To get a detailed insight into the shortcomings of western mathematics taught in educational institutions and to know why Bharatiya mathematics is the perfect replacement for it, GoaChronicle got in touch with Jonathan J. Crabtree who, having initially studied economics at the University of Melbourne, is an autodidact, studying the history of mathematics since 1983. Being an erudite scholar of mathematics history, Crabtree aims to see Bharatiya mathematics introduced into the Indian education system.
Today, elementary maths historian and www.podometic.in founder Jonathan J. Crabtree is a guest lecturer at schools, universities, and mathematics conferences. Having reviewed writings in Latin, Greek, Arabic, Sanskrit, and many other languages, his provocative presentations reveal how pedagogies arising from foundations of ancient Indian mathematics are often faster, simpler, more intuitive, and better connected to the laws of physics than many western pedagogies followed today.
Jonathan, having a stroll down his memory lane to explain the beginnings of his journey said, “It is a story that began in 1968. When I was in class II, I had an argument with my school teacher about the way she was explaining multiplication. I realized she was making a mistake. She was explaining a method of doing multiplications. She told us what was being followed for over 398 years in the west, but if used, the answers we get are wrong. She explained a*b equals ‘a’ added to itself ‘b’ times. That has been the definition of multiplication since 1570. When I was a boy, at the age of seven, I thought it was wrong; even though it had been used for hundreds of years. As a grownup, you can easily see that it is wrong. If I ask you, what is 1*1, you know the answer is 1. But you follow this definition, 1*1 has to be 1 added to itself 1 time which is 2. So, it is a very simple definitional error at the very start of the explanation of abstract mathematics in the west.”
He went on, “I was always confused by mathematics, so I went into the history of the subject. Then, I did all the research to find out how and why this wrong definition came about. The first research paper I studied was about Euclid’s definition of multiplication which was translated wrongly from Greek into English in the year 1570. And because it was the first translation from Greek into English, people began to use it, even though it was wrong. During the renaissance, everyone who studied mathematics had to study Euclid’s definitions. So when it came to English, everyone thought it must be true because it is Euclid’s theory. But the translation was wrong. I checked the translation in about 17 different languages throughout history to prove exactly how, why, and when did that mistake entered mathematics. There were other mistakes which I found too; basically, because the west didn’t approve of the mathematics of India because of issues related to the church.”
“So the church didn’t like the idea of zero or the ‘void’ because the void was the realm of the devil and using would tantamount to heresy. And Indians also used the concept of infinity but to the church, only God was infinite. So, if one spoke about infinity in mathematics that would also be an insult to Christianity. So the west, in particular Britain, colonized various parts of the world, they spread these infected ideas of mathematics all around the world. People just thought that the British had worked down mathematics correctly because they had followed it from the ancient Greeks. But the ancient Greeks didn’t have concepts of zero or one as numbers. And you need zero and one as numbers for the foundations of mathematics to be correct. Finally, I stumbled across Brahmagupta and he had documented all of his laws on addition, subtraction, multiplication, and division; positives, negatives, and zero”, Crabtree continued.
He further said, “He did that in the 7th century. Brahmagupta’s laws are consistent with the laws of physics. But the mathematical ideas of Great Britain and the British Empire don’t agree with the laws of physics. I discovered a law of Vedic mathematics in about 1983 but Vedic mathematics didn’t really give me the answers that I was looking for. It was about calculations but what I wanted to understand was the bits and pieces when put together, create the foundation of mathematics. If you have the correct and simple ideas of Brahmagupta, then so many areas of mathematics that are very confusing today can become very simple for children to understand. That’s how I began with my journey in 1968. I made a promise to fix mathematics in 1983. In 1983, I broke my back and I wasn’t sure whether I would walk again. So, I just made a deal with God that if he let me walk again, I would devote my life to fixing mathematics. My spine was very badly crushed, I should have been left a paraplegic, but I regained my health and obviously, I was able to walk, I had children later on. I had to fulfil my promise to God because I had a miracle when I needed it and so I had to give my miracle back, which I had promised in the intensive care ward of the Alfred Hospital on Friday, March the 18th, 1983.”
