ANCIENT BHARATA :: GENIUS IN MATHEMATICS

Our ancestors were wizards of Mathematics and Bharata  happens to be birthplace of this discipline of study. They taught Maths. to the world, applied mathematical models and tools in various other branches of knowledge. From Dirgatamas Mamateya  in BC 4500, an erudite scholar of King Bharata  who authored various Sloka-s of Rig Veda  to greatest mathematician Srinivasa Ramanujan (1887-1920), evolution of mathematics in Bharata  has been amazing. Ancient scholars like Baudhayana, Aryabhatta, Brahmagupta, Bhaskara  and Madhava  etc. were pioneers who contributed a lot to the evolution of modern mathematics, astronomy and other sciences. Western charlatans brazenly appropriated their original work during colonialism by floating dubious theories like Arayana  invasion etc. 

On April 5, 2016, International Conference on Zero was organised by UNESCO in Paris and a bust of Aryabhatta (476-550) was unveiled. Bharatiya  mathematician Aryabhatta  is the original discoverer of zero. First systematic application of number system for calculations and scientific research was done by Aryabhatta  alone. Another great Bharatiya  mathematician Brahmagupta  formulated rules for computations with zero which ultimately led to development of algebra. In his Brahmasphutasiddhanta  dated 628 AD, authored in Samskrita, he introduced negative numbers and created set of whole numbers. Famous science historian George Sarton declared him ‘one of the greatest scientists of his race and greatest of his times’. Four major Sulbasutra-s are those composed by Baudhayana, Manava, Apastamba  and Katyayana. After comparing their texts with contemporary Vedic  texts, the time zone of their composition falls between 800 BCE to 200 BCE. Those were all great Tapasvi-s and Sadhaka-s who used discern / perceive mesmerising knowledge in higher states of consciousness. These are verticals of major contribution of Hindu  mathematicians in ancient Bharata

 

Number System & Negative Numbers

Concept of Zero

Solutions of Quadratic Equations

Integral & Differential Calculus

Evidence of Greater Antiquity of Bharatiya  Mathematical Discoveries –

 

S.No / European Claims / Bharatiya  Claims 

1 – Pythagorean Triples, Pythagoras (540 BC) / Taittiriya  Triples, Taittiriya Samhita  (3500 BC)

2 – Pythagoras Theorem, Pythagoras (540 BC) / Baudhayana  Theorem, Baudhayana  (2000 BC)

3 – Heron’s Formula, Heron (10-70 AD) / Sulbasutra  Formula, Sulbasutra‘s (2000 -1700 BC)

4 – Backus-Naur Form Notation, Backus-Naur (1963) / Panini-Backus-Naur Form Notation, Panini  (700 BC)

5 – Pascal’s Triangle, Blaise Pascal (1623-1662) / PingalaVarahamihira  Triangle, Pingala  (700 BC), Varahamihira  (488 AD or 150 BC)

6 – Fibonacci Sequence of Numbers, Leonardo (Fibonacci) of Pisa (1202 AD) / PingalaVirahanka  Sequence of Numbers, Pingala  (700 BC), Virahanka  (6th century)

7 – George Cantor Theory (Concept of infinity and Theory of infinite Cardinal Numbers) George Cantor (1845-1918) / Jain-Cantor Theory, Jain Canonical Works (500-200 BC)

8 – Joan Napier Logarithms, Joan Napier (1550-1617) / Virasena  Logarithms, Virasena  (760-830 AD)

9 – Extended Euclidean Algorithm, Euclid (300 BC) / Aryabhatta Algorithm, Aryabhatta  (476 AD or 2742 BC)

10 – Wilson’s Theorem, John Wilson (1741-1793) / Bhaskara’s Theorem, Bhaskara I  (570-650 AD)

11 – Pell’s Equation, John Pell (1610-1685 AD) / Brahmagupta  Equation, Brahmagupta  (598-668 AD)

12 – George Cantor’s Theory of Sets, George Cantor (1845-1918) / Virasena-Cantor’s Theory of Sets, Virasena  (760-830 AD)

13 – Newton-Gauss Interpolation Formula, Newton (1643-1727) Gauss (1777-1855) / Govinda Swami  Interpolation Formula, Govinda Swami  (800-860 AD)

