World's first Zero in an Interesting and Mysterious Bakhshali Manuscript - Ancient Indian Mathematics

The Bakhshali Manuscript, is an ancient Indian mathematical manuscript, important, interesting, with a touch of mystery, and at the same time fascinating too. Bakhshali Manuscript has been recognized by Oxford University as the world’s first recorded utilization of the numerical symbol for zero, five hundred years earlier than suspected. It was previously thought that the earliest documented instance of using zero was a ninth-century inscription on a wall in a Gwalior temple, India.

 Bakhshali manuscript, was written on birch tree barkImage Source: wikimedia

Discovery: 

The manuscript was found in 1881 in the village of Bakhshali of undivided India, but now in Pakistan. The first research on the ancient manuscript was done by A. F. R. Hoernlé, 

(German-British Orientalist), after it was unearthed from a field. This ancient and important historical manuscript, was written on birch tree bark, therefore making it very fragile. But preserved as best as possible, at a constant temperature, and low humidity, in the Bodleian Library, of the University of Oxford. The manuscript is written in seventy leaves of bark, it is about different kinds of equations, like quadratic, linear, second degree, and indeterminate equations.

Image Post for Social Media Sharing on Bakhshali Manuscript

A mathematics professor at Oxford, Marcus du Sautoy, said, “We now know that it was as early as the third century that mathematicians in India planted the seed of the idea that would later become so fundamental to the modern world "

Contents:

Also has explanations about arithmetic, algebra, and geometry problems. Beautiful in its own right, as mathematics is. It is interesting how the mathematical problems were written. The author wrote the problems in verse, after solved, and explained, this was written in prose, by using this innovative way, it is easier to remember, and understand, all this important and useful.

Carbon Dating:

There is some degree of disagreement as to when these manuscripts were originally written. Carbon dating of different portions of the manuscripts suggested three different centuries, sometime between AD  224–383, 680–779,and AD 885 to 993, results from radiocarbon dating of other portions. A slight mystery is how pieces of this manuscript from different centuries were added together, perhaps, leaves from the manuscript were preserved through the centuries, and more were added.

   Gwalior Fort Temple, India.
 Image Source: wikimedia

Interesting facts about the Bakhshali Manuscript:

It seem that probably, its original author was, Chajaka's son, (a "king of calculators," for the use of Vasiṣṭha's son Hasika ) a Brahmin. In the manuscript a dot inside a circle, Sunya, or bindu, was a way to represent zero, at that time, and could be one of the oldest representation of zero. Even older than the one in the Gwalior Temple in M.P. The manuscript also includes quotes from the Hindu Scriptures, square roots, arithmetic, and geometrical progressions, and measurements. Hundreds of zeroes were discovered in the text,the idea of the symbol as  we now understand and use it originated as a small dot, commonly used as a 'placeholder' to describe magnitude instructions in the ancient scheme of Indian numbers – for reference 10s, 100s, and 1000s. It features prominently in the manuscript of Bakhshali, commonly recognized as the oldest Indian document of mathematics. The fact that the Bodleian Library kept the manuscript not available to other scholars has made a great difference in the study of this fascinating manuscript as made. It seems through the years even different times local languages had been added, from Sanskrit to local languages. Due to the fragility of the leaves, it is not easy for this important manuscript to be really examined, and studied. We hope this great manuscript will be preserved for many future generations. In a statement Oxford university said,

“Scientists from the University of Oxford’s Bodleian Libraries, have used carbon dating to trace the figure’s origins to the famous ancient Indian scroll,"

The Science Museum in London displays a folio from the Bakhshali manuscript as the 

centerpiece of the main exhibition, Illuminating India: 5000 Years of Science and Innovation By exploring its important contributions to topics as varied as space exploration,mathematics, communication and engineering, the exhibition celebrates India's high 

position in the history of science and technology.

Significance of 108, Why it is Considered as Sacred Number in Yoga and Hinduism.

In Sanatan Dharma the number 108 has a great importance. As Sanatana Dharma (Hinduism) is associated with ancient science, so one can see the number 108 has an interesting significance each in science and mathematics.The number 108 is taken into account sacred both by the Buddhism and Jainism. The number 108 can be derived as 1+0+8=9, 1-0-8=7, 18, 1x8=8, now these numbers (108, 9, 7, 8, 18) have fascinating roles both in science and spirituality. First of all we need to perceive that both science and spirituality (Sanatan Dharma) search for the ultimate truth, the answers of the questions we often forget to ask ourselves that Who we are..? What is the purpose of our life..?  
Science deals with material objects and their behaviors in various circumstances, where Hindu Spirituality always wants to decode the logic behind the universe. Here in this article we will see how the number 108 became a significant splendor for both science and Hinduism.

