Mathematics in Tirukkural




Mathematics in Tirukkural—A brief study


     The famous Tamil work Tirukkural written by Thiruvalluvar believed to have been written during the Sangam period of Tamil (500 to200 BC) has been acknowledged as a great work akin to the Vedas, providing, like the Bhagavad Gita, guidance for a happy life here as well as hereafter. It has been called as Tamil Marai (Tamil Veda), Poyyamozhi (Words that do not lie), and Daivanool (Divine text).  The fact that it has been translated into different languages speaks volumes for its universal values and its catholicity of outlook. It expounds in aphorisms in the form of Tamil couplets called venbas, and deals with aram, porul and inbam, that is, dharma or righteous way of life, wealth and happiness. It is interesting to note that aram or dharma comes first and then only wealth and then happiness, signifying thereby that wealth earned according to dharma alone can lead to happiness.  Like the Bhagavad Gita, it can be studied from various angles.  In the present article, it is proposed to outline in brief how mathematics in the form of numbers, and those in the decimal system of numeration, have found a habitat in this work. The very name of the author Thiruvalluvar in Tamil contains 7 letters. The sum of the numerical values represented by the letters in the name Tiruvalluvar is said to add to a total of 133 which is again 7 x 19.

    The form of couplets in this work follows the venba pattern, that is, with seven metric or feet, with four in the first one and three in the second one.  Reckoned in terms of syllables, it contains 14 syllables in each venba. It contains 133 chapters, the number being a product of two prime factors 7 and 19 and it contains 10 couplets in each, with a total 1330 couplets, the number 1330 being equal to 7 x 19 x 10.  Every chapter contains 7 x 10 metrical feet, and the entire work contains 9310 = 7 x 19 x 10 x 7 metric feet. Thus, the number 7 happens to be at the base of this work.


    A glance at the couplets shows that the numbers 1, 2, 3, 4, 5, 6,  8, 10, crore, 10 crores, 70 crores have also found a mention as shown below:


                         1 and 2

ஒருதலையான் இன்னாது காமம்காப் போல
இருதலை யானும் இனிது                         1196


                One sided pains; love in both souls          1196

                Poises well like shoulder poles.





ஒற்றும் உரைசான்ற நூலும் இவையிரண்டும்
தெற்றென்க மன்னவன் கண்                   581


                      A king should treat these two as eyes        581

                  The code of laws and careful spies.


ஊறொரால் உற்றபின் ஒல்காமை இவ்விரண்டின்
ஆறென்பர் ஆய்ந்தவர் கோள்.                662


                       Shun failing fuss; fail not purpose             662

                  These two are maxims of the wise.


இருநோக்கு இவளுண்கண் உள்ளது ஒருநோக்கு
நோய்நோக்கொன் றந்நோய் மருந்து    1091


                           Her painted eyes, two glances dart          1091

                      One hurts; the other heals my heart.





ஒற்றெற் றுணராமை ஆள்க உடன்மூவர்
சொற்றொக்க தேறப் படும்.                       589


                Engage the spies alone, apart                    589

                When three agree confirm report.


அறிவுரு வாராய்ந்த கல்விஇம் மூன்றன்
செறிவுடையான் செல்க வினைக்கு           684


                    Who has these three: good form, sense, lore  684

                Can act as bold ambassador.



மிகினும் குறையினும் நோய்செய்யும் நூலோர்
வளிமுதலா எண்ணிய மூன்று                       941


               Wind, bile and phlegm three cause disease      941

            So doctors deem it more or less.


   ஒழுக்கமும் வாய்மையும் நாணும் இம் மூன்றும்
    இழுக்கார் குடிப்பிறந் தார்.                               952


                      The noble-born lack not these three:               952

                  Good conduct, truth and modesty






                 அழுக்காறு அவாவெகுளி இன்னாச்சொல் நான்கும்
                 இழுக்கா இயன்றது அறம்                                   35


                 Four ills eschew and virtue reach,                     35

                 Lust, anger, envy, evil-speech.


           அன்பறிவு தேற்றம் அவாவின்மை இந்நான்கும்
            நன்குடையான் கட்டே தெளிவு                     513


              Trust him in whom these four you see:            513

               Love, wit, non-craving, clarity.





ஐந்தவித்தான் ஆற்றல் அகல்விசும்பு ளார்கோமான்
இந்திரனே சாலுங் கரி                                        25


                  Indra himself has cause to say                          25

              How great the power ascetics' (who

              Have controlled the five senses) sway.                                   


