British Maths was built for 1, 2, 3... based on Ancient Greek philosophy and looking to the ground 300 BCE. India's simpler Maths was built for ...-3 -2 -1 0 +1 +2 +3... based on science and looking to the stars 628 CE.
“And is India’s HRD Minister a British Sepoy or a supporter of Bhāratīya Maths?”
India’s children are taught 5 – 2 in Class 1.
Then, in the British system, they wait 5 years to be taught 2 – 5.
Yet maths lessons taught today remain badly broken! Read on…
1 Brahmagupta defined zero as a number and wrote simple laws of maths in the 7th century. 2 Yet his definition of zero and laws of (+ – × ÷) on positive and negative numbers were not understood in the Arabic world! 3 Maths is confusing today because the British got its knowledge of India’s maths via the Arabic world! 4 After the British knew of Bharat’s superior maths they kept it quiet!
By teaching broken British maths, India ranked 2nd last in maths out of 74 countries. So you might think fixing maths education would be a high priority. If so, you’d be wrong.
Ramanujan was embraced by the British. Yet after months attempting to contact Dr Ramesh Pokhriyal ‘Nishank’, Minister for Human Resource Development, it appears his staff are unwilling to let India embrace the superior maths of Āryabhaṭa, Bhāskara and Brahmagupta. If Nishank supports Bhāratīya Ganita (Indian Maths) I invite him to reply.
Imagine you’re in Class 1 and it’s time to play the Happy Harappan Brick & Hole Game! In this story, you have a square-sided bucket and spade along with 2 cube-shaped bricks you made the day before.
Yet, today’s challenge is to sell 5 bricks! Starting with two bricks, five bricks need to be taken away! (This is a real-world story for 2 – 5.)
You don’t have enough bricks, so you dig 3 holes and make 3 more bricks. Now there are 5 bricks and 3 holes. 5 bricks get taken away and 3 holes remain!
Pretty soon, perhaps by Grade 2, some children will be extending their imagination from pictures to words and then symbols like 2B – 5B = 3H before they arrive at ⁺2 – ⁺5 = ⁻3.
The Harappan or Indus Civilisation flourished around 5000 years ago. It was famous for its precise math-based brickmaking. In 1947 it became part of Pakistan with the exit of the colonial British Raj rulers and the formation of ‘modern’ India.
From fixing the arithmetic of positive and negative numbers, we can also explore new and improved geometry. After almost 2500 years trying, the West finally concluded it was impossible to ‘square a circle’ with western tools of compass and straight edge.
OK, so what if we use rope, as they did in Bharat 800 BCE? Then squaring the circle is simple and geometry lessons become more powerful than ever before! The cartoon below shows how. (Click CC for the lyrics of the song.)
For teachers interested in a geometric proof of the maths above just, CLICK THIS LINK. for a proof to print out using similar triangles, or CLICK THIS LINK for an interactive proof following the Baudhāyana Theorem. It’s likely you won’t have seen such proofs because they involve rope.
In Bharat 800 BCE when the Śulba Sūtras (rules of rope) were written, ropes were used for altar construction. Is there a reason why Dr Ramesh Pokhriyal ‘Nishank’, refuses to acknowledge India’s own history of science? The team at NCERT he manages repeatedly promotes the false history that the Greek Pythagoras was the first to state the area rule a² + b² = c². This theorem was mentioned around 200 years earlier in the Baudhāyana Śulba-Sūtras! The modern diagram below lets you ‘see’ a proof.
Compare the above proof with the original proof Euclid gave.
British maths education has been built upon arithmoi or Ancient Greek pure number theory when it should have been built on the arithmos or applied applications of Ancient India. Ancient Greek arithmetic was based on theoretical logic where geometry was not allowed to have numbers by people like Aristotle and numbers were not allowed to have units by people like Nicomachus!
So, the maths education ideas the British Empire spread throughout its settlements and colonies were based on ideas that were almost 1000 years out-of-date! You update your computer’s operating system every few years. You might also update your phone every few years. What about your maths?
Today India’s children are taught the obsolete idea that negative four is greater than negative seven, which is and has always been absolute nonsense! Teachers often say negatives are like debts, yet a debt of $7 is GREATER THAN a debt of $4.
ARGUMENT 1 Larger numbers squared exceed smaller numbers squared.
⁺7 × ⁺7 = ⁺49 and ⁺4 × ⁺4 = ⁺16. As 49 > 16 we MUST accept ⁺7 > ⁺4.
⁻7 × ⁻7 = ⁺49 and ⁻4 × ⁻4 = ⁺16. As 49 > 16 we MUST accept ⁻7 > ⁻4.
ARGUMENT 2 Equality is preserved across sign.
⁻4/⁻7 = ⁺4/⁺7 as both ratios of top/bottom are the same.
4 negatives are less than 7 negatives just as 4 positives are less than 7 positives.
ARGUMENT 3 The East got it correct!
In both ancient Chinese and Indian maths, a larger number subtracted from a smaller number of the same sign changes the sign of the answer.