14 – Herigone’s Formula, Herigone (1580-1643 AD) / Mahavira’s Formula, Mahavira  (814-880 AD)

15 – Newton-Stirling Interpolation Formula, Newton (1643-1727) / Brahmagupta  Interpolation Formula, Brahmagupta  (598-668 AD)

16 – Modern Formula for solving Quadratic Equations / Sridhara’s Formula, Sridhara  (750 AD)

17 – Newton-Gauss Backward Interpolation Formula, Newton (1643-1727) Gauss (1777-1855) / Vateshwara  Backward Interpolation Formula, Vateshwara  (880 AD)

18 – Rolle’s Theorem, Michel Rolle (1691) / Bhaskaracarya  Theorem, Bhaskara II (1114-1185 AD)

19 – Fermat’s Factorization Method, Pierre de Fermat (1601-1665) / Narayana Pandit’s Factorization Method, Narayana Pandit  (1325-1400 AD)

20 – Newton’s Power Series, Newton (1643-1727) / Madhava  Series, Madhava  (1340-1425 AD)

21 – Taylor Series, Brook Taylor (1685-1731) / Madhava  Series, Madhava  (1340-1425 AD)

22 – Gregory Series / Madhava  Series, Madhava  (1340-1425 AD)

23 – Leibnitz Series, Leibnitz (1646-1716) / Madhava Series, Madhava  (1340-1425 AD)

24 – Euler Series, Euler (177-1783) / Madhava  Series, Madhava  (1340-1425 AD)

25 – Lhuilier Formula, Lhuilier (1782) / Parameshvara’s Formula, Parameshvara  (1360-1445 AD)

26 – Tychonic Planetary Model, Tycho Brahe (1546-1601) / Nilakantha’s Planetary Model, Nilakantha  (1444-1543 AD)

27 – Tycho Brahe, Inventor of the Technique of “Reduction to Ecliptic” (1546-1601) / Acyuta Pisārati, Inventor of the Technique of “Reduction to Ecliptic” (1540-1621 AD)

28 – Hipparchus, Father of Trigonometry, (190-120 BC) / Surya Siddhanta, “Father of Modern Trigonometry” (800 BC or 3000 BC)

29 – Diophantine Equations, Diophantus (3rd century) / Aryabhatta  Equations, Aryabhatta  (476 AD or 2742 BC)

30 – Kepler (1571-1630), Formulae for finding volumes of a frustum of cone and pyramid / Brahmagupta  (598-668 AD) 

…………………….and so many more. 

One really envies monumental and mind-boggling advances achieved by Hindu Rsi-s and Maharsi-s centuries ago. There are lot many others who cannot stomach those advances compelled by their sinister, vested interests. We must remain on our toes always and ever against such reprehensible acts perpetrated upon Hindu-s by hostile anti-Hindu  forces. 

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IS MANUSMRITI BIASED ??

Sudro Brahmanatameti Brahmanascaiti Sudratam  I

Ksatriyajjatamevam Tu Vidyadvaisyattathaiva Ca  II X / 14 II

Sudra  may become Brahamana  and BrahamanaSudra. Same is true with Ksatriya  and Vaisya  too.  

Four orders of Varna-s of BrahamanaKsatriyaVaisya  and Sudra  are meticulously defined on the basis of abundance of Guna-s alone. No other criterion exerts any role in that process. As a measure of natural corollary, if a Brahamana  loses his attributes essential for being a Brahamana, he may be re-categorised KsatriyaVaisya  or even Sudra  based on abundance of Guna  in a revised situation. Primacy of Guna-s and Karma-s is thus, re-established being sacrosanct.

 

Vipranam Vedavidusam Grhasthanam Yasasvinam  I

Susrusaiva Tu Sudrasya Dharmo Naisreyasah Parah  II X / 7 II  

Serving Brahmana-s being knower of Veda-s and accomplished householders is the natural Dharma of Sudra-s. 

Only reason for being Sudra  is aversion to learning. In absence of learning and erudition, only occupation left for a Sudra  is serving those who are engaged in service of society and humanity on higher planes of rendition. It is well established that Sudra-s enjoy a respectable domain in Maharsi Manu’s ordered society and they are mandated to serve only the accomplished ones.