Significance of 108, Why it is Considered as Sacred Number in Yoga and Hinduism

Mathematically and Geometrically:

1. There are 108 Free Polyominoes of order 7.

2. A self number is an integer that cannot be written as the sum of any other integer n and the individual digits of n. This property is specific to the base used to represent the integers.108 is a self number, because no such combination can be found.

3. 108° degrees on inner angles of a pentagon.

4. 108 pattern in reduced Fibonacci numbers.
5. 366 days in sidereal year; 3x6x6 = 108.
6. 1 squared plus 2 squared plus 3 squared equals 108.

7.  108 is a Harshad number (1+0+8=9) / 108 is divisible by 9.

Science:

1. About 108 Earths fit across the Sun. About 108 Suns fit in between Earth and Sun. And , about 108 Moons fit between Earth and Moon. The number 360 is encoded in these distances when measured in miles.

2. The distance of Earth from the Sun is about 108 times the diameter of the Sun (actually closer to 107.51, as per definition of the AU, there might be Errors of measurement).

3. 108 is the Atomic Number of Hassium.

4. 108 degrees Fahrenheit is the internal temperature of Human body at which the body's important  organs start to fail for overheating.

Hinduism:

1. According to Ayurveda, there are 108 pressure points in the human body, where consciousness and flesh intersect to give life to the living being.

2. Lord Vishnu has 108 Divya Desams (temples of Sri Vishnu). 

3. 108 energy lines or nadis converging to form the heart chakra.

4. In Indian astrology we have 12 houses and 9 planets. 12 times 9 equals to 108.

5. In Tantra, it is estimated that every day we breathe 21,600 times out of which 10,800 are solar energy and 10, 800 are lunar energy. Multiplying 108 X 100 is 10,800.

6. In Indian astrology we have 12 houses and 9 planets. 12 times 9 equals to 108.

7. In Sanatana Dharma we have 27 Nakshtrams where Every Living thing is born in anyone of these Nakshtrams. Each nakshtrams have 4 Padams. 

So totally by calculation 27 x 4= 108.

8. The famous saint Bharata wrote “The Natya Shastra” which has 108 karanas (Movement of hand and feet).

9. The powerful Sri yantra intersects in 54 points each with a masculine and feminine quality, totalling to 108.

10. There are 18 Puranas and 108 Upanishads. 

11. The Mahabharata contains 18 Chapters, The Kurukshetra war lasts for 18 days. 12. There were total 18 armies in the battle.

13. There are 54 alphabets in sanskrit language, each has two forms one feminine and other masculine, Shakti and Shiva, now, 54x2=108.

14. 108 beads on prayer mala.
15. 108 repetitions of a mantra.

16. 108 dance forms in Indian traditions.

Jainism

Jainism:

1. Total number of beads in a rosary representing a total of 108 virtues of Arihant, Siddha, Aacharya, Upadhyay and Sadhu.

2. 1008 shubh (auspicious) marks on the divine body of a Tirthankar.

बुद्धं शरणं गच्छामि |

Buddhism:

1. Buddhists worship 108 small Buddhas for good luck. 

2. There is a tradition in Buddhist culture to ring a bell 108 times to celebrate a new year. 

3. There are said to be 108 virtues to cultivate and 108 impairments to avoid.

Thus the number 108 is fundamental to Indian spirituality.
The number 108 or the multiples of 9 is indestructible supply of good health, wealth, predetermination, love, success, satisfaction, and other worldliness. It is quite reasonable to think of it as a holy number of this universe.

Number Rules the Universe - Pythagoras.

11 Unknown Facts - Hindu-Arabic Number System Originated in Ancient India

The ten digits from 0 to 9 are known as the Indian-Arabic numerals or Hindu-Arabic number system. These numerals 0,1,2,3,4,5,6,7,8 and 9- are used in most of the countries of the world. In Vedic Era it was believed that Mathematics serves a connection between understanding material reality and perceiving the spiritual conception. Mathematics were often presented in a very different format by Vedic mathematicians. 

Number System In Hinduism

Al-Biruni and Kitab Tarikh Al-Hind

In 1017 Al-Biruni traveled to the Indian subcontinent and authored “Kitab Tarikh Al-Hind”

(History of India) after exploring the Hindu culture as well as Vedic science accomplished in India. Al-Biruni,had visited India on several occasions and made comments on the Indian number system. The number system was first developed in Ancient India, and then adopted by the Arabs in 9th century. It was initially known in the West as Arabic numerals, because Arabs introduced these numbers to Europe through Arabic texts in the 10th century. The Europeans therefore attributed the numbers to the Arabs, even through the Arabs themselves called them Indian Numerals. 

'Zero' Contribution

It was India that gave the world the concept of Zero. In AD 628, Indian mathematician Brahmagupta developed a symbol for zero, and developed mathematical operations using zero.

