Mathematics: A Scientific tool!
When we talk about ‘mathematics,’ many times, it is a mixture of complex calculations, equations, tables, and unsolvable difficult calculations. Some people have a fear of such concepts and some literally break out in sweat. This is because of the phobia of the subject and its inaccessibility has been ingrained somewhere in the mind, maybe from ancient times!
In fact, it should not be because mathematics is all around us. In the rhythm of our breath, in the movement of our footsteps, in the graceful movement of animals, in the laws of creation and even in the birth of the universe!! Mathematics is a language through which humans have developed many theorems, theories, and elaborate techniques to understand the truth, to know the principles of creation and to express it. Based on the strength of which today he is unravelling the secrets of the ultra-microscopic Nanotechnology to the ultra-vast universe. Today, a basic question is being asked in the world, ‘Mathematics is discovery or invention?’
As we see, many birds migrate hundreds of kilometers every year, how do they determine their route? Turtles lay their eggs on the shore according to the motion of the moon and the tidal cycle, and on high tide days the hatchlings hatch and are pushed into the water by the waves and their life cycle continues. Who teach turtles about tides and calculation of phases of moon? Flowers and leaves are arranged in such a way that each flower will attract insects and each leaf will receive sunlight. How does a tree learn the rules to maximize sunlight for so many thousands of leaves? Why does a bee choose a hexagon when choosing the shape of its hive?
From all these examples we can see that nature seems to use many ‘rules’ of mathematics. The most important rule nature uses are ‘Optimization’ which means making the most out of the least resources. Birds choose their route in such a way to cover the maximum distance within their capacity. Turtles lay their eggs at a time when nature allows most of their hatchlings to survive, making the maximum application of the tidal force. The ‘Fibonacci sequence’ in mathematics is particularly evident in the composition of leaves, branches, and flowers. As a result, the leaves appear to be designed using specific geometric principles in a minimal space. The beehive is hexagonal because the hexagon is the shape that can store the maximum honey in the minimum amount of space. In modern mathematics, this principle is known as ‘Penrose tiling’. Today, all these principles are discovered by man through his mathematical research, but does this mean that nature already knew them? And how much truth is there in human conjuncture that we ‘invented’ mathematics? That is why the question arises, ‘Is mathematics a discovery or invention?’
Let us think about this question. Many mathematical thinkers came forward to answer this and gave some opinions. Famous scientist Albert Einstein says,
“How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”
That is, ‘abstract mathematics’ which is the essence of human thought, how exactly does it apply to many things in the real world?’ That is, even a thinker like Einstein had this question.
Let us think through the perception of ancient mathematics to find the answer to this question. Basically, ancient Indian mathematics, do you know how ancient it is? It is as old as the Vedas, i.e., around 3000 BC. In Yajurveda Chapter 18, Kandika-2 the verse contains the names of each of the places in the ‘Dashmana’ system or decimal system from place values of Units, tens, hundreds, thousands and so on till ten to the power of twenty-three. This indicates that, during Vedic time also the decimal system of counting was existed pre-dominantly in that society. In many ancient cultures there is a connection between the five elements of nature and the numbers that represent them. Pythagoras considered the fire, air, sky and earth numbers to be Gods because he noticed somewhere the connection between nature and numbers. Indian mathematics was developed to explain the laws of various sciences like astronomy, grammar, Ayurveda, and music. Observations of many phenomena in nature are found to be correlated with astronomical mathematics.
For example, Agasti or Canopus is the dominant star in the south direction sky. But from India it is seen only in certain months. Due to Earth’s rotation, this star disappears around May 15, 16, every year after which rain arrives in 21 to 22 days i.e., on June 7, farmers start their seed sowing preparation in the fields after “Agasti Lopa” or after ‘disappearance of Agasti or Canopus’ from the south sky. This means that nature and mathematics known to man have been used in India since ancient times. Seasons, festivals, and specific food habits and diet in India, which have a hidden mathematics in it, are a good example of a balanced and regulated way of life that the world is researching today. So, the point is that if we adopt a way of life that balances the mathematics known to man and the principles of nature, the entire human race will benefit from it. This principle needs to be emphasized more today because we are in such a phase of environmental degradation that we are only postponing the impending natural calamities! The caution of environmental disaster has been observed and experienced several times till now. The enough human maturity is not seen to accept these facts.
