My google search (Wiki) makes me skeptic to believe that Under the heading 'Ancient Mathematicians' after Pingala (possibly c. 500 BCE) Panini's name is written but avoided his time and after that under the head 'Post-Vedic Sanskrit to Pala period mathematicians (5th century BCE to 11th century CE) the first name that comes is 'Aryabhata' mentioning his period to be 476–550 CE. This pushes us to conclude that there was no considerable mathematician for a period of 1000 year. I feel it to be absurd. As such Aryabhata should belong to the era before Christ. More over the names mentioned in ‘Ancient Mathematicians’ may not be said to be belonging to the periods belonging to the periods mentioned there against, as Maharshis like Bodhayana, Katyayana and the like belong to the preceding yugas during which yajnas were common phenomenon for the then kings and households and the calculations mentioned by the said sages are related to yajnas only.
Aryabhata - 4
Now we come back to finding the date of Aryabhata.
For that we have to find out which version of the following two slokas in Aryabhatiam is the correct one. Is it this one?
Shastyabdanam Shadbhiryada vyateetastra yascha Yuga padah l
Trayadhika vimsatirabdhastdheha mama janmanoatithi ||
“Shastyabdanam Shadbhi” means 60 x 6 = 360. Which places his birth at 2765 BC (360 -23 – 3102)
Or this one
Shastabdhanam shastardha vyatitastrashyam yugapadha|
Trayadhika vimsatirabdhastdheha mama janmanoatita||
Shastabdhanam shastardha means 60 x 60 = 3600
Which places his birth at (3600 – 23 – 3102) = 475 CE
The resulting shift in the date of Aryabhata of 3240 years, makes him roughly 8 times higher in chronology, and has profound consequences for the Indic contributions relative to those of Babylonian mathematicians.
As I feel there is relevance to know about Vikram Samvat to arrive at the date of Aryabhata, let us now know a little about Vikram Samvat.
Vikram Samvat era started in 56 B.C. and was used by Javanees courts until 1633.
The Ujjain calendar started around 58–56 BC, and the subsequent Shaka era calendar was started in 78 AD at Pratishthana (Paithan).
The traditional New Year of Vikram Samvat is one of the many grand festivals of Nepal, marked by parties, family gatherings, the exchange of good wishes, and participation in rituals to ensure good fortune in the coming year. It occurs in mid-April each year, and coincides with the traditional New Year in Assam, Bengal, Burma, Cambodia, Kerala, Kashmir, Manipur, Odisha, Punjab, Sri Lanka, Tamil Nadu and Thailand.
In addition to Nepal, the Vikram Samvat calendar is also recognized in the North and East of India, and in Gujarat among Hindus.
The Vikrami calendar is the official calendar of Nepal. Sindhi poets also used this calendar's month in their poetry and older people at villages of Sindh have ideas of this calendar's month.
The luni-solar Vikram Samvat calendar is 56.7 years ahead of the solar Gregorian calendar. For example, the year 2075 VS began in 2018 BC and will end in 2019 BC.
This confirms that an emperor by name Vikramarka existed, ruled and extended his empire up to gulf also as I mentioned earlier.
We first try to fix the date of Varahamihira.
What does Varahamihira give as his date? In Panchasiddhantika, he gives the following data:-
సప్తాక్షి వేద సంఖ్యం శకకాలమపాస్య చైత్ర శుక్లాదౌl
అర్ధాస్తమితే భానౌ యవన పురే సౌమ్య దివసాద్యే ll
"Subtract 427 from Saka Kala, when the sun is half-setting at Yavanapuri at the beginning of Chaitra Sukla Prathipadi (that is when the Chaitra new moon ends), it is the beginning of Wednesday."
‘Wednesday’ is the reading given in some books, I have consulted; but in the text edited by Dr. Thibaut. सोम, సోమ(Monday) is put down instead of Wednesday. Sankara Balakrishna Dikshit gives भौम, భౌమ (Tuesday) as his reading. (Indian Antiquary Vol. XIX, page 45)-(Original Surya Siddhanta by Sankara Balakrishna Dikshit). Which are we to take? Dr. Thibaut, unfortunately, does not give the alternative readings, whereas S. B. Dikshit gives them, but prefers Tuesday to Wednesday. But both of them took Saka Kala as Salivahana Saka, which naturally led to textual modifications. Dikshit had to resort to many arguments and suggest alterations simply because he was under the impression that Salivahana Saka was meant whenever 'Saka' was used. His arguments and conclusions are defective, untenable and fallacious. (By Veda Murthulu Kota Venkatachalam Garu in Ancient Indian History.) Sri Venkatachalam Garu continues to say like this:
Now let us take the week days of Chaitra Sukladau for each of the Saka years 427 current and elapsed. I am following Swamikannu Pillai's Ephemeris for the calculations:-
Salivahana Saka:
(I) 427 (elapsed) Chaitra Sukla Prathipath begins at 10gh 10 v.gh, on Friday, March 3, A.D. 506.
