Mathematics  is said  to  be the  Queen  of Sciences. No wonder, as there is hardly any branch of knowledge devoid of mathematics. From a cattle census to satellite-imaging  technology, everything flourishes in the courtyard of mathematics. This omnipresence of mathematics was not alien to the ancient people who lived on the river banks of the Saraswati and the Sindhu. They expressed it in beautiful language. The Vedangajyotisam states:

Yatha sikha mayuranam
Naganam manayo yatha
Ganitam murdhani sthitam

"Like the crowning crest of a peacock and the shining gem in the cobra‚s hood, mathematics is the supreme Vedanga Sastra" There are six Vedanga Sastras viz. Siksa (phonetics), Niruktam (etymology), Vyakaranam (grammar), Chandas (prosody), Kalpam (ritualistics) and Ganitam (mathematics).

How could such a magnificent position be attributed to this sub­ject at a time when all the other five branches were in their pris­tine glory, in full bloom, vast and deep as an ocean? The only logical conclusion to be drawn is that ganitam (mathematics) had also attained such perfection. And what was the need for such intellectual luxuries as science and mathematics for those nomads sitting around the fire, praying to the lord of natural forces, the forces of fire, air, water, thunder and lightning, out of sheer fear!? Though they were mostly forest-dwellers, living on mere roots and fruits, their enlightened souls kept the fire of knowledge burning, a knowledge which knew no barriers. They could penetrate deep into the subtler regions and into hidden truths, formulate principles, and illustrate mechanisms in beauti­ful language. These people who realised the ultimate forms of knowledge are known as rsis and the Sanskrit verses that they wrote took the form of the Vedas. There, hidden behind the met­rical syllables, sprung the basic tenets of the life sciences both physical and spiritual.

Who was the first to count, give shape and symbols for continu­ous counting from one to infinity? An inquiry will invariably reach the Vedas and frame charges against the Vedic rsis. In the Yajurveda the rsi after preparing bricks (Istaka,) for a sacrifice, prays thus:

Ima me Agna istaka dhenava santveka ca
Desa ca satam ca sahasram cayutam ca
Niyutam ca prayutam ca arbudam ca nyarbudam
Cantyam madhyam parardhascaita me agna
Istaka dhenavasantvamutramusmimlloke

"Oh! Agni (fire) let these bricks be milk-giving cows to me. There are (eka) 1, (desa) 10, (satam) 102, (sahasram) 103, (ayutma) 104, (niyutam) 105, (prayutam) 106, (arbudam) 107, (nyarbu­dam) 108, (antyam) 109, (madhyam) 1010, (paradham) 1011, bricks. Let these be milch kines in this world and the other world too."

This is no poetic imagination, but a cryptic description of the dec­imal number system up to twelve places, which is still in use today.   They had odd numbers (camakamantram), even num bers, fractions, sequences and more. Their efficacy in fundamental operations, especially in handling bigger numbers is still unmatched. The value of pi correct to five decimal places was known, as well as second degree equa­tions all used for the construction of sacrificial altars and sites.

Their knowledge was not limited to computa­tions. Simple point and line up to complicated figures like the sri cakram were at their fingertips. The knowledge of geometry (rekhagani-tam) that developed in those days was simply fantastic. The Pythagoras Theorem (540 BC) existed thousands of years before Pythagoras. The Sulba Sutra of Baudhayana, an ancient treatise on the construction of altars, says: In a rectangle (dirghacaturam), the square of a diagonal (aksnaya rajjuh) is equal to the sum of squares of its length and breadth. B.S.S. I (37). Geometrical figures like the triangle (tryasram), rectangle (caturasram), circle (mandalam), isosceles triangle (praugam) , as well as area, volume and many other principles were used profusely in Vedic sacrifices.

Other Sciences

To have a bird's eye view of the use of mathematics during Vedic times, we need to refer to some other branches of knowledge.
Astronomy (jyotissastram) was in its glory. The 12 moon signs each of 30° (amsa), are the Vedic descriptions of the solar sys­tem. The names of stars and planets, the time of eclipses, the revolution of earth, the calendar from ksanam (a moment) to kalpam (an aeon) are used even today. It is difficult to believe that the velocity of light given in Vedic literature is a true match to that of present-day science. Sayanacarya in his commentary of the Rgveda says: Salutations unto thee, Oh Lord! Who trav­els two thousand two hundred and two yojanas in half a nimisha. [R.V. (S.B.) 1-50-54].

