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National Year of Mathematics

 C K Raju |  2012-05-19 03:28:26.0  |  New Delhi

National Year of Mathematics

The PM has declared 2012 as the National Year of Mathematics. The terrible irony in this ought to be widely known.

First, we need some history. Europeans learnt basic arithmetic (algorithms for addition, multiplication, division, square roots, etc.) from India. Indian arithmetic was famous for its efficiency: it travelled to Baghdad, where al Khwarizmi wrote a book Hisab al Hind in the 9th c. Europeans called this technique Algorismus (after al Khwarizmi’s Latinised name). Florentine merchants understood that superior arithmetic gives a comparative advantage in commerce. Europeans eventually accepted the algorismus, rejecting as inferior the primitive abacus they earlier used.

Earlier European ignorance of  arithmetic is also reflected in their crude calendar. The year and months are based on the solar and lunar cycles, both of which involve fractions of days. But precise fractions cannot be readily written in Roman numerals. So, Europeans could not articulate the correct lengths of the month and the year. Instead, they pandered to the vanity of Roman emperors by adding extra days to July and August to honour Julius and Augustus Caesar. These days were pinched from February. The result is a thoroughly unscientific calendar with months of 28, 29, 30 and 31 days, unrelated to the cycle of the moon after which the month is named. Because Romans knew only a few simple fractions (like ¼) they wrongly stated the length of the (tropical) year as 365¼ days. This was hopeless even by contemporary standards: the 3rd c.
Surya Siddhanta
in India and the 5th c. Aryabhata both give far more precise fractions for the length of the (sidereal) year.

This inferior Roman calendar became the Christian religious calendar, used to fix the date of Easter, then the key Christian festival, which depends upon the full moon. Because of the wrong length of the year, the dates of Easter kept slipping on the Christian calendar. The church repeatedly tried to reform the calendar, but failed. The church then had full control over Alexandria, so these failures prove that the Alexandrian Greeks then lacked good knowledge of astronomy, notwithstanding the tall Western claims made on their behalf today. Those claims are based on the book called 
, which, like any scientific text, is accretive. Though it gives a better length of the (tropical) year,  even that inaccurate later-day figure  was never incorporated in the Roman calendar. The sixth-century calendar reforms by Dionysius Exiguus only retrospectively fixed the zero point of this calendar, which later somehow got related to the birth of Jesus due to the use of the terms AD and BC.

In contrast, the Indian calendar had critical practical applications. It was in this connection that calculus was invented in the 5th c. by Aryabhata, a low caste mathematician from Patna. Aryabhata used the calculus to calculate sine values accurate to five decimal places. This tradition was carried forward by the Aryabhata school in Kerala, which involved the highest caste Namboodri Brahmins, transcending north-south and caste differences. Over the next thousand years they calculated trigonometric values accurate to the 9th decimal place. Why did Indians need this phenomenal precision? What social need did it fulfil? The simple answer is this: the Indian economy depended on rain-fed agriculture. That required a good calendar to synchronise agricultural operations with  the rainy season. Constructing such a calendar, which could tell the rainy season, required accurate astronomical models and accurate trigonometric values. The other source of wealth in India was overseas trade, which too required  accurate trigonometric values for navigation.

In the 16th c., the European navigation problem was the key scientific challenge facing Europe. Its solution needed accurate trigonometric values. Hence, calculus texts of the Aryabhata school in Kerala were translated and imported into Europe by Jesuits based in Cochin. Europeans then found it difficult to fix even latitude at sea, because their calendar gave the wrong date of equinox. Matteo Ricci, who was in India, provided inputs to his teacher Christoph Clavius who authored the Gregorian calendar reform of 1582. Common Europeans were still uncomfortable with fractions, so that reform corrected the length of the year, not by stating it as an accurate fraction, but by an ad hoc system of leap years! It also cut out ten whole days which had piled up due to the error in the Christian calendar. Though Clavius published (in his name) trigonometric tables based on the Indian values, accurate to the 9th decimal place, he did not know even the elementary trigonometry required to determine the size of the earth! That was accurately known in India from before Aryabhata, and Caliph al Mamun had confirmed it by direct measurement in the 9th c. Columbus, however, underestimated the size of the earth bringing it down to 40% of the correct Indo-Arabic figure, to facilitate funding for his project of sailing west to go east. Consequently, Europeans then could not determine longitude at sea either - a problem they solved only in the late 18th c.
Westerners consistently wrote history to glorify themselves and belittle non-Christians, so they never acknowledged learning calculus from India. For centuries, the calculus was attributed to Newton and Leibniz. This false history was a source of political power: it was used by the Whig historian Macaulay to assert Western superiority and institute Western education in India, facilitating colonisation.

Naturally, the Western-educated learn the Gregorian calendar and the ADBC superstition. Most Western 'educated' Indians cannot even name the months on the Indian calendar. Since Indian festivals are fixed by the Indian calendar, but move on the Gregorian calendar, this invites cultural alienation — few know how to fix the date of Diwali, for example. The most tragic contemporary consequences are in agriculture, for the Gregorian calendar has no concept of a rainy season, like Sawan and Bhadon on the Indian calendar. Several times in the last decade, the monsoons were delayed on the Gregorian calendar. False anticipation of drought was  followed by floods in 2003, 2004 and 2009. But the rains arrived in time on the Indian calendar. So, was the monsoon delayed or is the calendar wrong? Anyway, the poorer farmers were ruined because they credulously believed the 'experts' (often seed-salesmen) and mistimed operations. 

It is, therefore, ironic that the 'National Year of Mathematics' is a year on the Western calendar. This rubs salt in the wounds of farmer suicides and helps to impoverish the Indian peasant, whether or not that is the intention. In the National Year of Mathematics, India ought to have celebrated the achievements of Indian mathematicians in calculus, which have only recently been highlighted by this author. But this is not even mentioned in our school texts which misspell Aryabhata’s name as Aryabhatta, changing his caste. Incidentally, Aryabhata’s technique of solving differential equations remains useful even for high-tech purposes, such as sending a man to the moon. The National Year of Mathematics should at least have been a year on the Indian calendar, and not the Gregorian year 2012.

We ape the West only because we uncritically believed false Western history which depicts us as inferior. That false history enabled the colonial capture of the mind, which craves Western approval. Despite the recent exposure of that false history, if we still choose the unscientific Western calendar over the practical Indian one, that suggests a dangerous agenda of recolonisation.

The author is Professor of mathematics at the University of Science, Malaysia. He authored the book Cultural Foundations of Mathematics.

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