We also see examples where a mathematical equation or theory was developed and a law of creation was later found to support it. For example, A mathematical equation formulated by Albert Einstein showed that the ‘universe is expanding’ but at that time there were no powerful telescopes or instruments that could confirm this principle. Eventually, Edwin Hubble observed through his Mount Wilson telescope and proved this principle which Einstein had seen mathematically but it was unbelievable by accepted theories during that time. He was not ready to accept it as his own mathematical principle. Then he adjusted the equation by adding a ‘term’ to confirm the theory of the steady state universe which is accepted by all. But the day he experienced the evidence of the expanding universe through the telescope, he was shocked and realized the error in his equation, which he later admitted as the ‘biggest blunder of my life’.
Another such example is the existence of ‘black hole’! A black hole is a star so dense that not even sunlight can escape, the existence of super-dense stars was first predicted in the language of mathematics and then proved as observational evidence given by powerful telescopes. Many black holes are known to us today and scientists has even photographed them. Stephen Hawking’s research in this field is very important. He researched black holes through mathematical rules and today his mathematical theory is getting experimental confirmation.
Another such developed branch is ‘Quantum Physics’ in which the existence of microscopic particles, their laws and principles are developed from a mathematical language using the principles of probability. It seemed impossible to prove it by observation, but as the branch of ‘particle physics’ or ‘microphysics’ developed, the particle accelerator was made, ‘a giant device’ with the help of which the mathematical laws of all microscopic particles were completely proved, which were made using the principles of Physics and ‘Particle physics’. The remarkable agreement of mathematical theory and experimental verification was observed in quantum mechanics.
Today another branch has emerged which is ‘Big data’ or ‘Data science’. In order to make sense of the vast amount of information, it is necessary to look for ‘patterns’ that can be used to discover the truth about the subject which may be quite shocking and unexpected. This science is used to reveal truths in financial fraud detection, Criminology, Psychology. Statistics and mathematics involved in these areas is developing rapidly nowadays and in which computer science also plays a major role.
Big data is analyzed with the help of computers, using many methods and software. This is an attempt to gather information. Once this information starts showing its characteristics, the details start to reveal. That is when the real fun comes because many unknown truths come to light which can be logically accepted and mathematically predicted about the future. Which is called ‘decision science.’ For example, what will be the Earth’s climate in 50 years? It can be analyzed using the data available till date and predictions can be made based on mathematical information about possible temperature rise, melting ice caps, increasing carbon dioxide levels. From these predictions we can decide what decisions we should take today. It is from this that ‘Sustainable development goals’ (SDG) have been decided at the international level. Which must be adopted by all countries. Only then we can save our mother earth.
All these examples tell us that ‘mathematics never lies’ in fact the biggest challenge is to develop the maturity in humans to accept what the language of mathematics telling us. This means that humans developed a beautiful ornament called ‘Mathematics’ to understand the language of nature. Mathematics is ‘discovery as well as invention’! An equally abstract language created to understand the abstract principles of nature is a great jewel of mankind. If we preserve, conserve and research it, we can unravel many secrets of creation. This is a kind of ‘sadhana’ which was practiced by many mathematicians from our forefathers till today. If your approach of learning mathematics is perceived like this, your interest in it will surely increase!
Prajakti is the Director of Institute of advancement of Vedic Mathematics (IAVM) which is UK based NGO devoted for popularisation and research of Ancient and Vedic Mathematics). Prajakti is a Visiting faculty at Symbiosis School of Economics and Gokhale Institute of Politics and Economics (GIPE), teaching undergraduate students Statistics and Mathematics. She takes workshops and sessions on Lilavati, Vedic Mathematics and ancient mathematics for school level as well as for teachers and adults. Prajakti has design a Mathematics and Statistics curriculum for State board textbooks, colleges and educational private institutes.