 

Sucirutkrstasusrusumrduvaganahamkrtaha  I

Brahmanadyasrayo Nityamutkrstam Jatimasnute  II X / 8 II  

Sudra  serving accomplished ones of Brahamana  and other Varna-s, soft-spoken, devoid of ego, pure and consecrated internally, are attained to Dvija Varna.

Even conscientious pursuit of SudraDharma  too, opens doors to higher planes of existence as selfless pursuit of one’s SvaDharma  leads to self-consecration followed by emancipation from Maya  ultimately. Serving three Varna-s by Sudra-s is as sacrosanct as learning of Veda-s by Brahamana-s, warfare by Ksatriya-s and pursuing commerce by Vaisya-s. Absence of egoism ensures, ripples of divinity emanating from the Absolute Infinite are duly received and assimilated.

 

Astapadyama Tu Sudrasya Steye Bhavati Kilvisama  I

Sodasaiva Tu Vaisyasya Dvatrinsatksatriyasya Ca  II VIII / 204 II

Brahamanasya Catuhasastiha Purnama Vaapi Satama Bhavet  I

Dviguna Va Catuhasastistaddosagunaviddhi Saha  II VIII / 205 II

Even as a lesser accomplished Sudra  be awarded punitive fines eight times, Vaisya  sixteen times, Ksatriya  thirty-two times and a Brahmana  sixty-four or hundred or one hundred twenty-eight times of the amount of wealth purloined.

Higher the status on social ladder of advancement, greater is the retribution for an offence of say, theft or corruption as mandated by Maharsi Manu. As socially advanced ones are regarded and emulated as font of inspiration, it is all the more imperative that their personal conduct is beyond reproach. In a bid to assure that, while Sudra  is ordained to be penalised by eight times,Vaisya  sixteen times, Ksatriya  thirty-two times and a Brahmana  sixty-four or more in consonance with the circumstances, of the amount of wealth purloined. Pillars of society must deport themselves beyond controversy.

 

If these are the words enshrined in the true and correct version of Manusmriti, who can claim and on what basis can be claimed that Manusmriti  is anti-Sudra / pro-Savarna ? Historic work of Manusmriti  is the saga of Varna  only, not Jati-s or castes as have been alleged by so many hitherto. Even when the term Jati  is invoked in Manusmriti, what Maharsi Manu  referred to was Varna  alone and certainly not Jati  as the term is understood today. Varna  order was based on very rational considerations with no ambiguity whatsoever. Not only Varna  order of Manusmriti  is the greatest civil code ever known to humanity, it is operational in contemporary society albeit with different contours altogether. While the Varna  order successfully functioned for hundreds of years, gradually it degenerated into Jativada  owing to several compelling reasons and factors.

Now the question arises, how to distinguish Varna  order from present day Jativada.  

When a BrahmanaKsatriya  or Vaisya  ostracizes a Sudra  only because he / she is a Sudra, it is an ugly manifest of Jativada  replacing Varna  order in entirety.  

If member of a Varna  offers a favour / denies a favour on the grounds of Varna  alone, irrespective of merits / demerits, it is a blatant display of Jativada. That way, pursuit of reservations is yet another form of Jativada  in contemporary Bharata.  

Sri Rama  hugged Nisada Raja  because He was not casteist at all !! He gladly accepted wild fruits from a tribal devotee Sabari, that too already defiled by tasting that by herself, because Sri Rama  was not a casteist. Had He been a Jativadi  i.e. casteist, He would not have even entered her humble mud-straw hut leave alone accepting those defiled fruits. Sri Rama  was an ardent Manuvadi  / Varnavadi  and that is the sole reason why he did not hesitate while embracing Nisadaraja  or sharing a morsel of food from Sabari. Scriptures are replete with such instances affirming and re-affirming, Jativada  is not the forte of Manusmriti  and it did not exist therein at all. Indeed, Jati  has several aspects of interpretation viz. StriJati / HinduJati / AryaJati  etc. and these have absolutely no tinge of discrimination at all. Gautama Buddha, born a Rajputa, regarded himself a Brahmana  being enlightened and a man commanding prestige. He never rejected Manusmriti  and most of his disciples were and contemporary Buddhista  thinkers Brahmana-s. Buddhista  tradition has already declared next Buddha  of future, Maitreya  to be a Brahmana. Moreover, Sakya Muni  was very much a Vedic Hindu  and Gautama Buddha, an incarnate of Visnu. Gautama Buddha  accepted the Upanisadic  view, “Not by birth is one a Brahmana, not by birth is one an outcaste; by deeds is one a Brahmana, by deeds is one an outcaste.”   

