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Australian Historian (Re)Introduces Ancient Mathematics Teaching Method

India prepares to adopt a new mathematics curriculum for its primary grade students tracing back to its ancient roots

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Niloy Chattaraj
Niloy Chattaraj
BE (Double Gold Medalist). Postgraduate Diploma in Cosmology from CalTech. MA in Indian History. Hawking admitted his mistakes pointed out by my research paper.

AUSTRALIA. Melbourne. An Australian mathematics teacher is determined to correct the mathematics pedagogy around the globe. For 37 years, John Crabtree has been researching the mistakes in methods of teaching “zero” and “negative numbers.” He came to the conclusion that ancient teaching of Bramhagupta is more effective, and he has evidence to prove his point.

When he was 7 years old, he asked a question about negative numbers. The teacher taught him the concept of negative numbers as debt. His teacher told him that you have a debt of $7, you can call it -7. But on a number line -7 is less than -4. John’s tender mind could not grasp the negative number concept. He asked,” If negative numbers are like debt then how can debt of $7 can be less than $4?” It was not reconciling with John’s mind at all.

A near-fatal accident

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While studying economics at the University of Melbourne he met with an accident. A heavy lorry hit him from behind and broke his spinal cord. He was told that he probably wouldn’t recover and would never have a normal life. What was needed was a miracle. Crabtree told Transcontinental Times, “I promised to God – If I ever live a normal life, I am going to fix mathematics and will resurrect the old Hindu teaching.”

The rigorous search for errors

To understand the flaw, he had to search for many mathematical books. He studied Vedic math of the sixteenth century, Trachtenberg mathematics, Shakuntala Devi and many more. But no mathematics books could explain how mathematics fit together. So, he shifted his focus on ancient texts. For this, he had to learn Greek, Arabic, Hebrew, German, Italian, Dutch, Russian, Czech, Spanish, Mandarin. “I discovered the gold at the end of the rainbow six years before,” he said. “When I came to know Brahmaputra’s mathematics in Sanskrit, I began to analyze the work of Aryabhatta, Brahmagupta, and Bhaskara and tried to make sense of math so that children could completely and intuitively understand mathematics which teachers are unable to explain.”

How zero travelled Photo Credit : www.podometic.in

Confusion traced to mistranslation

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When Arabs took Hindu numerals and spread them to the European world, they made grave mistakes. Al-Khwarizmi was the mathematician who translated Brahmagupta’s book Brahma Sphuta Siddhanta (BSS) into the Persian Language. Brahmagupta was a mathematician and an astronomer, whereas Al-Khwarizmi was an accountant. Mathematics took a wrong turn because of these misinterpretations.

According to Crabtree, “Brahmagupta’s zero concept was based on the addition of two equal and opposite numbers. It makes sense in modern physics. It is similar to the addition of a negative electron and a positive positron (with the same mass as an electron) and results in zero. His concept of zero is consistent with the laws of physics.”

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In the 9th century Arabic translation, the eighteenth chapter of BSS seems to have been missed, which gave the rules of algebra of negative, positive and zero. So, Arabs were not at all concerned with negative numbers and zero. When this concept traveled to Europe, first by Fibonacci, the “zero” was only a place holder and nothing more. So, 107 is 17 without “0”. Zero is like a number subtracted from itself, but this conception was against Brahmagupta’s understanding of zero. He pointed out the mistake in “multiplication is repeated addition”. It works for positive numbers like 2 x 3 = 2 x (0+1+1+1) = 0+2+2+2 = 6. But what happens when we try to multiply 2 x (-3)=2x(0-1-1-1)=-2-2-2=-6. Repeated subtraction! Similarly, 23 = 8, but 20 = 1, why ? Now when this contradiction occurs we force children to remember the law – minus into plus is minus[(-) x (+) =-)] and anything raised to zero is 1. These absurdities often create a complete dislike of mathematics for children.

