he earliest elements pertaining to the history of Indian mathematics and astronomy are found in the Vedas. These sacred texts, from the second millennium BCE, document an already advanced level of theoretical knowledge in the service of religion. Part mathematics, part geometry, they use algorithms to describe, for example, how to design and build sacred pavings, or the relation between numbers and figures that gives (cosmic) meaning to earthly rituals. Included are astronomical tables and theoretical propositions comparable to those of the Pythagorean theorem. Later, one of the first great Indian mathematicians, Aryabhata (476 – 550), proposed a treatise on mathematics and astronomy composed of 66 theorems, including an explanation of how to extract square roots and cube roots, an approximation of pi, and sine tables which are the basis of trigonometry. Interestingly, Aryabhata was one of the first to propose that Earth spins on its axis – although he did believe that the Sun orbited Earth, and not the opposite.

India is unique in that mathematical concepts take on a profoundly spiritual sense and are frequently expressed in poetic terms: an illustration of the refinement and subtlety of this mathematical and astronomical thinking.

Maharajah and astronomer

This poetic, even metaphysical dimension can be felt immediately on entering the Jantar Mantar in Jaipur. This monumental and magnificent “machine for calculating” solar time, lunar time, the equinoxes, the motions of the planets, the movement of the constellations... is a collection of sixteen instruments in masonry and six in metal. Together they form a highly sophisticated and precise astronomical observatory: a Giorgio de Chirico painting come to life.

Located at the centre of the old city of Jaipur, it is the most elaborate and complex of the five observatories built by Maharajah Sawaii Jai Singh II between 1724 and 1730 in Jaipur, Delhi, Mathura, Varanasi (also called Benares) and Ujjain. All, except the one in Mathura, are still standing.

Jai Singh II

Born in 1688 at Amber, a descendant of the Kachwaha royal dynasty who ascended the throne at the age of twelve, Jai Singh II is best known as the founder of Jaipur, the Pink City. In the early 1700s he took Pandita Jagannatha Samrat as his guru and later chief astronomer. Jai Singh, while aware that the telescope had been in use in Europe for almost a century, was instructed in astronomical calculations based on observations with the naked eye and through the use of an astrolabe, which was common in India. He was also aware that these instruments could become worn and therefore lose in accuracy, and so decided to build his astronomical observatories in stone, for stability, and on a very large scale for more precise indications. He constructed them at five different locations, again for the greater accuracy afforded by the ability to compare readings from different positions (not unlike today’s astronomers cross-referencing data from multiple telescopes), at the same time cementing his political power thanks to these ambitious scientific structures.

Supreme Instrument

The most impressive of these instruments is, without question, the Samrat Yantra. Also called the “Supreme Instrument”, it is one of the world’s largest sundials. Its gnomon – a monumental central staircase – rises 20.7 metres high and casts a shadow onto two, carefully oriented, giant quadrants on either side. As the shadow moves across the quadrants, it indicates solar time in Jaipur on a scale with divisions as small as two seconds!

The Samrat Yantra indicates solar time to within two seconds.

Another instrument, the Rama Yantra, comprises two cylindrical structures, open at the top, each with a pillar in its centre. The pillars and the cylinders are of equal height. The Rama Yantra serves to calculate the position of a celestial body by visually aligning it with an imaginary line that passes through the top of the central pillar and continues to a point on the floor. At the exact point where floor and wall intersect, the celestial body is at an altitude of exactly 45 degrees. Depending where this imaginary line falls, the angular distance of the object from the celestial equator is shown with an accuracy of +/- 1 degree of arc. The floor of each structure is divided into sectors equal to six degrees with an open space between each one. When one structure has an open space, the other has a sector. Switching from one structure to the other therefore forms a 360 degree scale.

The two cylinders of the Jaipur Rama Yantra and the smaller Digamsa Yantra. The Digamsa Yantra measures the azimuth of a celestial body and comprises two concentric cylindrical walls around a central pillar. The walls are marked in angular divisions of one tenth of a degree.

Inside the Rama Yantra

Because of the close ties between astronomy and astrology in Indian culture, Jai Singh also devised and had built twelve Rasivalaya Yantra, each of which relates to one of the twelve zodiac constellations. They all have the same basic shape, similar to that of the Samrat Yantra, though with slight differences and a different orientation. Each instrument’s gnomon and quadrants are aligned with the pole and plane of the ecliptic when the first point in the constellation crosses the meridian. The angle of the gnomons varies from 3.5 degrees (almost flat) to 50.5 degrees (relatively steep), and their orientation from north varies by 26 degrees in each direction.

The Kapali Yantra depicts one half of the celestial sphere and indicates the position of celestial bodies from the shadow cast by a wire onto the map of the heavens engraved inside its bowl.

These are just some of the twenty-two remarkable instruments of the Jantar Mantar in Jaipur: a cosmic clock that extends across an area of more than 18,000 square metres.

This breathtaking site is spectacular proof of Mughal India’s refinement and profound understanding of astronomy and the cosmos.