“The essence of mathematics is not to make simple things complicated, but to make complicated things simple.”
— S. Gudder
Mathematics is a study of abstraction and patterns in daily lives. Mathematics has evolved from basic counting to astounding theorems and concepts that transcend mere physical understanding. Mathematics serves as a modeling tool to understand different phenomena and be able to simplify solutions for real world problems. Maths, if viewed with the right perspective, appears to be beautiful in terms of method, experience, results, and philosophy.
Maths has been an essential field in the understanding and enhancement of technology. Branches of mathematics are extensively used in all engineering applications and are therefore, very important. An elegant and powerful tool such as maths does not receive due respect from many students as mathematics is found to be confounding and mysterious. The abstraction in mathematics due to heavy utilization of logical symbols, notation, theorems, and axioms appears to add to the confusion.
While mathematics can seem esoteric and recondite, the principles underlying in mathematics involves identification and understanding of different patterns that occur. A dizzying array of patterns and properties can be inferred from our understanding of basic counting, which is an intuitive tool we possess as a virtue of our intelligence. Keeping our eyes open for different patterns can help us understand and appreciate the true beauty of mathematics.
As Indians, we are blessed to be born in a land with geniuses who have revolutionized the art of understanding maths and the inherent patterns present in it. The first and foremost name that strikes us when we think about India’s mathematical geniuses is Srinivasa Ramanujan. Ramanujan contributed greatly to mathematics using his uncanny and intuitive pattern recognition and analytic skills.
An interesting and famous anecdote is that when the famous mathematician G. H. Hardy visited Ramanujan at a hospital, he mentioned that he arrived in a taxi whose number was 1729. Hardy considered this number as a ‘dull number’. To this, Ramanujan replied, “No, it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways.” Ramanujan impressed the world with what seemed like mysterious mathematics, but in essence was a simplified approach in understanding the principles that constituted mathematics in a very elegant manner.
To the observer, Ramanujan’s results were, as quoted by G. H. Hardy, “arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account”. The truth behind his intuitive approaches was the sheer love for his work. Ramanujan understood the beauty and importance of this subject and spent his time and energy in obtaining newer and deeper insights without having undergone formal mathematical training.
Ramanujan demonstrated his love and passion for mathematics by recognizing and analyzing new patterns, theorems, series, and geometric constructions with total dedication. Thus, Ramanujan was able to channel his genius in obtaining complicated mathematical results and interpreting them and analyzing them in a very simple, efficient, and aesthetic manner.
As students of maths, we need to inculcate the spirit of looking out for new patterns, understanding concepts with different viewpoints, and bring out the hidden Ramanujan within us. With the right mindset, spirit, motivation, interest, insight, and a thirst for obtaining solutions to problems, mathematical or otherwise, we will be able to see the hidden simplicity behind maths and appreciate the true beauty of a wonderful subject such as maths.