“Professor, 2 minutes remaining!”
“OK, I am about to finish, ... so I can skip this now”; the
speaker says thinking of the content that he “must” say before he stops; “… so
coming to conclusion…” and then he finishes his talk. Exactly 15 minutes after
that for question answer session and as the minutes hand meets the hour hand in
the clock to state 12 noon, the second plenary session of each day would
conclude.
Well, as Dr Agarkar put it in his thanksgiving address at
last, it would have been unfair or sort of disrespect to Bhaskaracharya; had
the schedule not scrupulously been adhered to! One of the motives of such
events is to show a new perspective for looking towards ourselves and indeed,
this seemingly small thing called punctuality made everybody feel that in India
as well, we can ruthlessly stick to the planned schedule. Such a disciplined organization made “Bhaskara 900” really memorable for everybody who
participated. I have not seen such punctuality at any other public
events in India.
I am talking about Bhaskara 900 – a conference arranged in
memory of a great poet, mathematician, astronomer and learned scholar of 12th
century India – Bhaskaracharya, also known as Bhaskara II in literature. Probably, he is the pre-modern Indian mathematician with maximum surviving literature. In fact, some of his texts are still taught in traditional Maths (मठ) and Peethas (पीठ). The conference was held, as the
name suggests, to celebrate 900th birth anniversary of Bhaskara.
Yes, he was born about 500 years before Newton and Leibnitz!(#)
The conference was arranged by Vidya Prasarak Mandal (VPM) a
private educational trust in Thane, Maharashtra, and held at Joshi Bedekar College Campus,
Thane. It started at 19th of September and ended on 21st
of September. A day before that, i.e. on 18th, Dr Anil Kakodakar inaugurated the conference.
All the three days were filled with scholarly talks and discussions
in a healthy academic atmosphere. Eminent scholars like K Ramasubramanian from
IIT Bombay to Bhalanchadra Rao from Bengaluru and from Kim Plofker in US to
Michio Yano in Japan made conference really an intellectual treat to
experience. A day would start with three plenary lectures starting from 9.30 am
to 1 pm. Afternoon session was devoted to paper
presentations. That would run upto 6 pm.
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| Dr Bedekar with Prof Ramasubramaniam |
Topics for plenary lectures were chosen from wide spectrum
so that no corner of the Bhaskaracharaya’s life should remain unexplored. On day
1, renowned mathematician Prof S G Dani, who is now Emeritus Professor at IITB,
set the context for the conference. He said that "observing events in hindsight i.e. history, by itself, is a new branch of study per. Hence, the discipline of history of science and
mathematics is still "newer"... While studying life and works of any mathematician, his place of origin
or nationality should be a secondary aspect compared to his texts or mathematics". In next lecture Prof K Ramasubramanian illustrated the “Leela in Leelawati”; i.e. the charm in
Leelawati (Leelawati is the first part of Bhaskara's Siddhanta-Shiromani). He uncovered poetic aspect of Leelawati so well, that audience felt
like attending a literature class. Prof Pierre Filliozat would talk on a
similar topic the next day. As most of the Indian mathematicians’ work is in
non-prose form, poetical aspects of the work also present a distinctive branch of study in itself.
Particularly, the Leelawati is no less than a masterpiece of perfect blend of
Maths and Poetry.
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| Prof Pierre illustrating poetic aspects of Leelawati in a plenary talk |
On the last day Prof S R Sarma talked about instruments
used in Bhaskara’s time. "While Bhaskara describes many instruments in his work, he
disqualifies all of the complicated instruments like Golayantra and Vadhuvarayantra (वधूवरयन्त्र )
against a simple shanku (शङकू) or gnomon. Probably, he was concerned that the complicated machines are not required when results can be obtained with simple instruments. In one of the plenary sessions, Prof
Jamkhedkar from Mumbai University discussed times of Bhaskaracharya in his talk titled “Learning and
Patronage in 12th -13th Century A.D.: Bhaskarācarya and the Śāndilya Family”.
This lecture shed light on the socio-political situation of Bhaskara’s times.
"The central India or Deccan was in political turmoil in Bhaskara’s
period. Prof Jamkhedkar presented with many proofs how Bhaskara and his family defied the generalized law that political stability is essential for arts and science to
flourish - there were at least 8 generations in Bhaskara’s family who were
mathematicians, astronomers and astrologers – daivajna (दैवज्ञ)– one who know
fate.
