38 - The Evolution of Simple Sums


ISSUE No. 38

A warm welcome to new subscribers.

Vedic Mathematics is becoming increasingly popular as more and more people are introduced to the beautifully unified and easy Vedic methods. The purpose of this Newsletter is to provide information about developments in education and research and books, articles, courses, talks etc., and also to bring together those working with Vedic Mathematics. If you are working with Vedic Mathematics - teaching it or doing research - please contact us and let us include you and some description of your work in the Newsletter. Perhaps you would like to submit an article for inclusion in a later issue or tell us about a course or talk you will be giving or have given.

If you are learning Vedic Maths, let us know how you are getting on and what you think of this system.


This issue’s article is written by Dr Brian McEnery, an Irish computer expert and researcher who is developing a project called “Simple Sums”. More details about the web site are given later in this newsletter.

The Evolution of Simple Sums

Brian Mc Enery PhD

In the late 1980's whilst completing a PhD in computation in University College Cork, I observed the rapid development of graphical user interfaces, and the development of a number of software systems for doing computer based mathematics. I considered the potential for developing a system for both learning and teaching mathematics at home or in school. Such a system could employ the object oriented technologies then being developed to create 'intelligent' representations of mathematical objects and processes.

However I was also aware of the necessity to ensure that the computational technology did not overpower the student to the extent that they became a mere passive observer to the performance. Dynamic interaction and continued input from the student was a necessary design criterion. Students could be enabled to discover mathematics.

At this time, one thing that concerned me was the rigidity in thought which I encountered amongst students who were taking my course in Numerical Methods, which comprised, a little bit of mathematics, a little bit of physics, and a little bit of computing.

Many of these students performed very well in standard mathematical courses, however when it came to applying mathematics in a practical computational situation, they were often bewildered without a precise formula. It was as if they had become great symbol manipulators, but had little skill when it came to numbers. This concerned me, and I discovered why.

In all the six years that I lectured in UCC, only one lecture stands out. At the time I was endeavouring to teach the concept of errors in function approximation, a concept that students often had difficulty with. I also happened to be reading a book[1] about drawing, where the author discussed the concept of negative space. I realised a connection. To draw a chair you draw the holes, or spaces. The error in the function approximation was the negative space between the true function and it's approximant. I recall speaking for forty minutes on this concept, and its implications in the field of computation. Unusually you could have heard a pin drop. On my way back to my office, I thought, 'that was wonderful.' Back in the office I thought, 'but I can't examine

it.' I had realised that there was something fundamentally wrong. It wasn't the students fault, but their only experience was of an educational system geared towards the pedantic presentation of information as knowledge, for the purpose of examination.

A short while later I left the formal academic system to pursue independent research on a number of ideas. As luck would have it, or perhaps serendipity, I came across two little books, then being used to revive Vedic Mathematics in schools in India. They charmed me.

Here were techniques that I had never seen in school, Here was how computation could and should be taught to students. Here was the missing key element in practical mathematics.

So I set about studying Vedic Mathematics. I obtained a copy of Tirthaji's book [2], and I obtained some books from Kenneth Williams [3] in the U.K. It wasn't always easy. In a sense at times my own training rebelled.

I used to sit at the kitchen table doing my sums whilst at times I thought 'here am I a PhD, I should be doing something more important.' But I persisted and gradually began to comprehend the true nature of Vedic computation. It is much more than a set of techniques for developing skills in rapid mental calculation, or for performing algebraic manipulations with dexterity and ease, it is a framework within which any mathematical or computational process can be resolved. I used to feel that it was more akin to experimentation in Physics, than to the formal logical structure known as

Western mathematics. The beauty of it, is, that it can be systematically taught to young and old.

After five years of study and research, an opportunity arose to begin making practical demonstrations of Vedic mathematics. It was occasioned by the announcement. in September 1997, that the Department of Education were about to introduce a new curriculum. I wrote to the then Minister for Education seeking an opportunity to give a demonstration of these techniques. Whilst awaiting a response, I availed of every opportunity to give demonstrations to groups of parents, teachers and students. The techniques were always very well received.

After about six to eight months a meeting was arranged with two Mathematics Inspectors from the Department of Education. During the presentation I detected a little bit of reticence, in their response. They appeared to be more concerned that students would gain a deep understanding of a few computational techniques, rather than being exposed to a wide variety of computational skills. This concerned me, however I did get one idea.

At the end of our meeting, one of the inspectors said that if a computerised version of some of this knowledge suitable for schools, could be developed, then it may be much easier to integrate it with the current approach. I also realised one other important fact, that this approach to computation would have to be adapted into Irish.