(ii) 427 (current) Chaitra Sukla Prathipath begins at 4gh. 2 v.gh, on Saturday, Feb. 19-A. D. 505, but ends on Sunday 20-2-505 A.D. as pointed at by S. B. Dikshit.
Vikrama Saka:
(iii) 427 (elapsed) Chaitra Sukla Prathipath begins at 49gh. 50 v.gh, on Wednesday, March 2, 371 A.D.
Saka 551 B.C.:
(iv) 427 (elapsed) Chaitra Sukla Prathipath begins at 59gh. 56 v.gh. On Tuesday, i.e. early morning of Wednesday or 2-3-124 B.C. 3-3-124 B.C, is a Wednesday with Chaitra Sukla Prathipath fully current.
The results speak for themselves and do not require an advocate to prove that Varahamihira did not mean either the Salivahana Saka or Vikrama Saka when he used the word Saka, but meant some Saka commencing with 551 B.C., which I, for the sake of convenience, designate as the Andhra Saka. It is very clear from the above tabulation, that the epoch chosen by Varahamihira is Tuesday-Wednesday mid-night 3-3-124 B.C, corresponding to Chaitra Sukladau of Saka 427 (elapsed). आदौ (ఆదౌ) means the beginning and the beginning of Chaitra Sukla Prathipadi. i. e., the ending of Chaitra new moon, is to be taken as the moment of epoch. According to Hindu astronomy, when the Sun is half—setting at Yavanapuri, it is midnight at Ujjain a town on the standard meridian for India. Therefore, the first thithi of the bright fortnight of Chaitra, must begin at mid—night Tuesday—Wednesday at Ujjain. The moment of epoch we get in (IV) of the table given earlier is 15 ghatis earlier and the error is not serious and is within the limits of probability. Finally it is clear that the Saka of 551 B. C. is the Saka used by Varahamihira.
Thinking that Saka-Kala mentioned by Varahamihira is nothing other than Salivahana Saka, The oriental scholars have assigned 427+78 = 505 A.D. as the period of Varahamihira. Whereas according to the present scheme, his period must be about 123\124 B.C. (551-427). This result refutes the existing theory of all oriental scholars that the Indians were indebted to the Greeks for their knowledge of Astronomy; for Hipparchus, the first Greek astronomer, lived about 160 B.C. and Ptolemy came later and worked from 127 A.D. to 151 A.D.
What has been proved now helps us to clarify the doubts of Dr. Thibaut expressed by him in his introduction to Panchasiddhantika, page XXX:-
"There may have been special circumstances rendering the year 427 Saka a more convenient starting point than a later year; but I am not for the present able to point out any such."
"I consider it altogether improbable that any of the three treatises should have originated so late as 505 A.D."
Yes. These treatises were written about 600 years earlier, i.e., in 123 B. C. as per the great indigenous Indologist Veda Murthulu Kota Venkatachalam Garu in his Ancient Indian History.
While Varahamihra is said to belong to 123 B.C. The pity is that we cannot authenticate the life periods of several greats of our Indian shastras. We have to, by and large depend on astronomy or logic on the basis of popular events provided, the people in question left some clue to ponder over.
The main controversy that stands as a great wall is the vested interests of western and western bent historians, made his existence to the 6th century AD as stated above, and also made him a courtier of Chandragupta of Gupta Dynasty with the supposition that Guptha Chandragupta had the title Vikramaditya. Accepting this hypothesis can we say all the ‘Nava Ratnas belong to the same period and were in the court of Gupta Vikramaditya. Moreover it was only a title but as is referred earlier there was a real emperor who ruled this Bharata Khanda. Here a meticulous observation will make us to know that no king with the name Vikramaditya or Vikramarka was shot to fame as much as king Vikramaditya of Pramara dynasty who was otherwise also called as Vikramarka. The kings of various dynasties adopted that name as their surname to glorify there valor. Now we see a sloka that prevails, may be, from or after Vikramarka which goes as follows:
“Dhanvantari kshapankamararasimha Sankuh
Vetala Bhatta Ghatakarpara Kalidasa
Khyatho Varahamihro Nrupathe sabhaayah
Rathnanivaih vararuchir nava Vkramasya”
From this we gather a fact that Varahamihra belonged to the Navaratnas of Raja Vikramaditya of ‘Pramara Dynasty’. His period was proved to be 102 B.C. – 15 AD as proved by Bra. Sri. Kota Venkatachalam Garu in his books on Ancient Indian History as detailed above. Dr. Kosla Vepa, PhD also in his book ‘Vedic Mathematicians in Ancient India (Part 2)’, Varahamihira belonged to 123 B.C. Hence he should be a courtier of Vikramaditya. Moreover we find an adjective only for him among all the other navaratnas that includes Kalidasa also. I presume the reason, may be he was so famous by the time he became a courtier of Vikramarka by his in depth, impeccable and irreproachable astronomical and astrological knowledge. More so he was considerably aged also.
