* Vedic Mathematics, Ancient Indian Mathematics, & Some Of India's Greatest Mathematicians
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| Sri Bharati Krishna Tirthaji Maharaj : Shankaracharya of Govardhan Math Puri |
Vedic Mathematics is the name given to an ancient Indian system of calculation, which was rediscovered from the Immortal Hindu Scriptures Vedas between 1911 and 1918, by His Holiness Sri Bharati Krishna Tirthaji Maharaj (1884-1960), Shankaracharya (Pontiff) of Govardhan Math, Puri. According to Tirthaji, the whole of Vedic Mathematics is based on sixteen Sutras, or Word-Formulae. For example, "Vertically and Crosswise" is one of these Sutras. These formulae are intended to describe the way the mind naturally works, and are therefore supposed to be a great help in directing the student to the appropriate method of solution. The Western Scholars say, none of these Sutras has ever been found in Vedic literature, nor are its methods consistent with known Mathematical Knowledge from the Vedic Era.
Perhaps the most striking feature of Tirthaji's system is its coherence. The whole system is interrelated and unified. The general multiplication method, for example, is easily reversed to allow one-line divisions, and the simple squaring method can be reversed to give one-line square roots. And, these are all easily understood. This unifying quality is very satisfying, it makes arithmetic easy and enjoyable, and it encourages innovation.
Difficult mathematical problems and huge sums can often be solved immediately by Tirthaji's methods. These striking and beautiful methods are a part of a system of mathematics, which Tirthaji claims to be far more methodical than the modern system.
Vedic Mathematics is said to manifest the coherent and unified structure of arithmetic, and its methods are complementary, direct and easy.
The simplicity of Tirthaji system means that calculations can be carried out mentally, though the methods can also be written down. There are many advantages in using a flexible, mental system. Students can invent their own methods; they are not limited to one method. This leads to more creative, interested and intelligent students.
Interest in the Tirthaji's system is growing in education, where mathematics teachers are looking for something better, and finding the Vedic system to be the answer. Research is being carried out in many areas, including the effects learning the Tirthaji system has on children; developing new, powerful but easy applications of these Sutras in arithmetic and algebra.
The real beauty and effectiveness of the Tirthaji's system cannot be fully appreciated without practising the system. One can then see why its enthusiasts claim that it is the most refined and efficient calculating system known.
Vedic Mathematics refers to a technique of calculation based on a set of 16 Sutras, or aphorisms, as algorithms and their Upa-Sutras or corollaries derived from these Sutras. Its enthusiasts advance the claim that any mathematical problem can be solved mentally with these Sutras.
Swami Bharati Krishna Tirthajee Maharaj of Govardhan Mutt, Puri wrote a book on Vedic Mathematics, and first published it in 1965. It contains a list of ancient Indian Mental Calculation Techniques claimed to be based on the sacred Hindu Scriptures Vedasof India. Its characterization as Vedic Mathematics has been criticized by many academicians. Scholars emphatically argue that such mathematical Sutras are non-existent in the Vedas, and are not traceable anywhere in these Eternal Scriptures of the Hindus.
Academicians feel that Tirthaji had liberally interpreted three-word Sanskrit phrases to associate them with arithmetic.
Tirthaji claimed that he found the Sutras after years of studying the Vedas & deep meditation. However, the Vedas do not contain any of the Vedic Mathematics Sutras, mentioned in this book. Tirthaji’s description of Mathematics as a Vedic Science is most commonly criticised on the basis that, thus far, none of the Sūtras can be found anywhere in Vedic literature. When challenged by Professor K.S. Shukla to point out the Sutras in question in the Parishishta of the Atharvaveda, Shukla reported that Tirthaji said the sixteen Sutras were not included in standard editions of the Parishishta, and that they occurred in his own Parishishta and not any other.
"The Vedas are Infinite", says Paramacharya Shri Chandrashekharendra Saraswathi Swamigal of Kanchi Kamakoti Peetham, "If the cosmos of sound (Shabda-Prapanca) enfolds all creation and what is beyond it, it must naturally be immensely vast. However voluminous the Vedas are, one might wonder whether it would be right to claim that they embrace all activities of the universe. "Anantah Vai Vedah", the Vedas themselves proclaim so (the Vedas are endless). Only about a thousand Shakhas or recensions belonging to the four Vedas have been revealed to them."
Says Swami Krishnananda,"We are told in an anecdote that certain devotees went to Krishna Dvaipayana Vyasa and importuned him to explain to them the meaning of the Veda. It appears that he uttered one sentence: Ananta vai vedah. The Veda is infinite and, therefore, it cannot be explained in finite terms."
Why is it difficult then for us to believe that a part of the Vedas, which TirthaJee calls 'Vedic Mathematics' was revealed to him during his hours of communion while in silent deep meditation, like some of the Immortal Sages of Vedic times? How do we claim that all the Infinite Vedas have already been revealed to the seers in the perishable volumes that we have in our possession today? On what basis? The arguments of the scholars, with the reason they provide to support their view, sound really funny. With our finite mind & finite intellect, how do we claim to have an answer for everything, for everything in the Cosmos that's INFINITE, without a begining, without an end?
Although the book was first published in 1965, Tirthaji had been propagating the techniques all over the globe since much earlier, through lectures and classes. He wrote the book in 1957. It was published in 1965, five years after his death, as a book of 367 pages in forty chapters. Reprints were made in 1975 and 1978. Several reprints have been made since the 1990s.
Some of the scholars have pointed out that while Tirthaji's methods were not unique, they may have been invented by him independently, as Tirthaji held an MA in mathematics, & also that the term Vedic Mathematics is incorrect, and there are other texts that can be used to teach a correct account of the Indian Mathematics during the Vedic period.