New teaching method

Crabtree has developed a method purely based on the 1400 year old mathematics teaching of Brahmagupta. He calls it podometic. He said, “This is the simplest way mathematics can be taught. We study 5-2 in standard 2 (second grade) and then 2-5 in standard 7 (seventh grade). We can make children understand negative numbers in standard 2 only.” The present ranking of Indian students mathematics skill is ranking second from last among 74 nations.

“What happens in India?” He asked, ”Why the country who had given basic and even [advance mathematics] to the world is presently struggling with mathematics teaching?” He answered,” Because of rejection of their own traditional teaching method and mugging up British teaching method”. He is ready to teach children by his podometic method. ”I want to teach Indian students free of cost. I don’t want money or fame, I have an obligation to teach”.

He has delivered lectures in various parts of the world, including India (www.podometic.in). He has sent letters to the Human Resource Ministry of India, the Prime Minister of India, and the head of the RSS. But the present pandemic has negated his efforts. It is hoped he will have an opportunity to see his teaching methods implemented as he just been diagnosed with skin cancer.

Letter to head of RSS Photo Credit : Twitter


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  1. A great article it feels good to hear about our ancient teaching methods. I hope he is able to keep up the good work and gets adequate support.

  2. What an article by Prof. Niloy Chattaraj. He has brought forward the Gupta dynasties teachings of Mathematics and the concept of Aryabhatta teachings, through John Cabtree, Australian Mathematician and how he desires to change Indian system based on itself than the English version. An article so well researched with examples. A classic among the articles. Written with a scientifically accurate analysis and with fact we ourselves are unaware even today. Great man, Mr. Niloy ji. , if he can put across such wonderful ideas which are nurtured abroad. 😃👏🙌

  3. What an article by Prof. Niloy Chattaraj. He has brought forward the Gupta dynasties teachings of Mathematics and the concept of Aryabhatta teachings, through John Cabtree, Australian Mathematician and how he desires to change Indian system based on itself than the English version. An article so well researched with examples. A classic among the articles. Written with a scientifically accurate analysis, and with facts, we ourselves are unaware even today. Great man. Mr. Niloy ji. , if he can put across such wonderful ideas which are nurtured abroad. 😃👏🙌

  4. India must return to its heritage of Bharatiya mathematics.
    These greeks Arabs Britishers borrowed our knowledge, philosophies & advertised as their own to the entire world.
    Lot of things ve been manipulated by these invaders.
    Khwarizmi couldn’t even translate our documents in a proper manner if he could have translated the bhartiya mathematics in a proper manner then this messed concept of negative number could have never been rose. People are still learning wrong things .
    India needs to introduce its Vedic knowledge to the entire world. So the things which have been manipulated can be corrected.
    Brahmagupta is known as the father of arithmetic but it’s never taught his concepts is never taught in schools and colleges.
    This invaders tried to erase the enriched knowledge And history of India. This has to change.
    People should come to know that how prosperous our ancestors were.

  5. दुनिया में कुछ लोग जंगल के गिदड़ (लोमड़ी सियार) 【अवसरवादी ] इत्यादि की तरह जीते है ये बड़े शिकारियो के पीछे पीछे चलते है बड़े शिकारीयो द्वारा शीकार हो जाने पर अपना हिस्सा चोरी( चालाकी) से हासील कर लेते है लेकिन मनुष्य इनसे भी आगे है ये उस शीकार को हमने किया और पेपर में छपवाते है शिकार के अपने तरीके दुनिया पर थोपते है श्रेष्ठ को बाहर नही आने देते क्योंकि इनको अपने गणित( नाम )चलाने होते है दुनियाँ में ऐसा बहुत कुछ श्रेष्ठ होगा अतीत में जिसे वर्तमान ने अपने ढंग (नाम)से चलन में लाया होगा धन्यवाद इस ऑस्ट्रेलियन नागरीक को ईश्वर इन्हें जीवन की सारी ऊंचाइयां छूने की बुद्धि प्रदान करे
    [ जिन खोजा तीन पाईंया] गुरूनानक

  6. I can see the ray of hope for the students like me who never liked mathematics. Hope such initiatives will lead to better understanding and imagination of numbers among the students.


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