“I have done all this research because of a promise made in the hospital not because I loved mathematics. Rather, I hated mathematics. I had mathematics anxiety at school and once, I had even failed it. I even repeated a year of school. I struggled to understand it in school. I later realized that this was because many of the ideas that I was taught are wrong. If you really try to understand mathematics, it will confuse you because many of the ideas are wrong. The west didn’t have the correct understanding of zero, one, and negative numbers. Even today, the west completely messes up the way to explain mathematics at the primary school level. It sounds crazy to be true. For many years, I thought I was crazy, but I continued to research mathematical history in Sanskrit, Arabic, ancient Greek, Hebrew, French, Italian, Russian, and Mandarin, etc. And I kept on seeing the correct ideas of mathematics that the British were not teaching. Many cultures had developed very good mathematics, but the British didn’t care about that,” added the maths historian.
Crabtree explained, “As the British continued to colonize country after country, they squashed the native culture and wanted to prove British knowledge to be superior. Even countries like New England, which was the USA’s first name, had textbooks taught in institutions that were written and published in England. The British Empire had a fantastic export trade, publishing mathematics books and exporting them to their colonies. They would naturally want all their colonies to get their version of mathematics. Due to all these economic and cultural reasons, the correct mathematical laws simply never really emerged. Even from earlier than the Renaissance, there were problems in the transmission of mathematics through the Middle East. The writings of Brahmagupta and his ideas of basic arithmetic with zero as a placeholder went to people like Al Khwarizmi but the more abstract mathematics, the algebra of India in which all the laws of positives, negatives, and zero were given, was never understood by the Arabics.”
“The Arabs never wrote about negative quantities in their mathematics but the Indians always did. Unfortunately, the mathematics of Al Khwarizmi travelled to Europe via Fibonacci and when he introduced what was called the Arabic numerals, the original ideas of Brahmagupta did not migrate to Europe. Eventually, as mathematics got consolidated in Europe and spread throughout the world by the British Empire, real ideas were lost. I had sensed that something was missing in mathematics when I was just a child. I thought I was crazy but what you can call my intuition was right and things didn’t all fit together. Imagine you have got a 10, 000 piece jigsaw puzzle but the lid of the box is missing and you have got no idea what the picture is, that would be almost impossible to piece together. That’s how mathematics has been. Nobody has ever pieced the bits together to create a big and simple picture of how it works. That is what I have been focusing on doing. Through the writings of Aryabhata, Brahmagupta, and Bhaskara, I have kind of rebuilt the mathematics of India as it should have emerged in Europe but never did. On top of that, I have devised new teaching methods to make mathematics fun through cartoons, pictures, games, and songs, just like Shlokas. I have taken the spirit of the Hindu Rishis and Gurus and I am trying to imagine that they are speaking through me and guiding me in how to explain their simple ideas that they would have shared with their children”, said Jonathan.
He continued, “British mathematics has been confusing people for hundreds of years and the reason is that it is fundamentally broken. Over the years, I have had to be meticulous with my research in compiling all the writings. Who would believe me if I said the foundations of mathematics are wrong? I knew unless I kept detailed research, nobody would believe me. Even though I don’t have any formal mathematics qualifications, now, I travel and give lectures to mathematics professors. I talk at mathematics conferences, I give lectures at universities and I have all of the evidence and simple ideas about how it went wrong, who were the people who made the mistakes, what were the mistakes made in the past that led to this mess being created. Brahmagupta defined ZERO as the sum of two equal and opposite numbers. For instance, -2+2 gives us 0. So, Brahmagupta defined zero by addition. Newton’s third law of motion which states that every action has an equal and opposite reaction is consistent with Brahmagupta’s definition of zero. Zero is the sum of equal and opposite quantities. Unfortunately, the British never understood zero as being the mid-point between quantities that were equal but opposite.”
On being asked whether he wanted Bharatiya mathematics to be introduced only to India or to countries in the west too, Jonathan retorted, “I feel it belongs to India and it is your intellectual property. I want it to come home to India. It has been lost, I want to give it back to India. I wish that the Indian government responds to the letters I’ve been writing to them. I have been trying to contact Dr. Ramesh Pokhriyal Nishank every year. I want to help India, free of charge for the new Bharatiya mathematics curriculum. I want to help every child in India. Many people say that going to America and discussing this would help me gain the attention of the Indian government faster but I don’t want to do that. Otherwise, I have had been lecturing there but I have been lecturing in India.”
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