ATMW Development of Mathematics in India (2013)

Venue: IIT Bombay
Dates: 6th - 16th Feb, 2013


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)

Name K. Ramasubramanian     M. S. Sriram
Mailing Address Cell for Indian Science and Technology in Sanskrit
Department of HSS,IIT  Bombay Powai,
Mumbai - 400 076

Department of Theoretical Physics,
University of Madras,Guindy Campus,
Chennai - 600 025


Speakers and Syllabus 


(February 6–15, 2013)


8.30 – 9.30 (Jal Vihar Foyer)
Inaugural Function

Time: 9.30 – 10.45:  Venue: Jal Vihar Conference Hall

Introducing the Theme 9.30 – 9.35 Prof. K. Ramasubramanian
Coordinator of the Workshop
Opening Remarks 9.35 – 9.40 Prof. K. Narayanan
Head, Dept. of HSS, IIT Bombay
Welcome Address 9.40 – 9.45 Prof. Devang Khakhar
Director, IIT Bombay
Inaugural Address 9.45 – 9.55 Prof. Anil Kakodkar
Chairman, Board of Governers, IIT Bombay
Keynote Address 9.55 – 10.40 Prof. Roddam Narasimha
FRS, Hon. Professor, JNCASR
Vote of Thanks 10.40 – 10.45 Prof. M. S. Sriram
Coordinator of the Workshop
High Tea

10.45 –  11.15  (Jal Vihar Foyer )


ATMW Development of Mathematics in India (2013) - Speakers and Syllabus

1 .Introduction
Mathematics has been pursued in different ways in different civilizations, depending on the social, cultural, economic, and even the religious contexts. Though the contribution of Indians like the invention of zero, the decimal place value system, etc. have been recognized, not enough attention has been paid to the the many noteworthy and path-breaking developments in Indian mathematics, especially post-Bhaskara II, in standard popular accounts. Even many scholarly accounts are either not up-to-date or miss out on some important aspects of Indian mathematics.The proposed workshop aims to provide a comprehensive, detailed, and authentic account of mathematics in India starting from the Vedic times till the end of mediaval period to students and research scholars working in different areas of mathematics. It would also be open to some of the interested teachers of mathematics in colleges and universties who would be seriouslyinterested in learning the contributions of Indians to the advancement of mathematics. The workshop/conference would be held under the auspices of Cell for Indian Science and Tech-nology in Sanskrit, IIT Bombay during February 6–16, 2013.

2. Resourse Material
The first comprehensive account of Mathematics in India was provided by Datta and Singh about 6 decades ago. A number of  scholarly works have been written later by  A. K. Bag,   Saraswati Amma  and others, and recently there has also appeared a detailed survey of the development of Indian Mathematics by Kim Plofker.  As a part of the workshop, we intend to prepare resource material (≈ 400 pages) which may be given to the participants of the Workshop, which could serve as introduction and, wherever necessary, supplement to the above sources.

In the course of the workshop, we plan to present the growth of mathematics in India over a period of two millenia by broadly dividing it into three periods:

  • Mathematics in the Ancient Period (prior to 500 ce)
  • Mathematics during the Classical Age (500 – 1250 ce)
  • Mathematics in the Medieval Period (1250 – 1750 ce)


3. Resourse persons and disribution of topics

S.No. Name Affiliation
1 Prof. K. Ramasubramanian Dept. of HSS, IIT Bombay
2 Prof. M. D. Srinivas Chairman, Centre for Policy Studies, Chennai
3 Prof. M. S. Sriram Dept. of Theor. Physics, Univ. of Madras

We also plan to invite a few scholars such as Prof. Dani (formerly with TIFR), Prof. Amartya Dutta (ISI, Calcutta) and a few others to deliver guest lectures during the workshop, apart from their participation in the conference. Besides people from India, we expect a couple of international participants for the Conference.

The table below presents a brief outline of the topics to be covered/discussed by the resource persons during the workshop.

Resource person Outline of the topics to be covered
K. Ramasubramanian Mathematical concepts in ancient scriptures Vedas, Pur ̄nas,etc.; The geometry, arithmetic and algebra discussed in ́Sulbas ̄tras, including approximations to surds and construction of different types of citis; Mathematics in Jaina and Bauddha texts; Aryabhata’s number system, his construction of sine table, his discussion onsequences and series and the solution of quadratic and linear indeterminate equation, and so on.
M. S. Sriram Selected topics discussed in the Ganit ̄dhy ̄ya of Brahmagupta;Compuation of area and diagonals of a cyclic quadirlateral;Finding the volume of truncated pyramid; Solution to quadratic indeterminate equation; Second order interpolation formula dis-cussed in Khandakh ̄dyaka; The Bakshali Manuscript and some of the practical problems dealt in it; Certain interesting topics discussed in the works of Sr ipati; selected topics from the lilavati and Bijaganita of bhaskaracarya.
M. D. Srinivas Upapatti or Demonstration in Indian mathematics; Relation between mathematics and other S ̄stras; Detailed discussion onselected topics in Ganitakaumud ̄ of N ̄r ̄yana Pandita; The contributions of the Kerala school of mathematics; Discussionon the systematic exposition of mathematics in the works of Jyesthadeva and Sankara V ̄riyar; Carrying forward the tradition of Bh ̄skar ̄c ̄rya; Brief survey of Indian mathematics in the modern period. Combinatorics in Pingala’s works;