Colleagues of Prof Ramasubramanian – Dr M S Sriram and Dr M
D Srinivasa delivered lectures on Vasanabhasya and Grahaganitadhyaya
respectively. Together, they have already compiled history of Mathematics in India in form a course available on NPTEL. Their talks were evidence of the depth of their study and the urge to decode the unknown
portions of works of Indian mathematicians. Apart from this, Dr Sita Sundar Ram
from Chennai spoke about Bijaganita (बीजगणित) in her plenary lecture. Bijaganita
is second section of Siddhanta-Shiromani and is a text primarily focused on algebra.
On the last day, Prof Bhalachandra Rao delivered plenary lecture on “Importance of KaranaKutuhala
as an algorithmic book”. Prof Rao is a retired professor of Mathematics. He
works at Gandhi Centre for Studies and Bengaluru and does research on works of
Indian Mathematicians.
Due to sheer number of papers, there was no alternative but
to run paper presentations in parallel. This is, in a way, a good indication to
the fact that more people have started working in this field. However, we,
participants had to choose only one of the two papers running in parallel. But,
due to strict adherence to the time table, it was never a case that a person
would miss a paper at a location, because paper at another location never exceeded the
prescribed time. Every paper presentation session was chaired by some renowned
scholar.
A session on Day 2 was particularly remarkable as it was devoted to the pedagogical aspects of Bhaskara’s works.
Particularly noteworthy were talks of Prof Hari Koirala who is originally from
Nepal, and now is Professor of Mathematics Education in US; and Dr S Agarkar
who is one of the organizers of the conference. Dr Agarkar has been conducting
workshops for students to let them sneak peek into Bhaskara's Mathematics and in particular, Leelawati. As per his observation, students in India are simply unaware about Bhaskara. He explained how interactive problem
solving (with problems in Leelawati), helps to keep school students engaged for 90
minutes. Almost all procedures/theorem in Leelawati are followed by a poetic verse which describes an example of the procedure just explained. For example, this verse appears after Bhaskara states about addition of numbers -
अये बाले लीलवति
मतिमति ब्रूहि सहितान्
द्विपञ्चद्वात्रिंशत्त्रिनवतिशताष्टादश
दश ...
Thus, Bhaskara is explaining the problem
in excellent “प्रासादिक” verse to little Leelawati. This poetic touch to Maths, imbibed within the textbook, can make Mathematics really interesting. Both Dr Agarkar and Dr Koirala discussed how these various methods can be
implemented. Prof Koirala explained how these methods coincide with some of the principles in common core standards formulated for Math education at secondary school level in US.
After a day of intellectual exercise, the two evenings were feasts of two
cultural programs. In particular, on 20th of September, we witnessed a great show. It was a perfect brew of Indian Classical music and dance
along with Mathematics from Leelawati. In Leelawati many verses are addressed to a girl or lady named Leelawati. This theme was
beautifully woven into a play presented by students of Rishi Valley School in
Andhra Pradesh. The verses in Leelawati were played in background as voiceover
while students acted and danced for the problems stated in the verse. E.g. For the famous
Peacock-Snake problem in Leelawati, a girl became peacock, another
personified a snake while a third one – the pillar. In the end, all formed a
right angled triangle. After the show, everybody was so mesmerized that people
forgot the dinner! It was not a surprise that it received a standing
ovation from the audience. It was really a beautiful portrayal of Mathematics.
 |
| Performers with Prof Ramasubramaniam and Dr Clemency |
The last session of the whole conference was also notable. Prof Kim Plofker
talked on Siddhānta-Karana Conversion: Some algorithms in the
Ganitādhyāya of the Siddhāntaśiromani and in the Karanakutūhala”. The last
paper was presented by Prof Clemency Montelle from Newzealand. She explained
about her work about decoding various tables used as reference to carry out
astronomical conversions.
Padmashri Dr D B Phatak was chief guest for valedictory
function. He is a professor in Computer Science Engineering Department of IIT
Bombay.
He emphasized on dire need of good teaching Considering sheer number of students in countries like India, and hence, the necessity of
online education and reaching to masses. While special domains like study of history of mathematics attract a small group of scholars, large population in Indian is simply not aware of the topics like these and hence we need to reach out to thousands to make these topics familiar to them. It may
happen that only 10 out of thousand will really take up this topic further. But
we do not know which 10!
 |
| Galaxy of assembled scholars |
Overall, the conference not only made me aware of the sheer depth as well as spectrum of topics covered by Bhaskara in his works but also the topics of research that are auxiliary to Mathematics in Bhaskara's work. While there is no Government event arranged for Bhaskara, the Government institutes are not inactive. An International Conference on History and Development of Mathematics (ICHDM) is arranged in November in Pune. People working in various disciplines of Science and Technology should look into its history as it is not only exciting field but also of importance from perspective of documentation of the same for future generations.
