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Research Into Indic Mathematicians
The Bernoullis of India

I am doing some research into the Daivajnya family a family of astronomers and mathematicians in Gujarat. Pl.... add anything you knw of this family ,, their dates of birth, their genealogy and their publicatons etc.

Ganesha Daivajna I (1505 CE son of Lakshmi and Kesava))

Kesava Daivajna
Krishna Daivajna Visvanatha Daivajna (son of Divakara Daivajna ) 1578 CE Vishnu Daivajnya (son of Divakara Daivajnya) same as Visvanatha ? probably not Narasimha Daivajna (son of Krishna Daivajnya) 1586 CE Rama Daivajnya , son of Madhusudhana Daivajnya Kamalakara , son of Narasimha Daivajnya ? , 1616 CE Ranganatha son of Narasimha Daivajnya ( 1643 CE) Lakshmidasa Daivajna Ganesha Daivajnya II (great grandson of Ganesha Daivajnya I (1600 CE) Nagesh Daivajnya (son of Shiva Daivajnya) (1619 CE)


some explanations are in order

Daivajna apparently is a synonym for Jyotish 0ne who deals with Astronomical and astrological matters.

So every person whose last name is a Daivajna is not necessarily related

still it remains an uncommon name. and all the daivajnas i have named are from
the Konkan region ( i said Gujarat but what do i know ) or on the north banks of the godavari in maharashtra.

If you have heard of a family called Daivajna from western India pl, have them contact me.

One possible thought is that they could have been saraswat brahmanas.

It appears that Aryabhata is also from the same region, which raises the interesting possibility that Aryabhata Ib (MY HUNCH is thst there were ar least 3 A) was also a saraswat Brahmana

Have you checked this?

From the dieties/temple they pray to, seems like they are/have close links to Gaud Saraswats.
How do you tell a Hayagriva murti from one of Kalki?
In T N, Kalki is shown with human body and horse head.

Is there any rule of thumb throughout India ?
Frommmm the catalog of sanskrit texts,,,, http://gist.ap.nic.in/cgi-bin/s1/s1bookd...?B=802&V=5

Book Number 802
Volume Number 5

Catalogues BBRAS.
Oxf. II.

Of Kausikagotra ; resident of Nandi grama in Konkana on the West
Coast; pupil of Vaidyanatha; son of Kamala kara Daivajna; father of
Ananta Daivajna (a. of Kalanirnayavabodha), Ganesa Daivajna (a. of
Grahalaghava, composed in 1520 A.D.) and Rama Daivajna (father of
Nrsimha Daivajna born in 1548 A.D. and a. of Grahakau mudi,
10.2945). His wife was Laksmi. A list of his works is given by Ganesa
Daivajna in his C. on Muhurtatattva. His Grahakautuka mentions the
year 1496 A.D. His Jatakapaddhati is ref. to in Muhurttamarttanda
composed at Devagiri (Daulatabad) in 1569 A.D.
See S. B. Dikshit, bharatiya Jyotisa (Hindi), pp. 357-8; also Ganaka
tarangini by Sudhakara Dvivedin, p. 173, which mentions some
additional works.
?Kayasthacaradharmapaddhati. Men tioned by his son Ganesa in his
C. on his Muhurtatattva. Bomb. Uni. 441. [This is to be added in
?Kundastalaksana. Mentioned by Ganesa.
?Ganitadipika Mentioned by Ganesa.
?Gotra(pravara)nirnaya (in verse). Cg. II. 63. Ptd. as
Gotrapravaramangalastaka in Mangalastakasangrahaf work no. IO,
Belgaum, 1924.
?Grahakautuka. Bd. 83. 307. K. 226. Oudh VI. 8.
?C. on Grahakautuka. Mentioned by Ganesa. See next.