Nimisha is a unit of time and yojana, a unit of distance. This is equivalent to 2.9 x 108 m/s; the modem measurement is 3 x 108 m/s.
What was the status of the physical sciences at that time? Of course, Ayurveda, the complete system of medicine was a wide­ly accepted branch of science from Brahma Himself! And the bril­liance of Patanjali, the author of the Yoga Sutras, the science of the mind; the Caraka Samhita the science of life; and the Mahabhasyam the science of words, are without parallel. Each had their own standard units of measurement.

All inhabitants of this world are classified as born from egg (andajam), born from sweat (svedajam), born from seedlings (ulbhijyam) and born from placenta (jarayujam). Is there a better start for a student of botany and zoology? The knowledge about the atom (anu), the molecule (dyanukam) and more, of the Samkhya philosophy and the science of substances (padarthav-ijnaniyam) of the Nyayasastra stand intact even after the pres­ent- day scientific explosion.

The science of mercury (rasavidya) of the alchemists was highly evolved. They could even melt iron into gold! Usmapa, the sci­ence of the metallurgy was highly developed. The Damascus Sword was of legendary sharpness and strength, and claimed to be able to cut through even rock. The steel originated in India.

The science behind this and the finest alloys used for aeroplanes and rocket engines, in the right proportions and the application of the exact degree of heat is hard to grasp. The Vaimanika Prakaranam of Bharadwaja, a treatise dealing with flying machines written in the 4th century BCE, says: (2150-51): Fill in the mould (nalikamusamukham), place it in the furnace (cakramukhakundam) and heat by a blower (ajamukhabhastram) up to 712° (dvadasottarasaptasatakaksyosnapra-manatah). This is to manufacture the metal for a rocket engine. The temperature is measured in standarised units.


What about discoveries? Who had the for­tune to make the flat earth into a round one!? Of course Copernicus and Magellan did it beautifully, but only after our Puranic poets perceived it. The Bhagavatham has a chapter by the name of Bhugolavamana, a treatise on geography. Aryabhatta (499 AD), a master of astronomy and mathematics, computed the circumference and diameter of earth, the distance to other planets and so on from this treatise. Newton (1671 AD) discovered the principle behind the falling apple. But Aryabhatta, after establishing earth's gravity (gurutva), wondered how we could say that it comes down or goes up when space is so bountiful. In his Golapadam (6) it says: "This earth has the power of attraction too, and by this it attracts things towards it. Though this looks like downward falling, how can we say that when space is so vast?" The concept of 'space' in modern science is only of recent origin.

The whole of the Renaissance and the Industrial Revolution gained momentum from automation. Who was instrumental in the invention of the automobile engine, the inter­nal combustion engine or the gasoline engine?

Bharadwaja, engineer par excellence writes in the 4th century BCE: [2099-2100] In front (top) of the gas combustion engine (Vatapacakayantrum), to burn the oil (tailam), a spark plug (dipaculli) is fitted. To spark the plug and to produce fire (agni) an electric device (vidyut yantram) is fixed with a switch. Do we need a better illustratioin or the inter-nal combustion principle?

Now, if we are presented with the puzzle-Electricity? In those days?, there is the whole of electrodynamics (saktitantram), coming from none other than the ancient rsi Agastya who even dried up the oceans. [2212-13] The dynamo (sangharsanam), hydroelectric power (jalapadam), battery (samyojakam), solar cells (kiranajanyam), etc. are the thirtytwo sources of electricity described in the Sastras. Of this, the battery (samyojakam) is suitable for aeroplanes. Materials like copper wire (tamratantri), iron magnet (ayaskantam) and coil (avrttanalam) were in use. Nowadays digital audio, video recording and transmission are mega-business. What does Bharadwaja have to say about this? [V.P. 1690-91] From the sounds of a heart beat (pranana) to a bang (sphotana), correspon­ding to their intensity and in their order by dig­ital code (samkhyanusarena) through the wire (nala) connected to the sound recorder (sabdaphenam) in that order. This means sound waves are converted to digital codes and sent by wire to a machine fitted with a recorder. Is there any difference from our present day analog-to-digital converter tech­nology? What is the speed of a supersonic jet? Bharadwaja's rocket propelled jets attained 400 yojanas per hour.
(1 yojana = 9.09 miles approx.) [V.P. 2462]

