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Students usually have a common view on their subjects. A single common view to study well for the subject, hand in assignments, and get an ‘A’ grade. Take mathematics for example. A typical 2-year junior college math course will start with algebra, tie up the student with angles and functions of trigonometry, greet him with the many facets of calculus and then probably ending with some mechanics. The student, throughout the course of learning the subject, will have this goal: learn the techniques, condition the mind in problem solving, and acing the final exam.

This is how it works in the schools. The exam marks the end of the learning, at least for most students. How pitiful it is. The student never really touches the more interesting ideas of mathematics because there is no reason to do so, no exam to prove his capability in learning. That is for today’s students. For the mathematicians in the past, the journey to learn took a very different picture.

At that time, say around the 16th to 18th century, learning mathematics was a battle to see who was the first to solve an equation, to find a link in the numbers or to proof some theorem where the winner would see his name printed on a revolutionary publication. Some mathematicians, usually those working in the same university or resided in the same country, teamed up knowing that their combined efforts would prove advantageous against their opposition. These were no easy battles as each player were fuelled with greed, ambition and jealousy to win.

One such battle was that between Newton and Leibniz on who should gain credit for inventing the calculus. Calculus is arguably the most important field of mathematics, and history shows that a concept this big would have ramifications involving countries.

Newton was an extremely gifted mathematician whose knowledge surpassed his teachers and even top mathematicians of that day. He invented the calculus, termed ‘fluxion’ at that time, to facilitate understanding of concepts physics. Around the same time, another mathematician Leibniz was developing his own ideas of the calculus but was used solely in mathematics.

It has been long thought that each mathematician’s development of the calculus was independent of each other. Here lies the battle of who was the first to have invented it. This battle was fought so intensely that other mathematicians were involved. John Wallis stood by Newton while Johann Bernoulli stood by Leibniz. The resentment between the two groups magnified to the point where the British was pitting themselves against the Continent, each arguing that the calculus came from their country.

When I read about these battles in mathematics, it gives me a different view on the subject. Why can’t learning mathematics be as exciting as it was in the past? I think that the subject has been degraded to a bunch of topics you need to study in order pass the course and that the possibility of exploration has been lost. There is no sense of a battle where students, arm with techniques of algebra and calculus, fight each other to earn a place in the podium.

How I wish mathematics could be like that. While I am not necessarily in an environment similar to that of Newton and Leibniz, I for one try to picture myself in a battle against other mathematicians. I have adopted a new viewpoint during my sessions of study. I’m in a battle to develope a new idea and that requires me to quickly learn whatever theorems I need in order to do so. Help comes in the form of textbooks that arms me with more ways to win. And should I win, I get the pride, honour, and joy in joining the ranks of these top mathematicians.

You can find many interesting topics regarding Newton’s work and Leibniz’s work in my website.