An observatory of the mind
In the 9th century, while much of Europe was in the Dark Ages, the port city of Kollam was a bustling center of global trade and scientific thought. Here, or in the nearby Chera capital of Mahodayapuram, astronomers and mathematicians established an intellectual observatory. While physical observatories with large stone instruments existed elsewhere in India, the strength of the Kollam school was its mathematical precision, preserved not in stone but in palm-leaf manuscripts.
This intellectual tradition coincided with a major civic milestone: the founding of the Kollam Era, or Kollavarsham, a sidereal solar calendar that officially began in 825 CE. This calendar is still used in Kerala today. Its creation required precise astronomical observation and calculation, establishing a new standard for timekeeping in the region. The astronomer Govindaswami, active around 800-860 CE, was a significant figure during this period, known for his commentary on earlier astronomical texts and his advanced work on sine tables.
Computation with poetry
The astronomers of the Kerala school developed unique computational methods. One of the unique was the Vakya Karana system. This method used vakyas—short, mnemonic Sanskrit phrases—to encode complex numerical data representing the longitudes of the Moon and planets. These phrases were easier to memorize and transmit than long tables of numbers, a practical advantage in an era of manual transcription. The original Moon-related vakyas are attributed to the astronomer Vararuci in the 4th century CE.
This system allowed astronomers to calculate planetary positions with remarkable efficiency. While the stone instruments that would have accompanied such work are now lost, they likely included standard tools of ancient astronomy like the gnomon (Shanku Yantra), a vertical rod whose shadow helps determine time and solstices, and the armillary sphere (Gola Yantra). However, the legacy of the Kollam observatory is the mathematical output, which was the basis for centuries of discovery.
The work that began in the 9th century blossomed into the Kerala School of Astronomy and Mathematics, which flourished between the 14th and 16th centuries. Astronomers like Madhava of Sangamagrama (c. 1340-1425 CE) used the principles developed by earlier scholars to make significant discoveries. Madhava derived infinite series for trigonometric functions like sine, cosine, and arctangent, centuries before Isaac Newton and Gottfried Leibniz. Using these series, he calculated a value for pi correct to 11 decimal places. Later, Nilakantha Somayaji (c. 1444-1560 CE) developed a planetary model where Mercury, Venus, Mars, Jupiter, and Saturn orbited the Sun, which in turn orbited the Earth—a geo-heliocentric model that was more accurate than the purely geocentric Ptolemaic system used in Europe at the time.