In this connection I bring a story relevant to my argument. Though I say it to be a story I strongly feel it contains an acceptable argument.
During the regime of Vikramarka, Varahamihira was his courtier according to the above hypothesis. Raja Vikramaditya had a son. Soon after the delivery he consulted Varahamihira to tell about his future. Varahamihira after thorough verification confirmed that the boy will meet death at his 8th year of age by a boar. With all his astonishment the king succumbed to Vikramaditya's word. The boy ultimately attained his 8th year. The King took all the care by providing a very spacious room on the top floor above which there was terrace having ample space to play. There was a huge mast to the top of which the kingdom’s national flag was waiving. In his room children of his age were provided and their every need was met with.
One day the children were playing hide and seek. Accidentally that was the date of death of the boy fixed Varahamihira. Soon after the muhurta fixed by Varahamihira the Raja had a deep sigh and told Varahamihira that his son crossed the death trap, as no boar entered into the palace. Varahamihira without any hesitation said the boy would have met his death. The king ran to the boy’s room. As he could not find him there he went to the roof. He found the boy dead due to severe fall of the wooden mast on him and flag there of consisting the symbol of a boar was spread and covered his body. However the King was consoled and ultimately he appreciated Varahamihira by adding Varaha which means boar in English, to the great man’s name which was till then only ‘Mihira’ which means ‘Sun’.
When everything like, the king, his capital city Ujjain, the boundaries of his kingdom and even the symbol of his flag, is available how can we score out the fact as a tale.
Emperor Vikramaditya of Ujjain
(Courtesy: https://www.booksfact.com/history/emperor-vikramaditya-ujjain-actual-dates.html)
Emperor Vikramaditya of Ujjain (city originally named as Ambavati) lived during 101 BCE – 19 CE based Jyotirvidabharana of Kalisada, Jyotishaphala Ratnamala of Krishna Misra, and history of Nepal, Kashmir, Stapatha Brahmana, and Bhavishya Purana. Hence he is actually part of history. He was even referred in Puranas.
Few Vedic astrology books written during his time prove his existence in 1st century BCE. Vikrama Saka (era) followed in Vedic panchangs since 57 BCE as Vikram Samvat.
Due to Jyotirvidabharana by a connoisseur various shastras and a great poet Kalidasa, and unparalleled Astronomer Astrologer and Mathematician Varahamihira the above fact is proved and they both were among the 9 gems in his court.
Even Kalhana‘s Rajatarangini (stream of Kings), Vikramditya’s contemporary Krishna Misra’s great astrologically work Jyotishaphala-Ratnamala and with a few mentions in Bhavishya Purana coupled with recorded history of Nepal prove his existence with correct dates and years.
EMPEROR VIKRAMADITYA
“Purne thrimsachchate varsheKalau prapte bhayamkareSakanamcha Vinasardham Arya Dharma vivruddhaye Jatassivajnaya sopi kailasatGuhyakalayat.”
– Bhavishya Maha Purana (3-1-7-14, 15 verses)
“Vikramaditya namanam pita Krutwa mumodahaSa balopi mahaprajanah pithruMathru priyamkarah” (3-1-7-16)
“Pancha Arche vayah prapte Tapasordhe vanam gatahDwadasabdam prayathnenaVikramena krutam tapah” (Bhavishya 3-1-7-17)
“Paschadambavatim divyamPurim yatah sriyanvitahDivyam simhasanam ramyamDwathrimsan murthi samyutam” (Bhavishya 3-1-7-18)
Translation : At the completion of 3000 years after the advent of the terrible Kaliyuga, (IE. 101 BCE.) a person descended from the abode of Guhyakas in Kailasa, at the command of Lord Siva, for the purpose of destroying the Sakas and uplifting Arya-Dharma. He was born to the Great King Gandharvasena. The father named him ‘Vikramaditya’ and felt very much rejoiced.
