Vedic maths. Facts + fiction = fantastic

It has been said that truth is stranger than fiction.  That is certainly true when it comes to the story of the origins of “Vedic” maths.  

Vedic mathematics first came to light in a book published in 1965 by the impressively named Bharati Krishna Tirthaji - an Indian mathematician ...and mystic. Tirathji claimed to have rediscovered Vedic mathematics after meditating on some neglected sacred scripts. This is where the story gets a tad bizarre - for there is no evidence in the Sutras of anything vaguely resembling the mathematics that Tirthaji proposed.  He is reported to have spent eight years meditating in a forest in order to discern the hidden mathematics.  This has been likened by Alex Bellos, author of “Alex’s Adventures in Numberland”, as  being akin to a “...a vicar announcing he had found a method for solving quadratic equations in the Bible”. When challenged by other Indian mathematicians who could read Sanskrit to identify the passages upon which he based his mathematics Tirthaji claimed that the messages were in his texts and in no other.  There was also mention of a 16 volume manuscript that Tirathji had written dealing with the subject - but which had somehow been lost prior to publication - indeed prior to him sharing it with a single other person. Such loss apparently did not disturb Tirathji who simply said he would re-write it from memory.  The first, and only book published (posthumously) was but a fraction of the mathematics that he claimed to have re-discovered in the sacred texts.   (A detailed discussion on the story of the “discovery” of Vedic mathematics can be found here.)  

In short, it appears unlikely that the mathematical techniques mentioned were “discovered” in any ancient Vedic text.  Intrigued by the power and simplicity of the mathematics Alex Bellos did some research to see if the techniques had been mentioned elsewhere, and it turns out that one of them, Vertically and Crosswise,  had been published in none other than Fibonnaci’s Liber Abaci (published in 1202 and credited with introducing Hindu-Arabic numerals and calculation techniques to Europe).  Another, All from 9 and the last from 10,  was apparently  a wide spread technique in Europe in the sixteenth-century - so wide spread that it may have been the origin of our current symbol for multiplication.

However, although many would find the story of the “re-discovery” of Vedic mathematics fanciful it is undeniable that the approaches  described in Tirathji’s text actually work.  In some cases they are no more efficient than contemporary approaches but in others they clearly are.  

Two of the techniques describes as “Vedic” maths that can be traced to European sources are All from 9 and the last from 10 and Vertically and Crosswise. Both are worth exploring.

All from 9 and the last from 10 is essentially a quick mental maths trick with limited application - the approach as depicted here can only be used when subtracting numbers from multiples of 10 (in other words 100, 1000, 10 000 etc.) but with minor modification can be used with any number ending in zero.  However it is useful in illustrating the nature of Vedic maths.  With this approach to subtraction you work from left to right and subtract all digits being subtracted from 9 except for the last digit which is subtracted from 10.

1000 - 578 becomes

1000
-  578 (SUBTRACT the 5 and 7 from 9 and the 8 from 10)
= 422

Although limited in application it is easy to see how this might be a useful skill when using money for example.

A technique with wider application is  Vertically and Crosswise which allows rapid calculation by multiplication. Consider 63 x 28. The Vedic method would be;

Step 1. Write the digits being multiplied on top of each other.

6 3

2 8

Step 2. Multiply the numbers in the right hand column (24).  Write the 4 in the units column and carry the 2.

6 3

2 8

                                                                   2  4
Step 3.  Multiply diagonally opposite numbers (cross-wise) and then add the products (multiply 6 X 8 = 48, 2 X 3 = 6, 48 +6=54.  Use the carried 2 from the previous stage = 56. Write the 6 and carry the 5

6 3

2 8

                                                                5  6 4
Step 4. Multiply the left hand column (6 x 2 = 12)  Add the 5 being carried (12 + 5 = 17). Write the 17 to the left of the answer thus:

6 3

2 8

                                                               1 7 6 4


For those who prefer a more visual explanation this video gives a good indication of how the process works.

At first glance using two digits like this the process might easily be dismissed as a novelty and only marginally more efficient than  the “traditional” approach.  But when three or four digit numbers are being calculated (or indeed any  large number) the same method is employed and needs only one line of working.  It is much quicker than the standard approach to this problem - much more efficient.

Those wishing to explore some of the techniques might like to visit this site which provides opportunities to practice some of the techniques and this link to a free manual for teachers. This latter resource contains much that is not purely related to “vedic mathematics” and offers some sound techniques for teaching mental calculation techniques.There are more techniques than presented here to examine and explore - far more than could be presented in a post such as this.

I believe it would be unwise to teach this approach to young children. However, to students who have been introduced to and understand the principles and concepts of conventional mathematics this approach might add interest  and intrigue - and would promote mathematics as something worthy of exploration.    

There is much of worth in Vedic mathematics.  The murky story of its “re-discovery” should allow the story teller that is  in every effective teacher to create the setting for some effective exploration of mathematics.  At worst it still has to be better than providing yet another worksheet...

~~~~~~~~~~~~~~~~~~

Credits;

• Image of Tirthaji: http://www.vedicmaths.org/Introduction/History/Tirthaji.jpg
• Links provided in text to original sources.
• Alex Bellos, 2010, Alex’s Adventures in Numberland”

If you enjoyed this post you may enjoy my other maths related posts available via the maths page or by clicking here.

Marcus' mental mathematics mistake

In 2009 Marcus du Sautoy, Professor of Mathematics at Oxford University and Simonyi Professor for the Public Understanding of Science, teamed up with an unlikely co-presenter,  comedian / actor Alan Davies, to present an episode of Horizon dealing with the joys or otherwise of mathematics - “Alan and Marcus go forth and multiply”. In one part of the documentary the two participate in an experiment to see if the brain of a member of the public who dislikes maths (Davies) and the brain of one of the most recognisable mathematicians on the planet (du Sautoy) process mathematics differently.  However, the interesting thing for me was this clip extracted from the session.

Play this embedded clip and pay particular attention to du Sautoy’s answer to the third question.

I need to make a clear statement here - it is not my intention to take a cheap shot at Marcus du Sautoy - just the opposite in fact.  Later du Sautoy easily answers more complex questions before I, in the comfort of my lounge chair,  have even processed the information required. He admits  that he was nervous about getting simple calculations wrong as it would be embarrassing for a man in his position to do so.  We can also assume that du Sautoy could have insisted that the error be edited out of the program - but clearly he didn’t and this reflects positively on him.

The interesting thing to me was that when nervous or under stress even one of the most prominent minds in the field of mathematics can make a simple errors.  If this holds true for an expert practitioner such as du Sautoy how much more significant might it be for students in school?

This may prompt some to review their teaching practice in mathematics classrooms. Reducing  stressful situations (and for some students stress may result from  something as simple as being required  to provide an answer publicly in class) would surely make the process more enjoyable for all - and it may just remove a barrier to learning.