WILTSE: Mathematics anything but boring

Dec 22, 2011

 

Usually, the conversation goes as follows:

“Are you retired?”
“Yes.”
“Where did you retire from?”
“Grand Valley State University.”
“What did you do there?”
“I was a professor.”
“What did you teach?”
I was dreading this question. “Mathematics.”
“Oh, yech. Math was my worst subject in high school. I hated it.”

It was this insipid comment that I was anticipating and dreading. It always makes me want to smack him or her, or to simply walk away. I have never done the former and have always attempted to do the latter.

I had one woman who gave me the worst of all answers to the question. She said: “Mathematics! How boring! How could you stand teaching such a boring subject?”

This was the closest I ever came to smacking the person. But I chose to walk away and hoped that I would never again encounter that individual.

Such people are clearly mathematical babies. There is no defense of the subject because they are such babies. You may as well have a philosophical discussion with a 2-year-old.

Can you imagine discussing ethics with a 2-year-old? It can be done. You start with “Paddy Cake” and proceed from there. You may reach the rudiments of ethics in about 18 years.

These people think of mathematics as being some sort of “super accounting.” They think of a mathematician as being some sort of nerd who sits in a corner adding columns of figures. They actually confuse mathematics and accounting.

They think of mathematics as memorizing multiplication tables, for that may be as far as they got in the subject.

Actually, I studied mathematics because there is little memorization; rather, it is a subject of reasoning.

They are also probably a product of a teacher of mathematics who also hated the subject, and therefore instilled this hatred in his or her students.

Also, the man in the street seems to think that almost all of mathematics is known and that there is little else to do. Actually, nothing can be further from the truth.

The mathematician Kurt Godel proved an amazing theorem. A slightly over-simplified version of this theorem says that in any system of mathematics which uses an infinite number of objects (e.g., numbers) there exist problems in that system which are solvable, but not solvable within the system.

For example, it has been proven that in Euclidean geometry that it is impossible to trisect an angle using a compass and ruler only. However, if one passes to analytic geometry and calculus, the problem is solved. Now, if we lump all of mathematics into one system, there must exist problems that are solvable but not solvable in the system.

It follows, then, that there must exist infinitely many systems of mathematics. Not only are there infinitely many problems, but there are infinitely many systems of mathematics yet to be invented. There remains a wealth of things to consider in mathematics and this will always be the case.

One doesn’t have to go to graduate school forever to appreciate the beauty of mathematics, however.

I read a short story once by Aldous Huxley in which he describes being on vacation in Italy and befriending a boy there. He showed the boy the fundamentals of Euclidean geometry. Then, while watching the boy from a balcony draw figures in the sand, he watched the boy discover and prove the Pthygorean theorem. What a beautiful thing that was.

As a matter of fact, there are probably thousands of novice mathematicians who have discovered that theorem independently of Pthygoras in a similar fashion.

Moreover, there are similar aspects of mathematics that are well-known, yet are discovered independently by amateur mathematicians and are just as beautiful to them as they were to the original discoverer.

To me, mathematics is the ultimate in beauty. To be told that mathematics is dull or boring is the ultimate in insults.

I don’t think that the people I have described above intend to insult me, but they do. I think they honestly believe mathematics to be boring and dull; but it has been instilled in them through poor teaching or through their own laziness.

In any case, have a Merry Christmas and enjoy your New Year and mathematics.

— By Ralph Wiltse, Tribune community columnist

 

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