?C. Mitaksara on (Sad) Grahakautuka. Ujjain Latest Additions 636.
?Grahacalana. Mentioned by Ganesa.
?Grahasiddhi. Mentioned by Ganesa.
?Jataka(karma)paddhati, Kesavi or Kesavapaddhati. IO, 3086-92.
6408 (with C. by Visvanatha). Oxf. II. 1572. Weber 869. 870. Ptd. (1)
Bombay, 1872. (2) Benares, 1925.
?C. on Jatakapaddhati. Mentioned by Ganesa.
?Tajikapaddhati or Varsa(phala) paddhati.Bikaner 5102-3. 10.
3060. 6352. Weber 872. Ptd. See IO. Ptd. Bks. 1938, p. 1843.
?C. on Tajikapaddhati. Hpr. IV. 107.Bik. 669,
Taksakakarmapaddhatitika is perhaps same.
?Tithisiddhi. Mentioned by Ganesa.
?-Muhurtatattva. BBRAS. 317. Bomb.Uni. 441. Ptd. (1) Benares,
1856.(2) Poona, 1927.
?Varsagrahasiddhi. Mentioned by Ganesa.
?Siddhantapatha or Si. upapattipathaniscaya or Si. vasanapatha.
Mentioned by Ganesa.
<span style='color:red'>The Discovery of "Aryabhatiya"</span>

How "Aryabhatiyam" was discovered? Bhau Daji (1824-1874) in 1864 discovered the manuscripts of Dasagitika and Aryabhatiya. He had great difficulty in collecting the manuscripts of Aryabhatiyam, as by that time the European scholars started smuggling out thousands of manuscripts. They started confusing and meddling with the "Aryabhatiyam" manuscripts also, as pointed out by Bahu Daji.

Aryabhatiyam – original Texts not found: As a great many of the quotations of aryabhata are second hand, for it appears that the original works were ptactically lost for centuries or the original works were neither available npor existed onm;ly in mutilated condition in the 14th century as note by G. R. Kaye (Notes on Mathematics No.2 – Aryabhata, JRASB, New series, Vol.IV, 1908, p.111). It is evident that the extant works might have been taken away by the Chginese, Arab and Christian missionaries, as they were very much interested in collecting manuscripts, scrolls, tables, charts etc. sending them to their respective countries, as pointed out by themselves and getting translated into their languages for further study.

Bhau Daji, who dealt with the age and authenticity of the works of Aryabhata, Varahamihira, Brahmagupta etc., quoted a passage from Maha Aryasiddhanta to the effect that the knowledge from the Siddhanta produced by Aryabhata, which was destroyed, in recessions, by long time and hence, he had his own languages stated specifying in rule (Bahau Daji, The Date and authenticity of the works of Aryabhata, Varahamihira, Brahmagupta etc., JRAS, 1864, p.392; Brief Notes on the Age and authenticity of the works of Aryabhata, Varahamihira, Brahmagupta, Bhattopala and Bhaskaracharya, Bombay, 1974, pp.121-145).

Al-biruni recorded that he had not been able to find anything of the books of Aryabhata adding that what he knew of him was through quotations from given by Brahmagupta (c.628 CE).

Colebrooke opined that a long and diligent research in various parts of India failed of recovering the algebraic and other works of Aryabhata (H. T. Colebrooke, Miscellaneous Essays, ii, p.380).

Thibaut mentioned that the idea of earth rotating on its own axis was original and Aryabhata did not acquire such views from the Greeks, adding that he might have been the first or one of the firsts, to expound the principles of that system in highly condensed and technical form, and might have improved the general theory in details. Particularly, he noted that the main body of doctrine existed before him and he did not create it, but merely recast it in a different form (Thibaut, Indian Thought, 1907, p.215.).

Therefore, the Aryabhatoyam, as available today might have been written by the original Aryabhata or a work attributed to the name or school, as it had been so popular during 5th-6th centuries and before, but original work existing earlier. Writing and composing new works with all available knowledge and updated data abpout a subject and circulating or attributing to a celebrated scholar or school has been a common practice not only in India, but also in other countries (K. V. Ramakrishna Rao, Origin of "Aryabhata" and "Aryabhata's School, a paper presented in International Seminar and Colloquim on 1500 years of Aryabhateeyam" held at Thirivananthapuram from 12th to 16th January 2000, p.6).

Aryabhatiyam is in Arya-metre: The work "Aryabhatiyam" has been the one that was written in Arya-metre. Even words used have to follow the metre. If anybody had, and or talks about "Aryabhatta" instead of "Aryabhata", that means that such manuscript is forged / meddled one, because "bhata" is in Arya-metre and "Bhatta" is not. (Note, those who support the Keralite hypothesis mention as "Aryabhatta").

