Having studied maths at university, James taught at St James School, eventually becoming head of the maths department. Throughout this time he was also deeply interested in the methods of a system called Vedic Mathematics, which gives remarkably quick methods for solving problems. Since then he has started a global charity (non-profit) disseminating and developing this subject. What is this subject about? James is an alumnus of the School of Philosophy and Economic Science, which he attended for over 30 years.
James Glover, London
Nearly fifty years ago, when I was a teenager, my father showed me one of the Vedic Maths techniques. It was how to multiply two numbers like 97 x 98, using the sutra, ‘All from nine and the last from ten’. At the time I didn’t understand how it worked. However, as things turned out, that was the start of a life-long passion.
Vedic Mathematics origins
There is an old philosophical and spiritual tradition stemming from India called advaita, or non-dualism. Shankaracharya Bharati Krishna Tirtha, from this tradition, was renowned for exceptional intelligence and also a deep interest in mathematics. During his youthful years (1911 – 1919) he studied the Vedas with extreme depth and discovered, or intuited, a system of mathematical thinking comprising of just sixteen sutras. Sutras are extremely terse, pithy statements of concentrated knowledge. Bharati Krishna Tirtha left one illustrative volume that was published posthumously in 1965.
On the face of it, these sixteen rather cryptic and pithy aphorisms provide quick methods for solving arithmetic, algebraic or geometric problems. Of course, many of the illustrations and examples were mostly limited to school-level mathematics, prevalent at the time of writing. But this slightly facile view easily obfuscates a much deeper level of understanding.
Discovering Vedic maths
Leon Maclaren, who founded the School, deeply influenced me in many ways. He saw great potential in this book and set students in the School the task of discovering what the system was about. I was a member of various study groups engaged in practising and understanding the system.
Given that a spiritual leader of advaita wrote the Vedic Mathematics book, we were encouraged to study every word and practise every example. In my late teens, there was one sentence in the book that particularly caught my attention – a life-changing spark.
It said: “The sutras apply to and cover each and every part of each and every chapter of each and every branch of mathematics (including arithmetic, algebra, geometry: plane and solid, trigonometry: plane and spherical, conics: geometrical and analytical, astronomy, calculus: differential and integral, etc.). In fact, there is no part of mathematics, pure or applied, which is beyond their jurisdiction”.
This single sentence niggled away inside me. How could this possibly be true? On the face of it, this is a totally outrageous statement. The author had shown specimen applications of the sutras in various arithmetic and algebraic instances and then came out with a universal statement like this!
Testing Vedic Mathematics
My decision was to take this as a hypothesis and put it to the test with the groups in which I was working. So we looked into our mathematical workings and found that the key was to look at the mental movements when engaged in mathematical problems.
We employed two simple questions. Firstly, what sutra is operating in the present moment when solving a problem? Secondly, how do any of the sutras extend and develop our mathematical knowledge? To get to grips with these questions we had to appreciate mathematics as a human activity, albeit at the mental level.
Having spent many years testing this hypothesis, my current conclusion is that his statement is true. The sutras simply express how the human mind works when solving problems. Furthermore, the mind does not solve problems in a random way. It has specific channels or patterns of thought-process by which it solves problems again and again.
Think of music and the notes in the octave. With this limited number of notes, how many pieces of music can we compose? Of course, the answer is infinite. Similarly, the Vedic Mathematics sutras have an infinite range of uses. Each sutra has many applications.
At the same time, we know that any mathematical problem has several paths to a solution. It turns out that any single problem can be solved in different ways with different sutras. A simple problem such as finding the square of 45 can be achieved in many different ways; and each way has its own sutra or combination of sutras.
A major characteristic of Vedic maths is that there are special methods and general methods. It encourages us to follow the path of least action and not to constantly apply blanket methods. For example, suppose you wish to divide 73.21 by 5. One simple technique is to divide by 10, 7.321, and then double the result, 14.642, by the Proportionately sutra. The effect of this approach is to develop reasoning and strategic thinking.
This interconnectedness, as described above, leads to an appreciation of unity. Furthermore, many of the sutras themselves reflect the philosophy of unity, advaita.
Connecting with others
Just over five years ago, I felt there was a need for an organisation to act as a hub or point of contact for those interested in, or teaching, Vedic maths. This led to the establishment of the Institute for the Advancement of Vedic Mathematics (IAVM). We run conferences, courses, workshops, competitions, etc. It grows each year.
Our main activities have been in India, the Philippines and South Africa. The IAVM runs two annual international conferences each year, one online and one in-person, at which we present latest research, and provide workshops and activities. Our in-person conferences take place at different universities in India.
The IAVM has also been heavily engaged with teacher and student workshops in the Philippines (where there is a huge interest in Vedic maths) and South Africa, with its desperate need for training student teachers. In conjunction with this, we are developing courses for teacher training and engineering undergraduates at three universities.
Vedic Mathematics Olympiad
The latest venture is the International Olympiad which was due to start in August 2020. It’s a five-level competition testing Vedic maths ability, speed of thought and mathematical acumen. This will take place in 2021 in nearly 40 centres in various countries.
Vedic Mathematics offers a new paradigm, one which reflects the ancient teachings of advaita and also exposes the natural human thought processes. In respect of education, it offers fun and lively methods, together with a substratum of interconnectedness and development in strategic thinking – so valuable in modern-day job hunting.
Some people might say that during nearly 50 years of investigation, teaching and writing books, I have become a master of Vedic Maths. But I share the same sentiment as Isaac Newton when he said, “I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore… finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”
The nine numbers, together with the zero, and the sutras of Vedic Maths, are my friends. I meet them every day and am continuously inquisitive as to what they will show us next. The bottom line is that this system of Mathematics simply puts a smile across the face of anyone who meets it. That’s the real ticket!
See James on UTube for demonstrations: JGlover