a matter of faith than of mathematics. When I deduced that x equals 3 it was not an unquestionable truth but only a valid statement within the parameters of the system I was working in; what these parameters were--the assumptions I made, the type of logic I used--were matters of choice. I learned about such technical matters as consistency and completeness and many-valued logics and--the final coup-de-grace to my unadulterated view of pure mathematics--the discoveries of the logician Kurt Godel: there are undecidable propositions in mathematics. There are statements which one can not establish whether or not they hold, and it isn't simply a matter of having overlooked a critical axiomatic property--before one could arrive at a set of properties sufficient to establish whether or not every statement in the system is the logical consequent of these properties, one would have introduced a contradiction into the system. Thus, it turns out in mathematics, like everything else in life, one has to live either with open questions or contradictions.
I also learned as I progressed in my studies and was expected to provide my own solutions to problems and my own proofs for theorems and do original research, that logic alone was inadequate, something else was needed beyond the realm of logic--call it what you will, insight, intuition, revelation; ideas that come out of the blue that lead one in directions never before imagined. One can use logic to test their validity, but logic does not provide them.
Learning this about mathematics was at first upsetting; mathematics was not that orderly, well-governed, logical world I was seeking. But then I discovered that mathematics was a much more exciting world than I had imagined--a world of infinite possibilities and variety. And a much more human world; a world that was more than machine; a world where creativity and imagination were free to roam; where there was room for wonderment and what ifs and emotional responses. A world that includes logic, but in its proper role: a means for establishing the validity of our creative thought. Being proficient at math was much more than becoming skilled at carrying out routines in Spock-like fashion.
As long as math teachers view Spock as the paragon of mathematical virtue and devalue the wonderful vagaries of the human mind and the rich panoply of human emotion, classroom mathematics will be a sterile and mechanical subject, more fit for humanoids than humans.