John Bentley with forged Aryabhatiya works: John Bentley was having such forged or meddled copies or her himself could have meddled to confuse others. With such manuscripts, Bentley wrote that an Aryasiddhanta (Maha Arya Siddhanta) was written in 4423 Kaliyuga or AD 1322 and accordingly, he determined the date of Aryabhata as 1322 AD and therefore the work dated Kaliyuga 3623 or AD 522 was spurious one. Bauj Daji recorded aptly, "Strtange to say, the date corresponding to AD 1322, mentioned by Bentley, is not to be found in my copies". So the fact being that Aryabhatiyam copies were taken away by Bentley and others.

The different dates of Aryabhata: That the verse 10. of Kalakriya was also subjected to criticism is evident from the interpretation of the verse. There had been different versions in reading and interpretation of the verse as expressions found in the manuscripts:

60 x 60 = 3600 – 3101 = 499 – 23 = 476 AD / CE.

60 x 60 = 3600 – 3101 = 499 + 78 = 554 AD / CE.

AD 522 according to Saka 444; thus, 444 + 78 = 522 AD / CE.

3623 years elapsed; 3600 – 3101 = 522 AD / CE.

60 x 6 = 360; 3101 – 360 = 2741 – 26 = 2715 BC / BCE.

All manuscripts were available, when these scholars were debating about it. Naturally, the western scholars were so bewildered about the last one. So they cleared off such manuscripts as possible. However, that some Indian scholars were quoting it proved that such manuscripts were there.

Colebrooke commenting without seeing "Aryabhatiyam": Colebrooke, not even having the works of Aryabhata before him, suggested that the oldrr work might be a fabrication, but from citations and references to Aryabhata in the works of Brahmagupta and Bhatta Utpala, came to a singularly accurate conclusion as to the age of Aryabhata, whose works he thought were different from either treatise in the possession of Bentley.

Bibhutibhusan Datta concluded that "…….Al-biruni's first wrong impressions about the existence of two Aryabhtas originated when he was in Arabia" (Bibhutibhusan Datta, Two Aryabhatas of Al-biruni, BCMS, Vol.XVII, No.2 & 3, 1926, p.74).

Al-ntf: What is the work "Al-ntf" mentioned by Sachau in Albiruni? We know that Zij, the so-called Indian astronomical tables were characteristically mentioned and it was derived - Sind-hind > Sinhi > zinji > znij > zij. As one astronomical work was accepted but its name was not known in the "Aryabhatiyam" context, it could be derived as follows: Hind-Aryabhat > hindarbhat > hindaf > ntf with al- added. The Arabs added al- making it Arabic and the Europeans used it accordingly. The expressions al-gamest, al-exandrine, al-gorism, al-gorithm, al-gum, al-gebra, al-kali, al-kaloid, al-lah, al-chemy, al-cohol, al-embic, al-manac, al-mighty, al-mond, al-kaya, and so on tell the fact. These names were derived from the works of Siddhas during Siddha-Sufi encounters.

<b>Not to be quoted without permission from:</b>
Institute for the Study of Ancient arts and Sciences,
25 (Old.No.9), Venkatachala Iyer Street,
West Mambalam,
Chennai – 600 033.

Kaushal from what information I have it seems gaNesha daivaj~na was a Konkani brahmin. From his title it is indeed possible that he was a Sarasvata rather than a Chitpavan. His patron was the Ram Singh the son of Mirza Raja Jai Singh and he worked mainly in Amber where apparently his patron had provided an observatory. After his death following the Assamese campaign, Daijna seems to have returned to Devagiri and possibly even observed from Nanded.
Thank you, HH. I have posted a genealogical tree of the Daivajnas at my blog. which people might want to correct for errors and discrepancies..... .I was nooot successful posting the image here



1. Great blog.
This may be a mistake: "Core values" #9 has the word "cull" instead of, I guess "cultivate". Cull means to willingly put to death, puppies in a litter that do not display "show potential" because of some minor defect are frequently drowned by breeders here, and this is called culling.

