This is the third part of my series on History of Mathematics. In my earlier articles, I had explored the concept of mathematics and how and where it emerged from. Though mathematics had made its way in India very early ,in Vedic texts,among mathematicians who lived before Christ,in Jainism/ Buddhism and in the language I am familiar with (in which I can read ancient texts)Tamil. I shall write about them. Now I shall attempt at the references to Mathematics in Vedic texts. One may note that the oldest literature known to man, Rig Veda is dated about 5000 years. My view is that it is older at least by few thousand years. I had written articles on this topic in this blog.

Vedas are called the Sabda Pramana. It means that Vedas are one of the tools of knowledge and it represents testimony. Vedas are Testimonies of Seekers of Truth and they had recorded their experiences in the Form of Sound. Vedas are one of the tools of knowledge recognised by Hinduism,along with Perception, Inference,Comparison ,Logic,Intuition,and Experience.

Sanatana Dharma recognised two levels of Knowledge.One is Para Vidya which is Absolute and another is Apara .It is lower knowledge in that it deals knowledge that is applicable and useful for day to day activities. It is lower knowledge as any thing that binds one to the world in the form of Birth ,death and the cycle involved , is treated as Inferior Knowledge.The knowledge that helps one realise Self is Real Knowledge and it is Absolute.

So references to Sciences as we know of today , as defined by Western thought, are not pursued as distinctly as the western system of Education. The information relating to these concepts are made in the passing so long they are relevant in Realising Brahman .So the scientist concepts as we know of know today are found in as much as they are found useful in the conduct of Vedic Rituals ,when King’ Prowess or skills are explained in Purana or Ithihasa. And in many an instance, the principles are inferred either from the results or understanding the Aphorisms. And this needs special skill set. As Nature is personified Attributes are ascribed and they reveal the level of scientific knowledge of the Vedic people. For instance, Sun is called Surya and Attributes of Surya include the composition of Light, movement of Sun in the Universe.One can find information about the planets, Galaxies,Stars , Blackholes, Wormhole, Concept of Time as Cyclic, which is now validated by Quantum Theory.And we have the Vaiseshika system deals extensively about Atomic Theory, Particles,sub particles. Nyaya system deals with advanced Logical systems. There are concepts which are applicable to Computer Languages. Binary principles, Binomial theorem, Pythogoras Theorem Trigonometry,Calculus…all are found in ancient Indian texts.

You may have noticed that I have referred to some systems which are not a part of Vedas. Reason is that Vedas alone do not contribute to Hinduism. Vedas are a Source of Knowledge. Other systems like Nyaya,Vaiseshika Sankhya,Yoga,Purvamimasa and Uttaramimasa are other systems of Indian philosophy. Of these Uttara Mimamsa is Upanishads which is a part of Vedas.Having this point in our approach, let us see what Vedas mention ,in the passing, about scientific, especially Mathematical Concepts.

Chamaka expresses Mitochondrial Pairs of DNA on the form of Mathematics.

Whe have, Vedic Mathematics. This helps one to handle fundamental mathematics easily.

1. Ekadhikina Purvena
   (Corollary: Anurupyena)
   Meaning: By one more than the previous one
2. Nikhilam Navatashcaramam Dashatah
   (Corollary: Sisyate Sesasamjnah)
   Meaning: All from 9 and the last from 10
3. Urdhva-Tiryagbyham
   (Corollary: Adyamadyenantyamantyena)
   Meaning: Vertically and crosswise
4. Paraavartya Yojayet
   (Corollary: Kevalaih Saptakam Gunyat)
   Meaning: Transpose and adjust
5. Shunyam Saamyasamuccaye
   (Corollary: Vestanam)
   Meaning: When the sum is the same that sum is zero
6. (Anurupye) Shunyamanyat
   (Corollary: Yavadunam Tavadunam)
   Meaning: If one is in ratio, the other is zero
7. Sankalana-vyavakalanabhyam
   (Corollary: Yavadunam Tavadunikritya Varga Yojayet)
   Meaning: By addition and by subtraction.Puranapuranabyham
8. Puranapuranabyham(Corollary: Antyayordashake’pi Meaning: By the completion or non-completion.
9. Chalana-Kalanabyha(Corollary: Antyayoreva)Meaning: Differences and Similarities.
10. Yaavadunam(Corollary: Samuccayagunitah)Meaning: Whatever the extent of its deficiency.
11. Vyashtisamanstih(Corollary: Lopanasthapanabhyam)Meaning: Part and Whole.
12. Shesanyankena Charamena(Corollary: Vilokanam)Meaning: The remainders by the last digit.
13. Sopaantyadvayamantyam(Corollary: Gunitasamuccayah Samuccayagunitah)Meaning: The ultimate and twice the penultimate.
14. Ekanyunena Purvena(Corollary: Dhvajanka)Meaning: By one less than the previous one.
15. Gunitasamuchyah(Corollary: Dwandwa Yoga)Meaning: The product of the sum is equal to the sum of the product.
16. Gunakasamuchyah(Corollary: Adyam Antyam Madhyam Meaning: The factors of the sum is equal to the sum of the factors. Source.Das, Subhamoy. “The 16 Sutras of Vedic Math.” Learn Religions, Aug. 26, 2020, learnreligions.com/vedic-math-formulas-177068 0. https://www.learnreligions.com/vedic-math-formulas-1770680

Check these sites.