Some time later together with two friends I initiated the Simple Sums Project, which in essence was to revive the software development idea of ten years earlier, but now including the missing key element of Vedic Mathematics. This project has continued since 1998.

At the outset we developed plans for the delivery of computer based knowledge, to home and school. We felt that it was important to include the facility whereby parents would have access to new knowledge, whenever it was brought into schools, thereby preventing the type of problem which arose with the introduction of the New Mathematics some decades earlier. We also began the process of software development, and after nine months were able to publish preliminary result on the Internet. These results included some adaptations of Vedic mathematics into Irish. A significant aspect of this period of research and design was the development of the conceptual basis for animating mathematics, including a number of examples. We realised that many of the techniques could be presented very clearly using simple animations. This has remained one of the core elements of the project. Another significant element at this stage was the conceptual design of an interactive calculator. A calculator which a student or adult could use, not just to get an answer, but to be shown a technique, or range of techniques for finding an answer.

Most of this early work was concerned purely with arithmetic, because we felt that here the key principles of Vedic mathematics could be presented most clearly. Also here was the most pressing need. During the many presentations which I continued to give it was always parents who expressed the greatest encouragement and support. Many were clearly unhappy with the current approach to teaching mathematics particularly in Primary schools. We felt that if the formal educational system could not accept this knowledge, parents at least would.

Over the ensuing years we explored the potential for developing mathematical animations in a number of software systems, always aiming at developing fully interactive, dynamic, object oriented components. Managing animations, simply, was a major focus of our development work. We also needed to ensure that our animathics as we now called them could be delivered in a variety of formats, either on CD, or in Games, or in a more standard learning environment suitable for schools and available on the Internet.

In parallel with the software development, a number of other opportunities arose. A series of short courses in national schools, in Cork. An opportunity to brief the Minister for Science and Technology on our work. The opportunity to present for the first time Vedic mathematics to a class of nine year olds through Irish. The opportunity to interact with teachers and students at the Young Scientist's and Technologists Exhibition in Dublin, in January 2003. All of these opportunities helped to develop our understanding of the type of software which we should develop. There

were even opportunities to make presentations on Vedic mathematics on the radio.

As a result of this work we launched a course entitled Simple Sums: Mental Tricks for Arithmetic, in Cork, in April 2003. The opening night was attended by parents, teachers, and parents with children. I particularly recall parents explaining the techniques which I demonstrated, to their children, whilst I led the adults to more abstract levels of understanding. The initial course lasted for five weeks, and formed the basis for the design of a two day immersion course which could be taken by students and their teachers in schools.

Meanwhile we had finally identified a suitable software system which would allow the development of fully interactive mathematical animations. We commenced work on this systematic research and design in September 2003 and completed this phase of the project in April 2004. As part of this research and design we had identified the key steps required to adapt the Simple Sums approach to more than twenty European and Middle Eastern languages. We had also identified the software system which would allow students, parents or teachers to write simple English like scripts to create their own animathics. Naturally these developments will take time.

We launched the Simple Sums web-site on May 1 2004, and included a Flash animation depicting an animathic for multiplying by 11. The site continues to develop. At present the animations are being produced using Objected Oriented components designed using Macromedia Flash. These are very good for displaying the concept and structures within the design, they are also widely portable across computer systems. However the development of scriptable animathics, giving the student, parent or teacher full access to the capabilities of Simple Sums will require the creation of a native Animathics Player, initially on one system. At present this looks most likely to be on Mac OSX using Cocoa and Applescript. This will also enable us to begin the detailed research and design for the interactive calculator.

As part of this project we have also explored the potential for using sound. In many multimedia presentations, sound is included, but is not integrated deeply within the knowledge being presented. We feel that this is an area which deserves a lot more research. Consider our conceptual example of, The Harmony of the Spheres. We build a computational model of the solar system. We represent the position and motion of the planets as sounds, based on measurements from Earth. We hear the retrograde motion of planets. We then move our point of observation towards the sun, on the

spaceship Gallileo. We begin to hear harmony and order. This in fact is where my own research began, I now call it acoustic graphics.

9 June 2004


[1] Edwards, Drawing on the Right Hand Side of the Brain, Fontana/Collins, 1979

[2] Tirthaji, Vedic Mathematics, Motilal Banarsidass, 1960.

[3] Williams, Discover Vedic Mathematics, 1984; Triples, 1984; The Cosmic Computer, Inspiration Books, 1997 ( with Gaskell).