2. Indic Maths is fantastic.
This may be a mistake: On slide 24, though, Aryabhatta is written in as Aryabatha in Devanagari..
Please put up a prominent link to Indic Studies on IF so that people like me go to the site! I found out about it just today, through the blog!
<!--emo&:cool--><img src='style_emoticons/<#EMO_DIR#>/specool.gif' border='0' style='vertical-align:middle' alt='specool.gif' /><!--endemo--> <!--emo&:cool--><img src='style_emoticons/<#EMO_DIR#>/specool.gif' border='0' style='vertical-align:middle' alt='specool.gif' /><!--endemo-->
<b>Shambhu, ON point 2 you are correct, the devanagari should indicate a bh instead of b, and a ta instead of a tta or a tha.

On point 1 i stand by my meaning of cull which is to select from a large population. The meaning you have given is merely illustrative as an example, than one which captures its general context.

anyway, glad you find the subject of interest. send me a PM if you wish to discuss further, we can exchange phone numbers,

Bodhi, thank you for psoting the material on A'BHatiya. Dr. Bhao Daji is credited with rediscovering A. However there may be more to the story.

The link to My Webpage

Kaushal </b>
Kaushaj-ji, very interesting subject and good job on the blog. Suggestion - please consider publishing a series of monographs through 'secular' outlets to educate the larger public.

Hope the recent findings of some UK-based historic-researchers have reached you - they have shown that a distinguished Kairaliya tradition of Indic Mathematicians (e.g. Neelakantha) that continued till 13th c, must be credited with the founding of calculus - centuries before Newton. And not only that it is not a coincidence that Europe/Newton suddenly discovered the subject - Jesuit missionaries and other Europeans of the period have the credit of smuggling / translating the Indic Mathematic treatise and transporting to Europe.

This was widely reported in Indian news papers last week.

For records, the accurate name is Aryabha<b>T</b>a and not aryabha<b>TT</b>a which is more popular - thanks to the European writers. This accurate naming has been thoroughly emphasized by the pioneers like Dr. Bhao Daji, and earlier TIkA-kAra-s.
Another note on the above subject, if someone is interested in this line of research.

Father of the famous William Jones the 'Sanscrit-Farsi' scholar and founder of the proto-AIT, was also known as William Jones (the sr). The father William Jones was a contemporary of Newton and a mathematician himself. The guy was of dubious reputation, and may have done plenty of plagiarism himself. At least some indications show that he collaborated with Newton on the subject of mathematic writings, was a fellow Royal Soceity member, and had helped Newton in the inquiries on IP infringement charges. I do suspect some potential for new and stunning information in this line.
Also Kaushal, a search with the similar sounding surnames in the Dr. Ambedkar's database of Brahman-s in India (link) , gives the following streams:

A) Dravida >> MAHARASHTRA >> Devarukhas
B) Gauda >> KANYAKUBJA >> Upadhyaya >> Devarainya
<!--QuoteBegin-Kaushal+Aug 23 2007, 11:28 AM-->QUOTE(Kaushal @ Aug 23 2007, 11:28 AM)<!--QuoteEBegin--><b>Shambhu, ON point 2 you are correct,  the devanagari should indicate a bh instead of b, and a ta instead of a tta or a tha.

On point 1 i stand by my meaning of cull which is to select from a large population. The meaning you have given is merely illustrative as  an example, than one which captures its general context.

anyway, glad you find the subject  of interest. send me a PM if you wish to discuss further, we can exchange phone numbers,

The link to My Webpage

Kaushal </b>

About point 1: OK. I had not read #9 in depth. My mistake!

PM: I tried, it says I cannot send a PM. Is something wrong/mis-set with my account? Is there another email where I can contact you..


****Added later: i found your gmail address through your site..sent you mail..
from Kaushal's blog:
<img src='http://img.photobucket.com/albums/v130/indiaforum/daivajnas2.jpg' border='0' alt='user posted image' />
<!--QuoteBegin-Shambhu+Aug 22 2007, 12:36 PM-->QUOTE(Shambhu @ Aug 22 2007, 12:36 PM)<!--QuoteEBegin-->This may be a mistake: On slide 24, though, Aryabhatta is written in as Aryabatha in

The correct form of his name is AryabhaTa though even in Sanskrit literature we find the occasional misspelling in the form of AryabhaTTa. The meaning of the name is less clear. Arya is of course clear. But bhaTa typically means soldier or fighter. The smR^itis also mention a bhaTa guild which is supposed to be born of an admixture of a brAhmaNa man with an actress/dancer. We have no evidence what so ever for AryabhaTa having been a soldier or having the above parentage.

