On the uselessness of mathematics

Students (and their parents) sometimes ask why we should study mathematics beyond what is needed for day-to-day life. It's a good question. Only fools and philosophers willingly study the utterly useless.

In response, authoritarian governments are quick to offer self-serving utilitarian justifications, such as the need to balance checkbooks, pay  taxes, calculate the trajectory of missiles, and get a good job.

The lazy are likely retort, “But calculators and spreadsheets do all that for us. Why should we bother?”

"Another very good question!" replies the sage, who continues...

Consider the modern jet, so easy to operate that anyone with some luck can get one off the ground. Landing is tougher, but if you follow directions from the tower they will gently guide you down to earth or even take remote control of the aircraft for you. On a day-to-day bases, jet pilots use little of their professional knowledge, but when an engine blows, it's good to know that there's a qualified pilot up front who can do a lot more than follow simplistic directions.

Following a simplistic instructions from the tower is similar to trusting in a calculator to give us answers that we don't actually understand. It works as long as we're lucky. But what happens when we need to think for ourselves? In today's over medicated, air conditioned society such situations don't occur as often as in former times, but when they do occur it's good to have a little real world experience and wisdom to fall back on.

Like jet pilots, most of us don't often need to think mathematically, but when

• tempting credit card scams arrive, or
• the value of a house goes underwater, or
• the friendly tax collector calls, or
• you are asked to believe that 'three out of four [experts] say you absolutely need [silly product A], or
• powerful corporate personhoods are "legally" emptying the retirement system you've paid into all your life, or
• you live in a large, energy-wasting nation where your vote on issues of global warming matters very, very much...

...your ability to think mathematically becomes crucial to your continued well-being. When such moments arrive, we often need enough mathematical understanding to separate comforting illusions from cold realities. Therefore, strictly from a utilitarian perspective, we should learn all the mathematics we can. Our life, and the very survival of our planet depend on it.

A better question is, "How much mathematical understanding matters during the significant moments of life?" Although better, this question is much harder to answer. So what! Since when do truth seakers reject a questions simply because it is hard to answer?I leave you to find your own answer (or not) in freedom. Moving on...

Although these utilitarian questions may be interesting, they are too narrow, situation-specific, and self-centered to satisfy for long. They fail to touch the awe-inspiring scope of mathematics--its amazing symmetry, beauty, consistency, mystery, and predictive power. They awesomeness of mathematics is sufficient. Something is happening here. Whatever it is we are a part of, the language of mathematics seems to model it better than anything else we know.

Suppose for a mathematically short moment that mathematics is "only" as useful as music. It's not hard to see the importance of music. It enriches our lives. It bridges cultures. It heals souls. It rouses the naively patriotic to foreign wars and brings solace to their many victims.

Most of us enjoy music and feel that alone is reason enough to justify its existance. We would feel our world far emtier without music.

The beauty of mathematics is more difficult to experience. It requires study, training, and worst of all real effort. But note that music, with its rhythms, intervals and frequencies--is based on clear mathematical patterns. What we call noise is distinguished from what we call music by only one thing: recognisable mathematical patterns. Thus, the enjoyment of music nothing more than the intuitive enjoyment of pure mathematical patterns.

Mathematics is at least as useful as music simply because without mathematics there is no music. But mathematics underlies far more than music. It underlies so much else that some wonder if it may be the language of reality, no matter how reality is defined. Others go so far as to suppose that mathematics is reality, and that everything we experience is an aspect of mathematics. Noise would then be sounds that conform to mathematical patterns that are too complex for us to intuitively follow as music.

We finally arrive at the ultimate reason for learning mathematics. Reduce the noise!