 British occupiers of Bharata  appointed a few pseudo-scholars of Samskrita  to defile and contaminate pristine and pure Manusmriti  with the sole motif of Divide, Rule and Destroy Hindu  society. It goes to the immense credit of Arya Samaja  founded by Swami Dayananda Saraswati  which identified all additives and contaminants, sifted that out altogether to leave behind a Manusmriti, as sacrosanct as ever.  

Then how and why did Varna  order degenerate into Jativada  at all in recent centuries??

In the year 1871, British occupiers who had forcibly grabbed power to govern Bharata, enacted a despotic, derogatory and discriminatory law, The Criminal Tribes Act to brand hundreds of occupational groups and communities, steeped in grinding poverty, as ‘Born Criminals’. The inhuman Act was first notified and enforced in northern provinces, followed by being extended to Bengal and other provinces. The Act notified 160 Hindu  occupational communities as Castes, now known as ‘Dalita-s’ with criminality by inheritance on the ground that they were organized communities passing on acts of criminality viz. thievery, burglary, house-breaking, robbery, dacoity and counterfeiting of coins from one generation to another !! Total headcount of such branded tribes at that time stood at approximately six crores i.e. 60 millions constituting almost 30 percent of the Hindu  population. Quite deviously, they did not include any Muslim group in this Roll of Dishonour. According to Census Report 1871, population of Bharata  stood at 20,34,15,000 with Hindu-s constituting roughly 17 crores or so. Since all members of the so-called ‘Criminal Tribes’ were Hindu-s, British Occupiers reduced 30 percent of the Hindu  population to the status of criminals by inheritance who were in reality, manual workers serving the entire society. And majority of them did not even know about the malevolent havoc wrought by those British occupiers !! There is no other instance available in annals of world history wherein such a large body of human beings were codified and branded criminals before. Before enactment of the Act, anything evenly remotely resembling Scheduled Caste / Scheduled Tribe etc. did not exist at all. 

In the Criminal Tribes Bill introduced in 1871 by the British Jurist, JF Stephen (incidentally, he also authored The Indian Evidence Act), considerable emphasis was placed on the Theory of Hereditary Caste System which defined their background, upbringing and professions. The weird doctrine advanced by Stephen intended to deprive hapless poors of basic human rights and cripple their socio-economic development by restricting their mobility, “……. people from time immemorial have been pursuing the caste system defined job-positions, weaving, carpentry and such were hereditary jobs. So there must have been hereditary criminals also who pursued their forefathers’ profession.” The absurd law was thus, based on an irrational Christian assumption and not guided by any empirical research on ground at all. On another occasion he commented, “When we speak of professional criminals, we …… (mean) a tribe whose ancestors were criminals from time immemorial, who are themselves destined by the usage of caste to commit crime and whose descendants will be offenders against the law, until the whole tribe is exterminated or accounts for in the manner of thugs”. Ostensibly, these communities were forced into crime through a legal instrument of ex-communication and social boycott. It was later, intensified by Mughal occupiers too.  

The inhuman discrimination continued for 76 long years i.e., for almost three generations. It was undone post-1947 by rescinding The Criminal Tribes Act. Throughout history of Hinduism, those occupational groups by now known as tribes and castes, were never ever condemned or branded as criminals by inheritance or otherwise. The grave human rights violation was enacted by British despots alone and it was confined to that only. While British occupiers degraded them as ‘Dalita-s’, it was so-called ‘Savarna-s’ who agitated for abolition of The Criminal Tribes Act as well as enactment of The Untouchability Offences Act 1955 and not really by Christians or Muslims. Subsequently, there have been several social reformers who relentlessly campaigned against the evil of social discrimination through untouchability. Swami Dayananda SaraswatiLokmanya TilakaVira Savarkara, MK Gandhi, Guru-s Ravidasa / Nanaka / Govinda Singh / Ramanuja  then, Vira Brahmendra Swamy  in AP, Mysuru  Minister Basesvara, Minister Brahmananda Naidu  in AP, GK Ranade, Mahatma Phule  etc. have been pioneers of social equity and justice in subsequent years.  

