### The wonderful world of mathematics

September 3, 2014

“You are the mathematician among us, so figure out how much tip we need to give,” my friend, Rina, said when a few of us were dining in a restaurant.

I replied, “Rina, you work for a bank and can figure out the amount faster than me.”

Rina gave me a mischievous smile and said, “Well, we need $**. ** for tips, and each of us needs to pay $**. **.”

Rina is very good at computation. Sometimes she can compute faster than a graphing calculator.

However, she is not at all interested in mathematics.

It is a myth that mathematicians can compute accurately. Rina knows this well, since we have been friends a long time, and on many occasions I’ve made computational errors.

Computations are important in mathematics, but they are more important to *the users** *of mathematics…

If an engineer makes a computational error, a building may collapse or a plane may crash. If a doctor makes a computational error in calculating the dosage of a medicine, a patient may die. If an accountant makes an error in calculating tax, the client may receive a summons from the IRS.

Computations in mathematics are like grammar in a language: If you make a grammatical error in writing, it is still possible to convey your thoughts to the reader without jeopardizing the concepts. In the same way, it is possible to communicate mathematical ideas, even with computational errors.

Now, I am not at all promoting writing with grammatical errors and solving problems with computational errors. As you all know, you will not get full credit if you make computational errors in solving a problem or grammatical errors in writing an essay.

You may now wonder, then, what is mathematics—and what do mathematicians *do?*

## The great math misconception

The great misconception about mathematics is the notion that mathematics is about formulas and cranking out computations.

It is the subconsciously held delusion that mathematics is a set of rules and formulas that have been worked out by God knows who for God knows what, and the student’s duty is to memorize all this stuff.

Such students seem to feel that sometime in the future, their boss will walk into the office and demand quickly, “Medha, what is the solution of a quadratic equation?” or “Dilip, I need to know the equation of a circle.”

The truth is there is no such employer*.*

Mathematics is not about answers. It is about the process of solving a problem.

When a new building is made, a skeleton of steel struts called scaffolding is put up first. The workers walk on the scaffolding and use it to hold equipment as they begin the real task of constructing the building. The scaffolding has no use by itself. It would be absurd to just build the scaffolding and then walk away, thinking that something of value has been accomplished, yet this is what seems to occur in all too many middle and high school mathematics classes.

Students learn mechanical techniques for solving certain equations, finding derivatives of functions, etc. But all of those things are just the scaffolding. They are necessary and useful, sure. But by themselves, they are useless.

Doing only the superficial and then thinking something important has happened is like building only the scaffolding. The real building in the mathematics sense is the true mathematical understanding, the true ability to think precisely and analyze mathematically.

It is these qualities that employers are looking for. And in fact, mathematicians are always in the top 10 in a list of 200 jobs.

To most students, mathematics is a pure science, because 1 + 1 is always 2. But if we change our commonly used base 10 system to a binary system, which has only two numbers 0 and 1, then 1 + 1 is zero in that system.

I am not creating this number system just to make a point. Electrical engineers and computer scientists are using this number system to build a circuit or design a calculator. For example, for electricity there are only two stages: either current is flowing (1) or not flowing (0), which is the root of creating the binary system.

By changing the base of the number system, mathematicians are creating new mathematics.

A mathematician’s job is to help scientists to find formulas so that they can send human beings into space; or to help computer scientists to feed a huge data set so that the search engine can search trillions of pages in less than a second; or to help pharmacists to figure out the dosage of a lifesaving drug; or to help airline carriers to schedule flights.

Still, these are significantly small parts of what mathematicians do.

A mathematician’s larger job is to create and recognize patterns.

## The art of the pattern

According to one of the greatest English mathematicians, G. H. Hardy, “A mathematician, like a painter or poet, is a maker of patterns. If his or her patterns are more permanent than theirs, it is because they are made with ideas.”

Patterns are everywhere. You need mathematics in order to recognize and understand them.

When dancers are dancing, subconsciously they are creating patterns. The planets are moving around the sun in patterns; since the planets’ motions have patterns, scientists are able to represent the motions by mathematical formulas. Musicians create music with patterns (and nowadays, computers play a significant role in creating music, because musicians are recognizing the patterns in their music and able to simulate them on a computer). When artists draw pictures, they need to know proportion as well as projection of three-dimensional objects on two-dimensional papers.

When you conduct an experiment, the goal is to find a pattern between the input and output, and if you can find a pattern, you are able to represent it either by a formula or by a graph.

These are all related to mathematics!

Experiential learning is one of the core values of Jesuit education, and mathematics is, in its essence, experiential learning.

Remember as you study for a test or struggle with a particularly difficult problem that education, like mathematics, is not about answers. It is about the process of solving a problem.

Learning is a result of taking away knowledge and experience from the process—not the ability to find the solution.

Dipa Sarkar-Dey, Ph.D., is chair and associate professor of the mathematics and statistics department at Loyola.

## 4 Comments

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Professor Sarkar-Dey,

What a great piece. Thanks a million!

Wonderful article for common people like me

to understand mathematics. Thank you for

mentioning my name in the article.

Thanks for the insightful article. I enjoyed it very much.

Very well said! Thanks, Dipa!