அடல்வேண்டும் ஐந்தன் புலத்தை விடல்வேண்டும்
வேண்டிய வெல்லாம் ஒருங்கு                     343



                  Curb the senses five and renounce                   343

              The carving desires all at once.


                 பொருள்கருவி காலம் வினையிடனொடு ஐந்தும்
                 இருள்தீர எண்ணிச் செயல்.                               675

                Money and means, time, place and deed          675

                Decide these five and then proceed


உடைசெல்வம் ஊண்ஒளி கல்விஎன்று ஐந்தும்
அடையாவாம் ஆயங் கொளின்                     939


               Dress, wealth, food, fame, learning-these five  939

               In gambler's hand will never thrive.


உடைசெல்வம் ஊண்ஒளி கல்விஎன்று ஐந்தும்
அடையாவாம் ஆயங் கொளின்


              Love, truth, regard, modesty, grace                983

             These five are virtue's resting place.





ஆபயன் குன்றும் அறுதொழிலோர் நூல்மறப்பர்
காவலன் காவான் எனின்                                  560


              The *six-functioned forget their lore               560

              Cows give less if kings guard no more.

            * the six functions are: learning, teaching, giving,

               getting, sacrificing, kindling sacrifice.

               These are duties of Vedic savants.




     The number seven or its multiples find abundant mention in the venbas of Tirukkural as shown below, since they find a lot of mention in Hindu mythology as indicated below.

    (To digress a little, the number 7 is associated in Indian mythology with various things, places or individuals. For instance, we talk of the saptarishis or 7 sages, namely Atri, Bhrigu, Kutsa, Vasishtha, Gautama, Kashyapa and Angirisa.  We talk of seven swaras in music, namely Sa, Ri, Ga. Ma, Pa, Dha, and Ni.  The Lord who resides at Tirupati is known in Tamil as “Ezhumaliyaan”, that is, one who resides amidst seven mountains, namely Srigiri, Vrishabhadri, Seshasailam, Narayanadri, Natvrishadri, Garudachalam and Venkatadri.  There are seven higher worlds which are talked of, namely Bhu, Bhuva, Suva, Maha, Jana, Tapa and Satyam, which are recited before the beginning of pranayama. There are seven lower worlds which are mentioned, namely atala, vitala, sutala, talatala, mahatala, rasatala and patala. There are seven planets, namely Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn and the days of the week are seven in number, named after these seven planets. (Rahu and Ketu are called shadow planets or chayagrahas and not counted as planets as such).

   According to the Tantrik school of thought, there are 7 chakras in the human body, namely Muladhara, Swadhishtana, Manipura, Anahata, Visuddhi, Ajna, and Sahasrara.  There are seven spheres or dweepas, namely Jambu, Plaksha, Kusha, Krauncha, Shaka, Shalmali, and Pushkara. There are seven oceans, namely lavana, ikshu, sura, sarpi, dadhi, ksheera and shuddhodaka (salt, sweet, intoxicant, ghee, curd, milk and pure water). There are seven mokshapuris or centres of salvation, namely Aydhoya, Mathura, Kashi, Kanchi, Mayapuri, Dwaraka, and Avantikapuri. There are seven forms of Shakti namely Brahmi, Vaishnavi, Maheshwari, Kaumari, Varahi, Aindri, and Chamundi. There are seven sacred rivers namely Ganga, Yamuna, Godavari, Saraswati, Narmada, Sindhu, and Kaveri. There are seven who are (relatively) immortals, namely Ashwathama, Bali, Vyasa, Kripa, Parasurama, Hanuman and Vibhishana. Agni is aid to have seven tongues, namely kali (black), karali (fierce), manojava (swift as mind), sulohita (red as iron), sudhoomravarna (smoke-coloured), Vishwaruchidevi (universally pleasing), sphulinga (cracking). There are said to be seven sheaths for the human body, namely Annamaya, pranamaya, manomaya, vijnanamaya, janah, tapah,  and Brahma. There are 7 colours in the solar radiation, namely VIBGYOR, namely Violet, Indigo, Blue, Green, Yellow, Orange and Red, referred to as the seven horses or rays of the Sun God.  According to Hindu law, a marriage becomes legal only when the saptapadi is performed, or when seven circumbulations are performed by the bridegroom and bride around fire, and the bridegroom placing the right foot of the bride seven times around a hard stone, with specific expectation from her each time, as to how she will live with him.