Ancient Bharata  had several highly accomplished Souls who were torch-bearers of Hindu  faith, held in a very high esteem. Maharisi Valmiki, author of Ramayana, was a fisherman and a highway robber who attained the status of ‘Maharsi’ by excelling in scriptures. Maharsi Veda Vyasa, author of Mahabharata  was son of a fisher-woman. Vidura, Chief Minister of Hastinapura  was son of a maid and an ardent devotee of Sri Krisna. Another sage from ostracised groups who rose to prominence was Maharsi MatangaGuru  of Sabari, a Bhila  woman whose berries were fondly relished by Sri Rama. It is believed that famous Hindu  Monarch Candragupta Maurya  rose from Muria  tribe who were traditionally ‘Mor Pankha’ i.e. peacock-feather collectors. Acarya Canakya, a Brahmana  mentored him in raising Maurya  dynasty when Hindu-s were threatened by Huns and Greeks. Let us celebrate facts that Sant RavidasaGuru  of Mira Bai  belonged to the occupational community of cobblers and Sant Namdeva  belonged to the community of tailors. They were all held in greatest esteem by Brahmana-s, Ksatriya-s and Vaisya-s across the country. Large section of storm-troopers of Chhatrapati Sivaji  included Kunbi-s and Mawali-s, members of castes declared as “criminal tribes” by British Occupiers of the country. Similarly, widely revered was Sant Tuka Rama, a Kunbi. There are several Gotra-s common across Brahmana-s, Ksatriya-s, Vaisya-s and so called Dalita-s implying they all hailed from same lineage, subsequently enslaved in diabolical casteism perpetrated from external sources.

Frankly, the divide between Hindu-s on the basis of high and low caste was accentuated by Bharata’s erstwhile colonial rulers, first by Muslims, then by British occupiers. Both occupiers pursued the policy of divide, rule and destroy. To avenge tyranny of Muslim invaders in Gujarat 1299 who had ransacked Somnatha Mandira  and plundered Anhilwara, a posse of 40,000 Barwari  soldiers reached Delhi, raided main Masjid at Siri and restored traditional Puja  after installing Murti-s of Hindu  deities. They all reverted to Hinduism  thus, for a brief interregnum, Delhi was re-conquered from Muslim occupiers by warriors of Barwari  community, branded by British occupiers earlier. So said Friedrich Nietzsche “Close the Bible and open the Manu Smriti. It has an affirmation of life, a triumphing agreeable sensation in life and that to draw up a law book such as Manu means to permit oneself to get the upper hand, to become perfection, to be ambitious of the highest art of living.” Manusmriti  is greatly honored in Myanmar, Thailand, Cambodia, Vietnam, Philippines and Indonesia as an authentic document that Kings were obliged to uphold. Filipinos believe, Maharsi Manu  and 6th Century Chinese philosopher Lotse contributed immensely to the formulation of their country’s code of conduct. In recognition of the sterling contribution, statues of both are installed at the entrance of their country’s Parliament.  

It was Swami Vivekananda  who advised deprived communities in Keralam  to discontinue going after discriminating Savarna-s, identify one among themselves to emulate and be more self-contained. Dr. Palpu, a Medical Officer of Bangalore Municipality located such a person in Sri Narayana Guru  of Ezhva  community who rose to become a highly adored figure. The Swami  even went to the extent of appealing to the deprived class to refuse to accept a Brahmana  who declines to impart free education to them. He strongly believed that even men of renunciation must hold the cause of downtrodden close their hearts.  

Today politicians are the most class and caste obsessed community in the country. They continue stoking fires to ensure the cauldron of society goes on boiling with casteism to harvest vote banks. The day these vote-seekers eschew casteist politics, the social menace shall die a natural death. Sooner it is accomplished, the better as it has already been procrastinated by six decades. 

 

Published @ http://patriotsforum.org/correct-interpretation-of-manu-smiriti-ramakant-tiwari/

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