Mathematics: Exciting or Hard?

– Pushpa Raj Adhikary
Traditionally mathematics has been an integral part of the courses in natural sciences and engineering everywhere. But experience has taught us that learning mathematics has never been a priority of majority students. The high rate of failure in mathematics of mathematics majors as well as Engineering students confirms this fact. Perhaps the motivation and encouragement given to learn mathematics are not sufficient.
Although mathematics is considered the most prestigious subject in the school curriculum at any level, it continues to be a subject taught more for enabling students to get through the examinations only. It is taught in an authoritarian fashion. There is least worry about motivation. At most, all emphasis is on solving tedious and rather complicated problems with little explanation on the inherent beauty and logic of the methodologies involved and their practical implications. Mathematics is one subject where the gap between the intended and the implemented objectives is wide. As a consequence, mathematics is considered a most difficult subject and is considered as a useless, boring and hard subject. Also, it is considered as abhorred by a majority of the educated people. This attitude of parents and educated people in the society is creating a negative impact upon the younger generation that it is a difficult and not so useful subject. This causes great panic among the students to study mathematics.
Part of the reason why mathematics puzzles the majority of persons is that it is hard for them to decide what kind of thing mathematics is. Is it a science? Is it an art? Is it a language? In fact mathematics is all three. Among all the existing sciences, it is the science which is least restricted to any one particular area of the world, real or imagined. It is hard to say all that mathematics is. The famous philosopher Bertrand Russell said that pure mathematics is something which we can talk about without understanding what it is.
Some parts of mathematics can be useful to any intelligent person. They help one to make better decisions. They help anyone to see the structure of the world more clearly and help in common activities. Graphs and tables summarize a lot of information. To be able to read a graph or a table makes the information accessible. Estimating is a technique of making good rough guesses about numbers. Models, plans, schemes, maps, diagrams are the representations or pictures of the real world. In all these activities, the results are not obtained without hard work. Moreover, such mathematical scales are a part of any skill/aptitude test for a job or for advanced study in any discipline.
Mathematics contains ideas that can be, and deserve to be, communicated to a wider public. But mathematicians claim that math is not a spectator sport. You cannot understand math, or enjoy it, without doing it. A mathematician who tries to communicate his subject to the layman soon finds himself in trouble because if he sticks to the truth he cannot communicate, and when he tries to communicate, he strays from the truth. Talking without being understood is pointless, lying is painful, so most often mathematicians abandon the attempt to communicate mathematics to others.
But this is not the case in other branches of science. Not only a geneticist doing research in recombinant DNA research knows about DNA but many others know what DNA is. Likewise, you need not be a Physicist or a Chemist to know that matter consists of atoms. But the reverse is true in case of mathematics. When mathematicians, physicists or electrical engineers talk about anything, sooner or later they scribble down formulas. To them formulas are the most precise and economical way of expressing their thoughts. Without formulas they think they cannot communicate well. But showing a formula to someone who can’t remember the symbols is something like encountering nightmares. An English major student once asked a mathematics professor to suggest him a book of geometry written in plain English without any mathematical formulas and symbols. Can mathematician write such books for students majoring other subjects?
Formulas do not scare only non-mathematicians, but sometimes even to the persons of science. Michael Faraday, best known English investigator for his pioneering work connecting magnetism and electricity, wrote the following to one of his junior, James Clark Maxwell:
When a mathematician engaged in investigating physical actions and results has arrived at his calculations, may they not be expressed in common language as fully, clearly, and definitely as in mathematical formulae? If so, would it not be a great boon to such as I to express them so?
If formulas in mathematics and other physical sciences are considered weapons of intimidation by others, cannot they be replaced by common language? But to explain the mathematical formulas in details, words are often clumsy and sometimes ambiguous.
Having talked about something on the nature of mathematics, now let us answer the question, “Is mathematics exciting?”. Today mathematical methods not only pervade the whole world of physical sciences and engineering but such diverse branches of knowledge as the social sciences, management  sciences, psychology, economics, biology, linguistics, and military affairs. Why mathematical methods are so popularly used is because it has ability to reduce complex problems into a set of simple step-by-step solutions. In the absence of such a technique, problem solving would mostly be a trial and error or a subjective matter.
We are living in the greatest age of mathematics ever seen. Mathematics started being more abstract since the beginning of twentieth century and many feared whether mathematicians would be working on silly intellectual exercise. Since World War II, it has became a single unified discipline having profound influence in the development of human civilization. So, learning and creating mathematics is a worthwhile way to spend life.
Now, to the second question: “Is mathematics hard?  Unfortunately most people confess that they are not good at mathematics.  You may not find a single good mathematician who claims that mathematics is easy for him or her. While mathematics is intensely enjoyable, it also requires hard work and discipline. Very bright students who are good in mathematics at high school do not graduate in mathematics courses and still a few eventually get their PhDs. The truth is that one should be driven to study mathematics and it is literally difficult to convince that they could shine in this discipline. But the fact is: it is exciting. The earlier frustration of learning mathematics should not deter anyone in the thrills of learning and creating new mathematics. Mathematicians are the only people who, by their mathematics, help to create new technologies and knowledge to enhance human civilization further.
Share on Social Media