Proponents of Vedic Mathematics however argue that the methods are not merely mathematical tricks and that there is an underlying psychology because the aphorisms describe personal approaches to problem-solving. As pedagogic tools, the methods are useful because they invite students to deal with strategies.
According to Scholars, Indian Mathematics emerged in the Indian subcontinent from 1200 BC until the end of the 18th century. In the classical period of Indian Mathematics (400 AD to 1200 AD), important contributions were made by Mathematicians & Astronomers like Aryabhata, Brahmagupta, Bhaskara II & Varahamihira. The decimal number system in use today, was first recorded in Indian Mathematics . Indian Mathematicians made early contributions to the study of the concept of zero as a number, negative numbers, arithmetic, and algebra. In addition, trigonometry was further advanced in India, and, in particular, the modern definitions of sine and cosine were developed there. These mathematical concepts were transmitted to the Middle East, China, and Europe and led to further developments that now form the foundations of many areas of mathematics.
Ancient and medieval Indian mathematical works, all composed in Sanskrit, usually consisted of a section of Sutras in which a set of rules or problems were stated with great economy in verse, in order to aid memorization by a student. This was followed by a second section consisting of a prose commentary (sometimes multiple commentaries ) that explained the problem in more detail and provided justification for the solution. In the prose section, the form (and therefore its memorization) was not considered so important as the ideas involved. All mathematical works were orally transmitted until approximately 500 BCE; thereafter, they were transmitted both orally and in manuscript form.
( Disclaimer : All images featured in this Blog-post, are the property of their respective owners. Our deepest sense of gratitude to all of them for making this gigantic project a reality. If you see your picture anywhere in this Blog and don't want it here, send us a message with the details and the link to the picture, and we will remove it right away. But at the outset, I just want to let my dearest readers know, that the noble purpose of this Blog, is to promote 'The Glorious Cultural Heritage of India' worldwide, to every nook & corner of the planet, and I would immensely love to see every single one of us, of Indian origin, passionately participating in this Mega-Project. I am right now in the process of adding the web-links to the sources of the innumerable images in this Blog. Till the work reaches completion, I would request the readers to use 'Google Image Search' to trace the source / multiple sources of these images on the web. The rich text contents througout this blog are based on well-researched aggregated and curated content from innumerable sources. But mostly and most importantly, these contents are based on my own personal experience of untiringly exploring the glorious cultural heritage India, and the ageless timeless ethnic arts, crafts, textiles, temples etc of the whole of India, during my stay across the length and breadth of this vast expansive Indian subcontinent for more than 5 decades of my long adventurous life. I have expressed my deepest gratitude to all the text sources on the 'World-Wide-Web', that have hugely contributed and added to my existing database of knowledge on this subject, by inserting appropriate hyperlinks throughout this blog, to connect my ardent readers from across the globe, to these rich sources of information on India's heritage. So Long, Mala Chandrashekhar )
According to Scholars, Indian Mathematics emerged in the Indian subcontinent from 1200 BC until the end of the 18th century. In the classical period of Indian Mathematics (400 AD to 1200 AD), important contributions were made by Mathematicians & Astronomers like Aryabhata, Brahmagupta, Bhaskara II & Varahamihira. The decimal number system in use today, was first recorded in Indian Mathematics . Indian Mathematicians made early contributions to the study of the concept of zero as a number, negative numbers, arithmetic, and algebra. In addition, trigonometry was further advanced in India, and, in particular, the modern definitions of sine and cosine were developed there. These mathematical concepts were transmitted to the Middle East, China, and Europe and led to further developments that now form the foundations of many areas of mathematics.
Ancient and medieval Indian mathematical works, all composed in Sanskrit, usually consisted of a section of Sutras in which a set of rules or problems were stated with great economy in verse, in order to aid memorization by a student. This was followed by a second section consisting of a prose commentary (sometimes multiple commentaries ) that explained the problem in more detail and provided justification for the solution. In the prose section, the form (and therefore its memorization) was not considered so important as the ideas involved. All mathematical works were orally transmitted until approximately 500 BCE; thereafter, they were transmitted both orally and in manuscript form.
( Disclaimer : All images featured in this Blog-post, are the property of their respective owners. Our deepest sense of gratitude to all of them for making this gigantic project a reality. If you see your picture anywhere in this Blog and don't want it here, send us a message with the details and the link to the picture, and we will remove it right away. But at the outset, I just want to let my dearest readers know, that the noble purpose of this Blog, is to promote 'The Glorious Cultural Heritage of India' worldwide, to every nook & corner of the planet, and I would immensely love to see every single one of us, of Indian origin, passionately participating in this Mega-Project. I am right now in the process of adding the web-links to the sources of the innumerable images in this Blog. Till the work reaches completion, I would request the readers to use 'Google Image Search' to trace the source / multiple sources of these images on the web. The rich text contents througout this blog are based on well-researched aggregated and curated content from innumerable sources. But mostly and most importantly, these contents are based on my own personal experience of untiringly exploring the glorious cultural heritage India, and the ageless timeless ethnic arts, crafts, textiles, temples etc of the whole of India, during my stay across the length and breadth of this vast expansive Indian subcontinent for more than 5 decades of my long adventurous life. I have expressed my deepest gratitude to all the text sources on the 'World-Wide-Web', that have hugely contributed and added to my existing database of knowledge on this subject, by inserting appropriate hyperlinks throughout this blog, to connect my ardent readers from across the globe, to these rich sources of information on India's heritage. So Long, Mala Chandrashekhar )
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