– Galileo Galilei

Ever since the early ages, there has been an everlasting curiosity in the mind of man for the world he lived in. The lives of so many men were dedicated to the comprehending of the forces of nature and extracting some meaning out of them.

Somewhere along the path of our understanding the Universe ‘numbers’ emerged. Interestingly enough humans seemed to have some remarkable innate skills to work with these numbers and relate them to the quantities of nature. As a result of continuous observations, it became evident that there is an underlying simplicity and regularity in the plentitude of phenomena we witness around us. The quantities of nature were observed to be interrelated and the rules, which established these relations assumed the form of laws. Surprisingly with the help of the very same numbers and a few symbols, which constituted the language of mathematics the statements of physical laws turned out to be exceedingly concise and clear. For example consider Newton’s law of Gravitation; “The force between two masses is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.” This when restated in mathematics as ‘F= Gm1m2/r2’ proves the point beyond doubt.

Thus over the ages mathematics evolved as a powerful tool for scientific study, so much so that it emerged as a subject in its own right.

Although mathematics is considered a subject just as physics and chemistry, there is a fundamental difference. Unlike the laws of physics and chemistry, which are fickle and can undergo drastic modifications under the influence of a single observation, the laws of mathematics are relatively permanent. In other words all knowledge of mathematics is ‘a priori’ (meaning coming before observation) whereas knowledge in most other disciplines is ‘a posteriori’.

This raises several questions. Do numbers and mathematics have its own existence independent of the external world or is it just a theological construct by humans? Can a human mind derive the laws of mathematics by pure thought or is it the case that he is born with them? The answers, unfortunately, are not easy. Philosophers and psychologists have greatly differed in their opinions on these matters. Empiricists on one hand believe that all knowledge is ‘a posteriori’ and a newborn mind is a ‘Tabula Rasa’ (an empty tablet). Moderate rationalists on the other hand say that all ‘a priori’ knowledge for example mathematics and logic, is innate but a posteriori knowledge is acquired. On the extreme, Plato a thorough going rationalist believed that all knowledge is innate and exists in the ‘world of ideas’. Whatever the case may be, the status of mathematics is not altered.

Development in mathematics has had a curious correlation with development in other sciences and the progress of the civilization. The birth of mathematical ideas in ancient civilizations was a marker of the progress they had made. The knowledge of math contained in the Vedas is indicative of the level of maturity reached by the ancient Indian civilization.

The development of mathematics was more or less gradual until a couple of centuries back when Newton ‘invented’ Calculus. This paved the way for a clearer understanding of physical laws. The laws of mechanics were parallely formulated by Newton himself and subsequently Maxwell formulated his laws of electromagnetism. With the advent of relativity, these laws were refined. Nothing other than mathematics, particularly calculus, was more suited for the purpose of understanding and working with these laws. As ideas in Quantum mechanics, Quantum gravity and Quantum electrodynamics gained ground, the use of mathematics became all the more necessary. These bizarre ideas cannot be comprehended but by the language of mathematics. Conventional language fails in this aspect. Thus a better understanding of scientific laws with the help of math facilitated the unprecedented growth in technology, witnessed by the 20th century.

Mathematics can not only be applied to areas of physics, but also in the domain of biology, chemistry, and even other disciplines like geography, economics, commerce, astronomy, statistical phenomena and also our daily lives. The potential use of computing machines in almost every field we can think of bears testimony to the fact that everything can be broken down to numbers, to a series of 0s and 1s, these computing machines being fundamentally nothing but devices that can carry out mathematical and logical operations with these numbers. From weather forecasting, simulations of real life activities, predicting eclipses to artificial intelligence and electronic design, mathematical equations can just about describe anything.

Apart from ‘applied mathematics’, which help in describing physical phenomena ‘pure mathematics’ has also attracted a lot of attention. Number theories, for instance have always formed the basis for mathematical recreation. Study of prime numbers, infinities, divisibility and rationality of numbers apart from being serious had at times also been carried out just for fun. Unsolved problems like the proof of Fermat’s last theorem or the Goldbach’s conjecture have spurred a lot of interest in mathematicians.

We are what we are today, thanks to mathematics, the seed of all understanding. Indeed if we want to ‘read’ God’s mind, as Stephen Hawking might put it, we must first understand God’s language.

- K Vikram