Jain will be one of the guest speakers at the next International Nexus Conference (Friday 24th—Saturday 25th—Sunday 26th September 2004. Venue: The Chifley at Lennons, Queen St., Brisbane, Australia). He would like to invite you to attend a fascinating 1 and a half hour Lecture on the bridging of Vedic Mathematics, Magic Squares and Sacred Geometry on Friday the 24th September 2004, 11.30am to 1pm. 

You can also check his website: www.jainmathemagics.com for further details to book online for a post-Conference 2-day workshop on the 27th and 28th September.

He will also be teaching in Sydney and Canberra all of June and then to America as a guest speaker at the International Feng Shui Conference in San Luis Obispo, California from the 6th to 8th August. Boulder, Colorado in September. Back to Brisbane for the Nexus Conference).


1) August 1st week : VM Workshops for 2 / 3 days in Ahmedabad; WAVM in collaboration with L D Institute of Indology

2) October 2nd week : VM Workshops for about one week in Varanasi; WAVM in collaboration with Krishnamurti Foundation of India, Varanasi

3) Negotiations are still on with N. I. E (Newspaper in Education - TOI) for organising / conducting Introductory workshops in Delhi schools & this time WAVM will cover many more schools extensively & intensively; these events may take place after monsoon.

To enquire further about these courses see the World Academy contact details later in this newsletter.





Overview by ABHISHEK BAGCHI (Currently pursuing research on image processing & neural network algorithms in ISI Kolkata)

                 The World Academy for Vedic Mathematics, an integral part of the main foundation in Nagpur, the International Research & Resource Foundation for Indian Heritage is the most respected body working for the cause of Vedic Mathematics across the world. The Academy, in association with Birla High School -Kolkata (Junior Section), organized an introductory workshop on Vedic mathematics in their school premises on 27th April 2004.The workshop though initially was planned for two and half hours continued for half an hour more due to the positive response of the participants. Debmalya Banerjee, the faculty of the academy on the subject from KOLKATA, conducted the event.

                  The response of the crowd was overwhelming. Lot of questions were asked as the workshop had interactive session too. The expert not only explained the Vedic Methods of Calculation but also gave a brief introduction of the subject too. He also narrated to the crowd the kind of activities the academy has done in the past and what it intends to do in future. He also told the crowd in brief what activities are going on globally.

A comprehensive idea about Vedic Maths supported by examples in Nikhilam, Ekadhikena Purvena, Urdhava Tiryagbvyam etc. were shown and also various types of multiplication rules were explained.

The most interesting observations of the Workshop are as follows:

·        The participants included 39 teachers of the junior section of the school.

·        The age of the participants ranged from twenty-three to fifty nine.

·        In the feedback worksheet that was given, most of the participants gave the rating as excellent due to the quality of the workshop.

·        The teachers openly confessed that they never felt bored at any time during the entire session.

·        The school is interested to organize a workshop for their senior students in the future.




Simple Sums OnLine

A new web site has just been launched at www.simplesums.ie, featuring mathematical animations which incorporate aspects of Vedic mathematics.

The Simple Sums project was founded  by Dr. Brian Mc Enery who holds a doctorate in modern computation from University College Cork in Ireland. For the past twelve years he has been conducting research on the correlation between the methods of Vedic mathematics and the methods of modern computation. In 1997 after a meeting with the Department of Education in Ireland he was inspired to initiate a project to develop a computer based system for both learning and teaching computation  The simplicity, accuracy, variety and dynamism of the Vedic techniques immediately suggested the development of mathematical based animations.

The Simple Sums web site features aspects of the research and design phase of the project and over the coming months the site will be expanded to include areas of interest to students, parents, teachers, and software designers who would be interested in pioneering a new, and innovative approach to expressing both mathematical and computational knowledge.

Of particular interest to the site designers at present is to make contact with people who would have an interest in localization, the adaptation of the animathics into their own local expressions of knowledge. Dr. Mc Enery and his team have already begun this work by developing an expression for the first sutra "one more than", in more than twenty European and Middle Eastern languages.

The site features a simple animation which depicts a method for multiplying a number by 11. This is available in both Irish and English, and suggests one intriguing possibility. To use the simple techniques of Vedic computation in arithmetic to establish a completely new way for teaching languages. Use simple sums as the common bridge.


The first two of a series of CD’s are available from Leading Edge Solutions and marketed by BPB Multimedia: www.bpbonline.com


Lui Di Martino who wrote an article for this newsletter some time ago has completed a book. He writes: “Just writing to let you know that I have finished a book I have spent fifteen years getting together. There is a lot of information in this book about the Vedic square and how it relates to music , as well as being a catalyst for a unique "mirror structure". It can even be shown that the Vedic square is  running through the veins of other systems, like the I-Ching hexagrams, the Tzolkin grid, the Fibonacci numbers, and the astrological charts of the twelve star signs. I am not sure if it has any mathematical inspiration for anyone, but nevertheless the information in the book does show some new insights into this Vedic Square.”