Session 1
   Session 2
   Session 3
   Session 4
Inauguration Function



Mathematics in Vedas and Sulvasutras (KR)





Introductory Overview (MDS)




Jaina Mathematics and Decimal place value sytem (KR)
Mathematics in
Aryabhatiya: Part I (KR)
Brahmagupta’s Brahma-sphuta-siddhanta (MSS) Mathematics & Other Sastras: Panini & Pingala
Seminar Presentation by Participants
Mathematics in
Aryabhatiya: Part II (KR)
Combinatorics (MDS) Mahavira’s Ganitasarasangraha
Seminar Presentation by Participants



Bhaskara’s Lilavati:
Part I (MSS)
Bakshali Manuscript (KR) Bijaganita of Bhaskara (MDS) Tutorial 1
Feb 10 Bhaskara’s Lilavati:
Part II (MSS)
Development of Calculus in Kerala School (MDS) Ganitakaumudi of Narayana Pandita: Part I (MSS) Tutorial 2
Ganitakaumudi of
Narayana Pandita:
Part II (MSS)
Magic Squares (KR) Proofs in Indian Mathematics (MDS) Kuttaka and Cryptography (AD)
Feb 12 Jyanayanam: From
Aryabhata to Madhava (KR)
Trigonometry of Bhaskara II & and Later works (MSS) Indian Mathematics in Modern period (MDS) Valedictory Function


MDS M. D. Srinivas
KR K. Ramasubramanian
MSS M. S. Sriram
AD Amartya Dutta (ISI, Calcutta)