• 29 Vedic Formulas
• Vedic Maths
• https://balaganabaudhik.blogspot.com/2012/03/vedic-mathematics-session-1.html?m=1
• Vedic mathematics Pdf

The secularists dismiss this as Tricks!

These statements have been since rejected in their entirety. Krishna Tirtha failed to produce the sources, and scholars unanimously note it to be a mere compendium of tricks for increasing the speed of elementary mathematical calculations with no overlap with historical mathematical developments during the Vedic period. However, there has been a proliferation of publications in this area and multiple attempts to integrate the subject into mainstream education by right-wingHindu nationalist governments. https://en.m.wikipedia.org/wiki/Vedic_Mathematics

Does Truth Matter? I Offer A ₹5,00,000 INR ‘Vedic’ Maths Reward  … For Serious Primary Evidence And Proof The 16 Mathematics Sutras Of Bharati Krishna Tirtha Irrefutably Exist In Any Extant Written Vedas.…

Jagadguru Shankaracharya Swami Bharati Krishna Tirtha’s view was that Vedic maths is NOT to be approached from a factual standpoint. If it is accepted that the Vedas are the source of all knowledge, then the 16 Sutras of Vedic Maths should have been contained in them.

Dr. V.S. Agrawala, friend of Bharati Krishna Tirtha and Editor of the book titled ‘Vedic Maths’.

Are The 16 Sutras Of Vedic Maths From India’s Ancient Vedas? What Do Indian Scholars Say?

VEDIC SCHOLAR PROF. DR. SUBHASH KAK

“First question: What is Vedic mathematics? It is not mathematics from the Vedic period. Rather it consists of many clever mathematical sutras and algorithms that were devised by Swami Bharati Krishna Tirtha (1884–1960) who for a long time was the Shankaracharya of Govardhan Matha in Puri.

The teaching of Vedic Mathematics cannot be justified on the grounds that it tells the students something about India’s ancient mathematical heritage. This heritage without even counting the invention of zero was brilliant and unique but Swami Bharati Krishna Tirtha’s Vedic mathematics has nothing to do with it.” Source…

MATHEMATICIAN PROF. DR. C. K. RAJU

“Advocating ‘Vedic mathematics’ as a replacement for traditional Indian arithmetic is hardly an act of nationalism; it only shows ignorance of the history of mathematics.

But where in the Vedas is “Vedic mathematics” to be found? Nowhere. Vedic mathematics has no relation whatsoever to the Vedas. It actually originates from a book misleadingly titled Vedic Mathematics by Bharati Krishna Tirtha. The book admits on its first page that its title is misleading and that the (elementary arithmetic) algorithms expounded in the book have nothing to do with the Vedas. This is repeated on p. xxxv: “Obviously these formulas are not to be found in the present recensions of Atharvaveda.”. https://kreately.in/is-vedic-maths-vedic/

And more from ‘open’ site.

As stories go, this is not a bad one, but the evidence does nothing to support it. The 16 sutras expounded by Tirathji do not appear in any known edition of the Atharva Veda. Tirathji’s defenders have claimed that Tirathji was so immersed in Vedic thought that he was able to glean what the Vedic seers had in mind even if it was not explicitly so stated anywhere in the Vedic corpus. If one were to actually concede this meeting of minds between Tirathji and the ancient Vedic seers, it would have the unfortunate consequence of implying that not just Tirathji but even these seers were limited in their mathematical understanding.

All the sutras largely do is make the burden of addition and multiplication faster (though never nearly as fast as the cheapest pocket calculator), and even that, they do at a cost. Students studying the traditional method of multiplication should ideally understand (and bad teachers themselves fail to grasp this) what multiplication is, how it works, and how it is in essence an act of repeated addition. Tirathji’s methods are just rules that make mathematics seem like a bunch of tricks which are easy to implement but difficult to understand.

Take, for example, the multiplication of 9 and 7. Line them along with their difference from 10. That is:

9–10 = –1 and 7–10 = –3

9–1

7–3

——

6   3

You obtain the answer in the following fashion: the unit’s digit is the two differences multiplied together, –1 x –3 = 3 and the other digit 6 is just either of the diagonals added together, that is, 9–3 = 7–1 = 6. This method can be extended to much larger numbers. It is a neat trick, but it does not make multiplication easier to fathom, quite the contrary….open the magazine

None of these scholars have disproved the fact that Vedic Mathematics sutras work.

How ridiculous can one be? The author of the book produced Non sense? The formulas work and as I mentioned at the beginning of this article that to understand Indian science, one has to understand Hinduism ‘s Concept of Knowledge first, before jumping into right wing bashing.

• How come Indian Panchang calculate Daily movement of celestial bodies, Sun Moon,other planets,predict Eclipses ,Solstices,
• Build temples without Trigonometry and Calculus,
• Build a temple tank where those who bathe in the opposite bank are invisible ? Magic?
• How did Rig Veda calculate the velocity of Light?
• How does Purushasuktha Produce Electricity?
• Yes. There is no reference to Vedic Mathematics, no science in Vedic Times,Vedic science is humbug,though it works by fluke,there are no architectural marvels and Indian temples were built without basic knowledge of Mathematics or architecture, Calculation of movements of celestial bodies by Panchang is non sense… And who say India had no science only are Educated ,Learned, cultured super Intelligent species!