Future Technology

We are in search of fuel which is easily avail­able and non-exhaustive. Although the source of energy is the sun (aditya), we have started from Fire, wood and coal for the steam engine, oil for the internal combustion engine, liquid gases for air and space engines. All these are from Earth (prthvi). The next natural choice is Water (ap). It is yet to be tapped. Our ancient scientists could visu­alise it clearly: [2165-67] The current (vidyuc-chakti) is supplied through the wire (nala) in its order using a switch (kilaka), which (sam-codayet) activates between two molecules of water (varikosadvaya madhye) to the pre­scribed measure. The water then decompos­es into hot gas (ousmyadhumakaram) and collects in two jars. This, exactly, is the hydrolysis of water.

2H20 current > 2H2 + 02

This nascent hydrogen is ignited in high pres­sure and escapes through nozzles to propel the aeroplane. It is astonishing to read the term which shows that they had full knowl­edge of the composition of water and that water molecules exist as H2O.


Why did all this wisdom, both pure and prac­tical, not pass to modern times? Science studies the property of matter and taps it to the furthest extent possible. This is true for all ages. Even the terminology at the functional level seems similar.

To achieve a particular objective the material selected may be slightly different as well as the process. Moreover, according to the Vedic calendar, in the Krta Yuga, there is no need of anyone's help. Everyone can make the effort and attain any desired goal. The other two yugas the Treta and the Dwapara are governed by mantra and tantra respectively. Only in the Kali Yuga man depends on instruments or machines (yantram). The most profi­cient mathematician of India, Aryabhatta, as early as 499 A.D., has unequivocally stated that the Kali Yuga started after the Mahabharatha war, fifty two centuries ago. Though the knowl­edge was there, it could be used only in the Kali Yuga. Still, there are standing monuments, some of which are puzzling even to modern scientists. The iron pillar of Delhi, the sites of Mohan-jo-Daro and Harappa, the poetry in stone of Ajanta and Ellora, the observatories of Jaipur, the colossal temple structures throughout India can speak volumes about the knowledge that was avail­able. From these we can easily infer that there was science as well technology with standardised units and measures, necessi­tating a high knowledge of mathematics.

Vedic Mathematics

We have already seen that the origin of mathematics is from the Vedas. But the Vedic tradition faded away in the ravages of time. Fortunately we were blessed with the birth of another seer, Jagadguru Swami Bharati Krisna Theerthaji (1884-1960), late Sankaracarya of Puri Govardhan Peethom. His Holiness had a brilliant academic career and he took eight M.A. degrees at the age of 20. Sanskrit and mathematics were among them. He served as principal of a college for a short stint. But his inner urge for higher truths took him to the Sringeri Mathom, where he con­tinued learning the Vedas and Sastras. His sharp intellect pierced into the hidden meaning of certain sutras. After eight years of tapas, he recovered sixteen mathematical sutras, supported by thirteen odd subsutras. He wrote sixteen volumes establishing the veracity of these sutras in the solution of problems in modern mathematics. He used to give demonstra­tions in colleges and universities at home and abroad. The man­uscript, kept in a disciple's house for printing, went missing. At the repeated request of his followers, Theerthaji started writing again, but could finish only one volume viz. Ancient Vedic Mathematics, which is the original text on this subject.

The Sankaracarya with unmatched calibre and erudition, though a contemporary of mathematical genius S. Ramanujan, gained little recognition. Swamiji lived fifteen years in independent India, but his book was published five years after his mahasamadhi. Indian Universities and academics were reluctant in taking up serious studies in this subject, whereas Western mathematicians have made great strides.

Three professors from England, A.P. Nicholas, J.R. Pickles and K. Williams have contributed on the use of Vedic mathematics in higher applications. Professor Williams published a book Triples as a fitting tribute at the eve of Theerthaji's birth centenary. In England Vedic mathematics is accepted as part of the syllabus and the authorities have started preparing text books. Dr. Narendra Puri of Roorkhee University (U.P) has also tried his best in the propagation of this subject.

The purity of Vedic sciences is really holistic as life itself. We may have tasty food cooked in sophisticated micro-ovens. But we cannot ensure a sound body better than that of the ancient earth­enware users. We are assisted with highly efficient IT. servers and all knowledge at our finger tips. Yet we are no more wise in our performance than those half naked saints. In the midst of all amenities and luxuries created by modern science and technolo­gy, sleep is but a half-note away.