Selected Applicants

Sr. SID Full Name Gender Affiliation State Position in College/ Univ. Univ./ Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Deg.
1 2296 Ms. Neha Yadav Male Motilal Nehru National Institute of Technology Uttar Pradesh Research Scholar Banasthali Univ., Jaipur 2009  --
2 2316 Mr. Manoj Kumar Patel Male FET-Gurukul Kangri Univ. Uttarakhand/ Uttaranchal Asst Prof Purvanchal Univ.,Jaunpur 2004 1 Jul 2011
3 2356 Mr. Arindum Mukhopadhyay Male IIT Kharagpur West Bengal Ph.D Student IIT Kharagpur 2009  --
4 2359 Dr. Anita Tomar Female Govt.Degree College Dakpathar Uttarakhand/ Uttaranchal Assoc Prof HPU Shimla 1985 10 Mar 2003
5 2371 Mr Tarun Kumar Gupta Male Gurukula Kangri Vishwavidyalaya Uttarakhand/ Uttaranchal Ph.D Student Gurukula Kangri Univ., Haridwar 2007  --
6 2382 Mr. Krishna Kumar Mohbey Male MANIT Bhopal Madhya Pradesh Ph.D Student RGPV Bhopal MP 2009 --
7 2389 Ms. Snehal Suryakant Mitragotri Female Department of Mathematics, Shivaji Univ., Kolhapur Maharashtra Asst Prof IIT, Roorkee 2009  --
8 2431 Mr. D. Easwaramoorthy Male The Gandhigram Rural Institute – Deemed Univ. Tamil Nadu Ph.D. Bharathidasan Univ., Tiruchirappalli. 2008  --
9 2489 Mr Sameer Ahmad Gupkari Male Got Degree College Jammu and Kashmir Asst Prof Univ. Of Kashmir 2003  --
10 2490 Mr Ajaz Ahmad Dar Male Govt Higher Institution Jammu and Kashmir Lecturer Univ. Of Kashmir 2003 --
11 2495 Mr Lok Bikash Gogoi Male Duliajan college Assam Assoc Prof Dibrugarh Univ. 1992  --
12 2531 Mr Laxmi Kalyan Paikroy Male Dalmia college , rajgangpur Orissa Lecturer Sambalpur Univ. 1991  --
13 2543 Dr Indrani Pramod Kelkar Female Acharya Institute of Technology, Bangalore Karnataka Professor I I T Mumbai 1986 25 Jun 2006
14 2622 Mr. Mahesh Puri Goswami Male Poornima Group of Institutions Rajasthan Asst Prof Central Univ. of Rajasthan 2012  --
15 2629 Ms. Arti Durlabhaji Chudasama Female Dr. Subhash Technical Campus Gujarat Asst. Prof. Sardar Patel Univ., V.V.Nagar 2010  --
16 2635 Mr Sajith Sajith Vs Male NSS College of Engineering, Palakkad Kerala Asst Prof Univ. of Kerala 2000  --
17 2643 Prof.K.Ram R Suresh Male Dept. Of Mathematics
College of Engineering
Kerala Asst Prof Univ. of Kerala 1988 --
18 2658 Mr. Abdul Nadim Khan Male AMU, Alighar Uttar Pradesh Research Scholar Bareilly college, Bareilly 2009  --
19 2694 Mr Manas Gajare Male KTHM College, Nashik Maharashtra Asso. Prof. KTHM College, Nashik 2012  --
20 2746 Mr. Ashesh Kumar Jharwal Male Shivaji College, Univ. of Delhi Delhi Asst Prof Ramjas College,Univ. of Rajasthan 2006  --
21 2764 Ms Vanishri Ganapati Bhat Female IIT Bombay Maharashtra Ph.D Student R S V P Tirupati 2007  --
22 2770 Ms. Swati Verma Female Banasthali Vidyapith Rajasthan Research Associate Delhi Univ. 2010 --
23 2780 Dr. Omkar Lal Shrivastava Male Govt. Digvijay P.G. College Rajnandgaon Chhattisgarh Asst Prof H.S.Gaur Univ. Sagar 1988 24 May 2007
24 2785 Ms. Rupali Vijay Kavishwar Female Univ. of Pune Maharashtra Ph.D Student M.A.(Sanskrit) 2005 --
25 2789 Mr. A Manivel Male Pachaiyappa's college Tamil Nadu M.Phil Univ. of Madras 2012  --
26 2794 Mr. Piyush Goyal Male S.C.D. Govt College for Boys, Ludhiana Punjab Lecturer Panjab Univ., Chandigarh 2011 --
27 2798 Mr. Sudhansu Kumar Nanda Male R.S.Vidyapeetha, Ttirupati Andhra Pradesh Research Scholar M.A. in siddhanta jyotish 2011  --
28 2807 Mrs Shailaja Mahadeva Female Government First Grade College, Bangalore Univ. Karnataka Asst Prof Bangalore Univ. 1992  --
29 2809 Mrs Rupa Ravi Prasad Female Global Academy of Technology Karnataka Asso.Prof M.Sc/MES college/Bangalore 1998 --
30 2815 Mrs Vanaja Venkatachalaiah C.N Female Government First Grade College Karnataka Asst Prof Bangalore 2001  --
31 2816 Ms. Kondapalli Krishna Sowmya Female Osmania Univ. College for Women Andhra Pradesh Asst. Prof. (c) National Institute Of Mathematics, Calicut 2010  --
32 2842 Prof. Ramana Murthy Venkata Josyula Male National Institute of Technology Warangal Andhra Pradesh Professor Regional Engineering College, Warangal M.Sc 1983 19 May 1991
33 2846 Mrs Santhi Thiagarajan Female JKK Nataraja College Of Arts And Science Tamil Nadu Asst Prof RIASM, Univ. OF MADRAS 2000  --
34 2855 Dr. Tarun Kumar Garg Male Working as Satyawati College Delhi Assoc Prof M.D.Univ. Rohtak, Haryana 1992 7 Jul 1999
35 2861 Mr. Vinay Arora Male Panjab Univ. Ssg Regional Centre Punjab Asst Prof Panjab Univ. CHANDIGARH 2001 --
36 2867 Dr Ram Prakash Sharma Male JECRC Univ. Rajasthan Professor Univ. Of Rajasthan 1992  --
37 2869 Dr. U K V Sarma Male IIT Bombay Maharashtra Research Associate Rashtriya Sanskrit Vidyapeetha, Tirupati 2003 18 Aug 2012


Waiting list

Sr. SID Full Name Gender Affiliation
State Position in College/ Univ Univ/ Institute M.Sc./M.A. Year of Passing M.Sc./M.A Ph.D. Degree Date
1 2318 Dr. Somna Mishra Female Institute of Management Studies, Noida Uttar Pradesh Asst Prof Gurukula Kangri Vishwavidyalaya, Haridwar 2002 12 Sep 2007
2 2598 Mr. Sanyam Gupta Male Delhi Univ Delhi Student Delhi Univ Awaiting Result --
3 2630 Ms. Arnika Tripathi Female NITK Suratkhal Karnataka Student DR B R A Univ Agra 2008 --
4 2703 Mr. Arjun Gupta Male Gurukul kangri vishwavidayalya Uttarakhand/ Uttaranchal Research scholar Kurukshetra Univ. kurukshetra 2003 --
5 2795 Mr G Arockia Prabakar Male The Gandhigram Rural Institute – Deemed Univ Tamil Nadu Research scholar Loyola College 2008 --
6 2804 Dr. Sanjib Choudhury Male North Eastern Regional Institute of Science and Technology Arunachal Pradesh Guest Lecturer Gauhati Univ 2003 6 Oct 2012
7 2840 Dr Ashok Kumar Goli Male M.V.G.R.R. Degree college Andhra Pradesh Reader In Mathematics Osmania Univ, Hyderabad 1986 4 May 1992