As boy he was very wise and pleased his parents.
When he was 5 years old, Vikrama went to the forest and did penance for 12 years. Having enriched his greatness by penance he reached the city Ambavati (Ujjain) and was anointed as a king on a golden throne decorated with 32 golden dolls.
To be continued...................
Borders of Vikramaditya's Empire
పశ్చిమే సింధు నాద్యంతే సేతు బంధేహి దక్షిణేl
ఉత్తరే బదరీ స్థానే పూర్వేచ కపిలాంతికేll
Paschime sindhu nadyante, setu bandhhehi dakshine l
Uttare badari sthane, poorvencha kapilantike ll
Translation: This verse from Bhavishya Purana states that, in the west the other bank of the Sindhu River; in the South the Setu; Badarinarayana in the Himalayas formed the North limit and the city of Kapilavastu, the boundary in the East. These were the limits of Vikramaditya's Empire.
Pramara Kings (https://www.booksfact.com/history/emperor-vikramaditya-ujjain-actual-dates.html)
Following is the list of Pramara kings, and their regime:
Name of King Years
Pramara (Paramar) 2710 – 2716 Kali Yuga (392 – 386 BC)
Mahamara
386 – 383 BC
Devapi
383 – 380 BC
Devdatta 380 – 377 BC
Sakas defeated next kings, who left Ujjain 377 – 182 BC
And fled to Srisailam
Gandharvasena (1st time)
182 – 132 BC
Sankharaja (son of Gandharvasena) went to forest for meditation and died without a child 132 – 102 BC
Gandharvasena (2nd time) returned from exile and took over the throne again
102 – 82 BC
Vikramaditya (2nd son of Gandharvasena born in 101 BC i.e. 3001 kali Yuga)
82 BC - 19AD
With all these evidences we have established that King Vikramaditya ruled India and he had Varahamihira and Kalidasa as two among the Navaratnas in his court. Varahamihira refers Aryabhata in his works. Is this not proving that Aryabhata is senior to Varahamihira.
Now we speak a little about Bhaskara 1. He is the earliest known commentator of Aryabhata's works. He mentions the names of Latadeva, Nishanku and Panduranga Swamy as disciples of Aryabhata. Moreover he says that Aryabhata's fame has crossed the bounds of the oceans and his works have let to accurate results even after so much time, this shows that Bhaskara 1 lived much later than Aryabhata.
We have arrived at the starting date of Kali Yuga as 3102 BC. In Aryabhateeya he gives the exact year of the beginning of Kali Yuga. He writes that he wrote the book in the "year 360 of the Kali Age" at the age of 23. As it was the 360th year of the Kali Age when he was 23 years old, the beginning of the Kali Yuga would come to [360 - (23 ) + 1 (As only one year elapses between 1 BC and 1 AD) = 338 BC.]
360+23+1=384 KE (Kali Era)
Most of the great historians are skeptic about the existence and the periods of great people who are greater than the greats like Alexander, Cyrus, Asoka and Akbar but did not find a place at least in the history subject of the academics. We never came across Vikramaditya aka Vikramarka, Raja Bhoja of Dhar (Dhara Nagar), Salivahana while the sloka mentioned above correlates with Vikram, the pseudo secular historians and scholars score it out as a fib.
Like a coin contains two sides, my thinking is that as to why they do not ponder about the other way round. A very simple question that occurs to mind is that whether have we to discard any dissemination that lacks proof for various reasons. I feel it all depends on the faith we repose on the predecessors or the ancestors. We have not seen our great grandfathers. Still if our elders say by showing an image hanging on the wall as our great grandfather, without asking for any proof we are accepting it. *******One important thing to consider is that, unless there is fire there cannot be any smoke. Moreover national history was mutilated by so many historians of western interest we do not have the clear period works and achievements of the monumental historical icons of this great country, nor they evince any interest to make research of Puranas and ethihasas of our land. Even in early 20th century Rama, Rama Sethu, Ravana, Krishna, Pandavas, Parikshit, Janamejaya were all mythological characters. Now they have become historical figures. Till we got Ramayana, Mahabharata proved to be history; the historians were never honest to accept the truth though it was absolutely prevalent through the country.
Some dedicated Indians who are historians too proved astronomically also the said facts. If we fix up the exact time period of these great Indian scholars we can build up the history on sound lines through which we can exhort to the world the greatness of our adorable icons and continue their legacy and make our national flag flutter sky high.
Swasti.
