How good you were in Maths !! - Tables !!!

 

How good were in you Maths !!  ~ remember that when we were young, we were taught Tables !  - upto 16 – in the class, students in chorus 1 x 8 = 8, 2x 8 = 16, 24,32,40,48,56,64,72,80,88,96 ………. 

This morning SYMA conducted a Medical camp at Chennai Middle School, Ramnagar, Triplicane – the infrastructure, class rooms, cleanliness all impressed me beyond a point ! [that will be subject matter of another post] – this about a blackboard containing tables ..  do children glued to mobiles and calculators still learn Tables ?!?!?

Perhaps  there isn't a single person who invented them. They developed gradually in ancient civilizations.  Some references put that the  earliest known multiplication tables come from ancient Mesopotamia. Babylonians wrote mathematical tables on clay tablets, using their base-60 (sexagesimal) system.   Egyptians had sophisticated methods for multiplication, but generally used doubling rather than memorising a complete set of tables. For example, to multiply by 13, they could successively double and add the required quantities.

                Indian mathematicians developed and used multiplication tables extensively. The decimal place-value system and zero, which emerged in India, made arithmetic and multiplication much easier. By the early medieval period, Indian mathematical texts contained systematic multiplication methods and tables. Chinese mathematics: China also developed multiplication tables very early. The famous “Nine-Nine Table” (九九表) was traditionally memorised as a sequence of products from 1×1 through 9×9.  

Nobody can really be called the inventor. Multiplication itself is thousands of years old, and tables evolved as a practical shortcut for repeated multiplication. The  “2 to 20 tables” tradition familiar in Indian schools is much more extensive than the standard 1–10 tables commonly taught in many Western countries. Aryabhata, Brahmagupta and Bhaskaracharya did not invent the school multiplication tables as such. They developed and codified arithmetic methods that made systematic calculation possible..

Before Aryabhata — multiplication was repeated addition -  5 × 4 = 5 + 5 + 5 + 5 = 20.  Indian mathematicians explicitly regarded multiplication as a form of repeated addition. The terminology was quite sophisticated: the number being multiplied and the multiplier had specific Sanskrit names, and the result had its own terminology.  Calculations were sometimes performed on a board covered with dust, hence the term dhūlikarma (“dust work”).  

Aryabhata, in his Āryabhaṭīya, gave a systematic treatment of mathematics (gaṇita) alongside astronomy. His importance to the later tradition is not that he created “2 times table, 3 times table…” but that he codified mathematical procedures in a highly systematic form. His work became the foundation for generations of Indian commentators and mathematicians. An important point is that these texts were written in compact Sanskrit verse, partly because mathematical rules were intended to be memorised. So there was already a strong tradition of learning numerical rules by heart—something that eventually fits very naturally with the school practice of reciting multiplication tables.

About a century later came Brahmagupta. His Brāhmasphuṭasiddhānta, written in 628 CE, contains an extensive treatment of arithmetic, including multiplication, division, fractions, negative numbers and zero.  Consider: 347 × 26. Today we instinctively understand that:

6 × 347 = 2082

20 × 347 = 6940

therefore 2082 + 6940 = 9022.

That depends on understanding place value — units, tens, hundreds — and the decimal numeral system. Indian mathematicians developed increasingly sophisticated arithmetic using this system. Historical descriptions of Indian multiplication methods show procedures remarkably close in principle to the long multiplication taught in schools today.   

Much later in the 12th century,  Bhaskaracharya’s famous Līlāvatī, part of the Siddhānta Śiromaṇi, contains extensive arithmetic and specifically discusses methods of multiplication and squaring. Bhaskara II gives methods of multiplication that involve arranging numbers in particular positions and multiplying their individual digits—methods that are recognisably related to the algorithms used later in traditional arithmetic teaching. And Līlāvatī is particularly interesting because it doesn't merely give rules. It presents problems for students to solve, including arithmetic progressions, interest, fractions, geometry and other numerical problems.

The modern Indian school tradition of Maths tables  is not something we can attribute to Aryabhata or Brahmagupta individually. Rather, it grew out of the broader Indian tradition of: number → place value → repeated addition → multiplication rules → memorised computational rules → school arithmetic. The fact that Indian mathematical texts were composed in concise, memorable verses also encouraged oral memorisation. Over centuries, this developed into the familiar practice of children reciting tables aloud.

The traditional Indian method of multiplication was so influential that medieval Europeans sometimes referred to Indian arithmetic as “modus Indorum” — the method of the Indians.  So when an Indian child today confidently rattles off “13 ones are 13, 13 twos are 26…”, there is a very long mathematical ancestry behind that apparently simple school exercise.

Interesting ! – back to Basics ! – back to schools !!

 

Regards – S Sampathkumar

4.10.2026