     We find reference to saptakanyas or seven virgins in Hindu Mythology.   There are seven main chhandas or metric forms of poetry in Sanskrit, namely Gayatri, Ushnik, Anushtup, Brihati, Pankti, Trishtup and Jagati.   There are seven main Devas, namely Agni(Fire), Vayu (Air), Arka (Sun), Vageesha (God of speech), Varuna (God of rain), Indra, and Vishwedevas).

  The 7 wonders of the ancient world are: Great Pyramid of Giza, Hanging Gardens of Babylon, Temple of Artemis at Ephesus, Statue of Zeus at Olympia, Mausoleum of Maussollos at Halicarnassus,
Colossus of Rhodes, Lighthouse of Alexandria. The 'Seven Blunders of the World' according to Mahatma Gandhi are: Wealth without work, Pleasure without conscience, Knowledge without character, Commerce without morality, Science without humanity, Worship without sacrifice, and Politics without principle.

     Hence, it is no wonder that the number seven or its multiples find abundant mention in the venbas of Tirukkural as shown below:




 Venba No.62 which reads thus:

                     எழுபிறப்பும் தீயவை தீண்டா பழிபிறங்காப்
                     பண்புடை மக்கட் பெறின், (62)

means that no harm will befall, in all the seven births, one who begets blameless children. 


எழுமை எழுபிறப்பும் உள்ளுவர் தங்கண்
விழுமந் துடைத்தவர் நட்பு                                 107


                        Through sevenfold births, in memory fares       107

                   The willing friend who wiped one's tears.


Venba No.398, which reads thus:

               ஒருமைக்கண் தான் கற்ற கல்வி ஒருவற்கு
                       எழுமையும் ஏமாப் புடைத்து,  (398)

means that the learning acquired in one birth protects the individual in the next 7 births. 


ஒருமைச் செயலாற்றும் பேதை எழுமையும்
தான்புக் கழுந்தும் அளறு.                                   835


                   The fool suffers seven fold hells                      835

                   In single birth of hellish ills.


ஒருநாள் எழுநாள்போல் செல்லும்சேண் சென்றார்
வருநாள்வைத்து ஏங்கு பவர்க்கு.                1269

One day seems as seven to those                1269                             Who yearn return of distant spouse.





கோளில் பொறியின் குணமிலவே எண்குணத்தான்
தாளை வணங்காத் தலை                                      9


                           Like senses stale that head is vain                         9

                     Which bows not to Eight-Virtued Divine.





பல்லார் பகை கொளலிற் பத்தடுத்த தீமைத்தே
நல்லார் தொடர்கை விடல்                                450


To give up good friends is ten times worse     450                      

Than being hated by countless foes.


                                        1 crore


                    பேதை பெருங்கெழீஇ நட்பின் அறிவுடையார்

                    ஏதின்மை கோடி உறும்.                                     (816)

   Crore times the wise man's hate                                   

   Is better than a fool intimate.                           816



                       அடுக்கிய கோடி பெறினும் குடிப்பிறந்தார்  954
குன்றுவ செய்தல் இலர்.


                   Even for crores, the noble mood                      954

                   Cannot bend to degrading deed.


             கொடுப்பதூஉம் துய்ப்பதூஉம் இல்லார்க்கு அடுக்கிய
              கோடியுண் டாயினும் இல்.                                         1005


                        What is the good of crores they hoard             1005

                   To give and enjoy whose heart is hard.


கரவாது உவந்தீயும் கண்ணன்னார் கண்ணும்
இரவாமை கோடி உறும்.                                     1061


                         Not to beg is crore worth                                1061

                    E'en from eye-like friends who give with mirth.




                                          10 crores



           பத்தடுத்த கோடி உறும்                                         817


                           Ten-fold crore you gain from foes                     817

                      Than from friends who are vain laughers.


                                         70 crores


பழுதெண்ணும் மந்திரியின் பக்கததுள் தெவ்வோர்
எழுபது கோடி உறும்                                               639


                           Seventy crores of foes are better                       639

                     Than a minister with mind bitter.


     Thus, we find that besides the numbers from 1 to 9, numbers in the decimal system of numeration also find a place in Tirukkural, e.g 1 crore, 10 crores, and 70 crores, or 107,  108 and 7x107, which is proof of the continuing prevalence of that system during Tiruvalluvar’s period (500-200 B.C., that is, before Bhaskaracharya's period, said to be the period for invention  of zero).