— Pushpa Raj Adhikary
For most mathematics is like an iceberg, a small visible portion above water and nine times as much submerged below, invisible. Most of us who have come to know a little of mathematics, under rather uncomfortable conditions, have no idea what mathematics is the way it is hard for us to form a clear idea about the submerged part of the iceberg. The best thing to do about an iceberg is to take an about turn to go to the opposite way. Most of us do the same about turn in case of mathematics as well.
Have those who take an about turn to go the opposite way ever tried to fathom what the subject is really about, what their own misimpressions are, and what sense it makes to those interested? Perhaps what puzzles non-mathematicians is the difficulty to realize mathematics. The explosion of the first atom bomb in 1945 was a reality out of a very famous mathematical equation of Einstein which says that E is equal to M C squared. If it makes no sense to you or to all non-mathematicians, it is because you never bothered to learn more about mathematics than what you know.
All the intelligent non-mathematicians may say, so what if I cannot make sense of the mathematical equation of Einstein while I know those disciplines of knowledge where mathematics has little or no use? But it is time to remind them that mathematics is no longer a subject they can dismiss easily. Mathematics is increasingly becoming important not to science and engineering but in industry, business, military affairs and many other human activities and innovations of new technologies in almost all areas of human endeavor. Space and deep sea explorations for tapping entirely new sources of energy, food and raw materials necessary to continue our development are impossible without the development of mathematics. So, there is a growing need for more and more persons to enhance their knowledge of mathematics. Mathematics no longer remains a subject of intellectual pursuit for a few but knowledge essential to create and respond to your daily requirements.
Why mathematics puzzles non-mathematicians is because they find it hard to decide what it actually is. Is it science? It is an art? Is it a language? In fact, mathematics is science, language, and art. Among all existing sciences, mathematics is the most general science. It is not restricted to any particular area of knowledge, real or imaginary. Mathematics deals with any objects, or observations, real or imaginary, and any thought however abstract it is. Numbers can count not only motor cars and people, but stars on the sky and molecules on a drop of water. No other science is as general as mathematics.
Mathematics is an art where creativity of highest order can be displayed by means of language, symbols, and a combination of both. Mathematics is also an art of reasoning and deduction. From such statements which are assumed to be true, we deduce, by reasoning, other statements that must inevitably follow them. For example, from the fact that 2 plus 5 equals seven, and some other statements, it can be deduced that 2222 plus 5555 equals 7777. No other art equals mathematics in the way of skillfully and correctly deducing.
Mathematics is also a language, the language of expressing scientific ideas. Natural laws are expressed correctly in the language of mathematics. Moreover, it is a language of calculation. In mathematics, any idea can be named, discussed, analyzed, and calculated (in exact reasoning process). Alfred North Whitehead remarked that a mathematician has weighed the earth and counted billions of molecules in a drop of water. In fact, no other language has such a degree of freedom, as in mathematics to use words or symbols for any idea one chooses. Precise deductions with these words or symbols lead to the calculation one desires. But let me remind the readers that mathematics in not only the language of calculation. Lots of calculations take place in an ordinary language, too. For example, removing ambiguity from sentences to make their meaning clear also needs calculations.
Some people have found out what mathematics is about, and what power it has. For such people mathematics is the most exciting instrument of human mind. But we can say that most people have not understood this. Education in mathematics, up to now, has not been able to impart this degree of understanding to know what mathematics is about.
The root cause of the trouble in understanding mathematics lies in the introduction to mathematical ideas which we experience as we grow up. The introduction usually begins with arithmetic. In the age where the idea of numbers is introduced, a child may not be able to conceive the idea of 2: which represents two eyes or two hands that we possess. Again the number 3 which is larger than 2 by 1, and any other latter numbers, seem inconceivable for a child unless he/she is matured enough to count. Education in mathematics begins at an age when a person does not know very much, nor is he/she able to know much. Besides, mathematical ideas are introduced not in a systematic manner but in bits and pieces which make little sense to the learners. Moreover, the authoritarian manner of the teacher “do this and this and never mind if you do not understand” would contribute a lot for the general dislike for mathematics at the earliest opportunity. Those who continue the study of mathematics do so because it helps them to secure higher percentage in the tests/examinations and is necessary to study various branches of science and engineering afterwards. The worldwide trend of decline in the number of graduates majoring mathematics confirms that majority of young people shun this field. This is definitely not an encouraging sign at the age of rapid technological developments, and when we are faced with a hoard of problems.
We are actually talking about non-mathematicians. So, as a non-mathematician have you ever reflected: “How much mathematics do I have to know? Can mathematics actually be useful to me?” If you are an intelligent person holding a responsible position, you need to know a host of things like how to read graphs and use tables, apply a few formulas, estimate the values of different items, take samples and make models and diagrams, determine chances, predict the future, and make appropriate decisions. All these are essential daily activities. Graphs and tables summarize a lot of information, and so do other mathematical ideas. These ideas help you to understand real world in much better way than without any mathematical ideas. As an intelligent non-mathematician you can think now how mathematical reasoning would help you and how much effort you have to make for acquiring broad and clear worldview.