Western scholars often overlook the traditional commentaries of AryabhaTa. One such is of the great mathematician nilakaNTha somayAjin (gaNita-pAda 10):
chaturadhikam shatam-ashTa-guNam dvA-ShaShTi-stathA sahasrANAm
Ayuta-dvaya-vishkambhasyAsanno vritta-pariNahaH.

This gives the approximation of PI ~ 62832/20000

nIlakaNTha comments that the word Asanno means that the value <b>approaches </b> pi and is incommensurate. This means that AryabhaTa had an idea of the irrationality of PI.


Something that might be of use to you: In marathi, the priests are called bhatji (bh from bharat, t from tamatar..I am using this because I do not have access to devanagari script here..)

In Konkani the priest is called bhatmaam (bhat as above plus maam, short for maamaa (uncle)

Good point about the irrationality of PI, HH.

There is no question that Nilakanta Somayajin ranks amongst the highest echelon of mathematicians of all time.

There is another point to be made. Namely the emphasis on sidereal measurements in Indian astronomy. The significance of this is not clearly brought out by Indic scholars. While there is no evidence of a clear exposition of t he Laws of motion as set forth by Newton, in the work of Indic mathematicians prior to Newton himself, the germ f the idea of an inertial frame of reference, is present when Indic astronomers introduced the Nakshatra system and integrated sidereal measurements in their calculations. Note that as late as 1530 when Mateo Ricci came to Malabar to learn Indic astronomy, sidereal measurements were unknown in the west. Conceptualization of the inertial frame of reference , a corollary of his laws of motion, was one of the great achievments of isaac Newton

As of now i am willing to accept that Newtons's work was original but we havent seen everything yet and there may be a possibility that Newton got some of his material from the Jesuits who in turn got it from the Kerala astronomers. Of course the Jesuits , who may have gotten the practical art of computation did not have the erudition and scholarship needed to conceptualize the laws until Newton came along.

But Newton when he saw the observations must have recognized the importance of sidereal date and the significance of a frame of reference which for all practical purposes could be considered at rest.

But the point i am making is that the indics were a hop step and a jump away from developing celestial mechanics (as opposed to the purely geometrical / trigonometrical calculations that they developed an immense facility in).

Shambhu, i got your email, will respond.

Bodhi , your remarks re. Newton have a lot of validity and need to be explored further

More later
bhaT (or bhaTT) remains one pan-Indian surname.

baT, bhaT in Kashmir
bhaT in kerala and Karnataka
bhaTTAcharya in Bengal
bhaT is very common in nepal

all are bhrAhmaN surnames.

Other than sarmA, varmA, guptA, pAl, and dAs, some more pan-India surnames that we can notice:

seTh, seThnA - central India
seThI - panjab
sheTTI - karnataka
cheTTI , cheTTiAr - TN
originally SreSThI. Higher class of vaishya-s


shAh - Panjab, Gujarat
sAhA - Bengal, Assam
sAhU - UP
sahAi - UP, Bihar
shAw - Gujarat?
<!--QuoteBegin-Bodhi+Aug 23 2007, 01:23 PM-->QUOTE(Bodhi @ Aug 23 2007, 01:23 PM)<!--QuoteEBegin--><b>Hope the recent findings of some UK-based historic-researchers have reached you</b> - they have shown that a distinguished Kairaliya tradition of Indic Mathematicians (e.g. Neelakantha) that continued till 13th c, must be credited with the founding of calculus - centuries before Newton.  And not only that it is not a coincidence that Europe/Newton suddenly discovered the subject - Jesuit missionaries and other Europeans of the period have the credit of smuggling / translating the Indic Mathematic treatise and transporting to Europe.

<b>This was widely reported in Indian news papers last week.</b>
[right][snapback]72392[/snapback][/right]<!--QuoteEnd--><!--QuoteEEnd-->Bodhi, would you post (any of) these links if you can? Thanks.

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