Bakhshali Manuscript

Bakhshali Manuscript

But in a recent studies it has been found that before AD 628 Indian used the 'Zero' for several mathematical operations. In 1881 a part of an ancient manuscript was found from a village Bakhshali, now in Pakistan, It is perhaps "the oldest extant manuscript in Indian mathematics. For some portions a carbon-date was proposed of AD 224–383. It contains the earliest known Indian use of a zero symbol. It is written in Sanskrit with significant influence of local dialects. The manuscript was unearthed from a field in 1881. The first research on the manuscript was done by A. F. R. Hoernle. The manuscript is famously known as Bakhshali Manuscript

Decimal System

Basic principles like counting 1, 2, 3, etc. to zero, were based on Brahmi Numerals or Sanskrit figures. In ancient times, mathematics was mainly used in an applied role. Thus, mathematical methods were used to solve problems for architecture and constructing Temples, in astronomy and astrology and in the construction of Vedic altars. 

Evolution of Brahmi numerals from the time of Ashoka.

From the Vedic Period

Period Hindu cosmology required the mastery of very large numbers such as the kalpa (the lifetime of the universe) said to be 4,320,000,000 years and the "orbit of the heaven" said to be 18,712,069,200,000,000 yojanas. Numbers were expressed using a "named place-value notation", using names for the powers of 10, like dasa, shatha, sahasra, ayuta, niyuta, prayuta, arbuda, nyarbuda, samudra, madhya, anta, parardha etc., the last of these being the name for a trillion (1012). For example, the number 26,432 was expressed as "2 ayuta, 6 sahasra, 4 shatha, 3 dasa, 2." 

Development In India

The form of numerals in Ashoka's inscriptions in the Brahmi script (middle of the third century BCE) involved separate signs for the numbers 1 to 9, 10 to 90, 100 and 1000. A multiple of 100 or 1000 was represented by a modification (or "enciphering") of the sign for the number using the sign for the multiplier number.

Brahmi numerals

Historians trace modern numerals in most languages to the Brahmi numerals, which were in use around the middle of the 3rd century BC. The Brahmi numerals have been found in inscriptions in caves and on coins in regions near Pune, Maharashtra and Uttar Pradesh in India. Those numerals were being used up to the 4th century with little variations. 

Gupta Era

During the Gupta era (4th century to 6th century), the Gupta numerals developed from the Brahmi numerals and were spread over large areas by the Gupta empire as they conquered territory. Beginning around 7th century, the Gupta numerals developed into the Nagari numerals.

Mathematician Brahmagupta

In 628 CE, astronomer-mathematician Brahmagupta wrote his text Brahma Sphuta Siddhanta which contained the first mathematical treatment of zero. He defined zero as the result of subtracting a number from itself, postulated negative numbers and discussed their properties under arithmetical operations. His word for zero was shunya (void), the same term previously used for the empty spot in 9-digit place-value system.

Adoption By Arab

Hindu Numerals adoption of Hindu Numerals by Arabs are described in Al-Khwarizmi's On the Calculation with Hindu Numerals (ca. 825), and Al-Kindi's four-volume work On the Use of the Indian Numerals(ca. 830). Today the name Hindu–Arabic numerals is usually used.

Al-Qifti (was an Egyptian Arab historian and biographer, ca. 1172–1248) said in his History of Learned Men: 

"... a personfrom India presented himself before the Caliph al-Mansur in the year [776 AD]who was well versed in the siddhanta method of calculation related to themovement of the heavenly bodies, and having ways of calculating equations basedon the half-chord [essentially the sine] calculated in half-degrees ... This isall contained in a work ... from which he claimed to have taken the half-chordcalculated for one minute. Al-Mansur ordered this book to be translated intoArabic, and a work to be written, based on the translation, to give the Arabs asolid base for calculating the movements of the planets ..."

According to the Nestorian scholar Severus Sebokht, the Hindu–Arabic numeral system was already moving West and was mentioned in Syria in 662 AD,before the rise of the Caliphate.

Adoption By Europe

Leonardo Fibonacci who was most famous and talented western (Italian) mathematician of the Middle Ages. His one of the great contribution is Fibonacci Series or Fibonacci Sequence, was actually taken from Ancient Indian mathematics. Leonardo Fibonacci studied mathematics in Algeria, promoted the Indian numeral system in Europe with his 1202 book Liber Abaci,

“When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else and I came to understand it.”

French mathematician Pierre Simon Laplace(1749–1827) wrote:

"It is India that gave us the ingenuous method of expressing all numbers by the means of ten symbols, each symbol receiving a value of position, as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit, but its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions, and we shall appreciate the grandeur of this achievement when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest minds produced by antiquity."