The book can be found at www.omtron.com

FROM Govind K. Bahroos

During the Summer Vacation in Mumbai (India)  I have taught more than 150 Students  and till date, i. e. unto 31st May 2004,more than 500 students have learned VM from me. I teach in School as well as privately in the evening time. (During the day I take care of my own Chemical Factory.) From next academy year from June I will teach VM in three more schools. 


From Govind K. Bahroos: Please let me know the name of tutor in Ahmedabad  in India. I have more than twenty students over there who want to learn VM.

You  can reply to Govind K. Bahroos or to us at mailto:



EMAIL:  It is confirmed to have VM methods as the best way for the competitive exams for students because of the fast mental calculations. Equally its wonderful tool for senior students of Pune University who are writing algorithms for complex mathematical problems in the area of linear programming, matrix inversions and optimizations techniques in Operations Research.

EMAIL: I am a Doctorate student at Rutgers University, NJ, USA. I have done by Bachelor of Engineering in Computer Science from SVNIT and worked as Software Engg. with Wipro Technologies and Hewlett-Packard before joining MS+Phd in CS at Rutgers University.

I have been an avid follower of Vedic Mathematics from a young age and have read a couple of books too.  Without doubt it has helped me sharpen my mathematical skills and made complex looking formulas and concepts look easy. I would like to be part of this global community to keep abreast with the current affairs in Vedic Mathematics and at the same time would be glad if I can contribute in any way towards the propagation of Vedic Mathematics.


World Academy for Vedic Mathematics – contact details

Registered Address: Vishwa Punarnirman Sangh, Raval Bhawan, Near Telankhedi Garden, Nagpur-440 001, India.

Contacts in other Cities in India :

Delhi                R.P. Jain, MLBD bookstore

91(011) 2385-2747 / 2385-4826 / 2385-8335 / 2385-1985.


Varanasi            91 (0542) 2352331
Kolkata            MLBD bookstore 91 (033) 22824872
Mumbai            MLBD bookstore 91 (022) 24923526 / 24982583
Nagpur             Alka Sahani 91 (0712) 2531363 / 2550906 / 2545637
Pune                 MLBD bookstore 91 (020) 24486190
                        Dr. Bhavsar 91 (020) 25899509 / 21115901
Bangalore                 School of Ancient Wisdom – Devanahalli, 91 (080) 768-2181 / 7682182 / 558-6837
                          MLBD bookstore 91 (080) 6533729 / 6542591
Chennai                    91 (044) 24982315


Your comments about this Newsletter are invited.

If you would like to send us details about your work or submit an article or details about a course/talk etc. for inclusion, please let us know on

Previous issues of this Newsletter can be copied from the Web Site: www.vedicmaths.org

Some articles from previous newsletters are:

Issue 1: An Introduction
Issue 2: "So What's so Special about Vedic Mathematics?"
Issue 3: Sri Bharati Krsna Tirthaji: More than a Mathematical Genius
Issue 4: The Vedic Numerical Code
Issue 6: The Sutras of Vedic Mathematics
Issue 7: The Vedic Square
Issue 8: The Nine Point Circle
Issue 11: Is Knowledge Essentially Simple?
Issue 14: 1,2,3,4: Pythagoras and the Cosmology of Number
Issue 16: Vedic Matrix
Issue 17: Vedic Sources of Vedic Mathematics
Issue 18: 9 by 9 Division Table
Issue 19: “Maths Mantra”
Issue 20: Numeracy
Issue 21: Only a Matter of 16 Sutras
Issue 22: Multiplication on the Fingertips
Issue 23: India’s System of Mental Mathematics
Issue 24: The Sign of Nine
Issue 25: Maharishi’s Vedic Mathematics
Issue 26: Foreword
Issue 27: Mathematics with Smiles: the Vedic Way
Issue 28: The Absolute Number
Issue 29: Report on India Tour
Issue 30: Vedic mathematics – excerpts from research paper
Issue 31: Why Vedic Mathematics?
Issue 32: Kolkata Workshop – an Overview
Issue 33: Report on Vedic Mathematics Workshop
Issue 36: WAVM Brochure
Issue 37: VM PROJECT

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Please pass a copy of this Newsletter on (unedited) to anyone you think may be interested.

Editor: Kenneth Williams

Visit the Vedic Mathematics web site at



15th June 2004


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