⁺4 – ⁺7 = ⁻3 therefore, ⁺7 > ⁺4
⁻4 – ⁻7 = ⁺3 therefore, ⁻7 > ⁻4
ARGUMENT 4 It’s how physics works!
7 positrons are greater than 4 positrons.
7 electrons are greater than 4 electrons.
7 (negative) electrons are greater than 4 (positive) positrons because after they meet 3 (negative) electrons remain, so ⁻7 > ⁺4.
Dishonest complexity is out and true simplexity is in! Symmetry unlocks secrets of physics more than any other principle and the same applies with Bharat’s original symmetric mathematics that today describes the physical laws of our universe.
Similarly, it’s impossible to have a number of actions that is ‘less than zero’. As you will discover at my new podometic maths website Ancient Indian Maths foundations are consistent with modern laws of physics from Class 1.
As a historian with decades of learning and research, it’s OBVIOUS to me why the world dislikes British primary level maths education. MANY TEACHING IDEAS ARE WRONG!!! My research (download PDF here) reveals the West NEVER updated its thinking from the 7th Century about the true meaning of India’s zero and negative numbers! That’s truly bizarre!
Importantly, so bridges didn’t fall down, many laws and rules were invented to FORCE answers to have the correct answer. Let that sink in a moment. Many laws and rules of maths we were told to commit to memory at school were actually workarounds and bug fixes needed to fix broken western maths foundations!
As Europe reverted to ancient Greek mathematics during the Renaissance, it failed to realise that the 300 BCE ‘Euclidean’ foundations that underpinned its definition of ‘number’ and ‘multiplication’ for example, should have been updated (as per the scientific method) around 700 CE after the writings of Brahmagupta, who gave mathematical rules of zero, negative and positive.
Around 300 BCE, Euclid (whom Prof.C. K. Raju argues may have been a black woman) had defined number as a multitude of units. That meant 1 was not considered a number because 1 was not a multitude. The Medieval Arabic world, as evident in the influential writings of al-Khwārizmī, al-Uqlīdisī and others, had also been led to believe that 1 was not a number.
Brahmagupta’s definition of zero as the number that is the sum of equal and opposite quantities, (consistent with modern laws of physics), sadly amounted to nothing.
From the early 1800s the British Raj should have known it was forcing a corrupted system of maths onto Bharat via the Macaulay education system. The works of people like Brahmagupta and Bhāskarā II had been translated into English. Ironically, in 1813, the algebra written by Bhāskarā II was translated and published by a member of the East India Company!
Soon after in 1817, Brahmagupta’s mathematical chapters also made an appearance.
You oppress people most effectively by denying them their own culture.
Indian Professor Dr. C. K. Raju has undertaken considerable (confronting) research into the history of mathematics his book ‘The Cultural Foundations of Mathematics’. Let me quote…
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“Decolonization requires contesting the false history of science used to set up colonial education essential to colonization — the same false history that was used to morally justify racism, by asserting the noncreativity of Blacks.” (Raju, C. K. (2017). Black Thoughts Matter.)
… for the colonized, “expertise” and the validity of all knowledge must be decided by reference to “reputed” Western (or Western-approved) experts. This epistemic dependence has political value, but for the master not the slave.
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Macaulay used a false history that science was a Western creation to justify imposing colonial education needed to win the consent of the ruled.
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This was the classic colonial line, to use colonial education to produce White minds in Black or Brown skins, enslaved minds who would hence help run colonial empires.
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To send a spacecraft to Mars, NASA still uses (a minor refinement of) much the same numerical method developed by Aryabhata, and today wrongly named as “Euler’s” method of numerically solving ordinary differential equations.
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Hence the conclusion to undo both colonialism and racism one must start by teaching a more honest history of science.
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The British Empire displaced indigenous knowledge bases and the world remains infected with mathematical nonsense today that without its bug fixes and workarounds (known as laws) has no connection with physical reality!
In accordance with Brahmagupta’s definition of zero as the sum of equal and opposite quantities, Newton’s 3rd Law states every action has an equal and opposite reaction.
So, to the reader of this page, if you’d like to learn more about the superiority of India’s ancient original zero-based mathematics, all the knowledge I have is my gift to India.
Lastly Dr Ramesh Pokhriyal ‘Nishank’ I provide examples of letters and emails to you and your team that might have been mislaid, as I’ve not yet received the courtesy of a reply.
Make Your Life Count!
Jonathan J. Crabtree
Education Researcher, Public Speaker + Historian
Founder of www.Podometic.in (Bharatiya) Maths
P.S. The story of how zero and the great ideas of maths teachers like Brahmagupta went astray are noted in the 36-minute slideshow below (followed by a Q&A).
P.P.S. Show some support! Sign the petition @ www.change.org/Brahmagupta
DISCLAIMER: The author is solely responsible for the views expressed in this article. The author carries the responsibility for citing and/or licensing of images utilized within the text.
