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Georges Ifrah
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Old 26-08-2014
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Georges Ifrah


Georges Ifrah ( ? ) French historian of Mathematics and author of the book, The Universal History of Numbers

"The Indian mind has always had for calculations and the handling of numbers an extraordinary inclination, ease and power, such as no other civilization in history ever possessed to the same degree. So much so that Indian culture regarded the science of numbers as the noblest of its arts...A thousand years ahead of Europeans, Indian savants knew that the zero and infinity were mutually inverse notions."

(source: Histoire Universelle des Chiffres - By Georges Ifrah Paris - Robert Laffont, 1994, volume 2. p. 3 ).

Claiming India to be the true birthplace of our numerals, Ifrah salutes the Indian researchers saying that the "...real inventors of this fundamental discovery, which is no less important than such feats as the mastery of fire, the development of agriculture, or the invention of the wheel, writing or the steam engine, were the mathematicians and astronomers of the Indian civilization: scholars who, unlike the Greeks, were concerned with practical applications and who were motivated by a kind of passion for both numbers and numerical calculations."

He refers to 24 evidences from scriptures from India, whose dates range from 1150 BC until 458 BC. Of particular interest is the work by Indian mathematician Bhaskaracharya known as Bhaskara (1150 BC) where he makes a reference to zero and the place-value system were invented by the god Brahma. In other words, these notions were so well established in Indian thought and tradition that at this time they were considered to have always been used by humans, and thus to have constituted a "revelation" of the divinities.

"It was only after the eighth century BC, and doubtless due to the influence of the Indian Buddhist missionaries, that Chinese mathematicians introduced the use of zero in the form of a little circle or dot (signs that originated in India),...".

The early passion which Indian civilization had for high numbers was a significant factor contributing to the discovery of the place-value system, and not only offered the Indians the incentive to go beyond the "calculable" physical world, but also led to an understanding (much earlier than in our civilization) of the notion of mathematical infinity itself.

“The real inventors of [the numeral system], which is no less important than such feats as the mastery of fire, the development of agriculture, or the invention of the wheel, writing or the steam engine, were the mathematicians and astronomers of Indian civilization: scholars who, unlike the Greeks, were concerned with practical applications and who were motivated by a kind of passion for both numbers and numerical calculations.”

Sanskrit notation had an excellent conceptual quality. It was easy to use and moreover it facilitated the conception of the highest imaginable numbers. This is why it was so well suited to the most exuberant numerical or arithmetical-cosmogonic speculations of Indian culture."

"The Indian people were the only civilization to take the decisive step towards the perfection of numerical notation. We owe the discovery of modern numeration and the elaboration of the very foundations of written calculations to India alone."

"It is clear how much we owe to this brilliant civilization, and not only in the field of arithmetic; by opening the way to the generalization of the concept of the number, the Indian scholars enabled the rapid development of mathematics and exact sciences. The discoveries of these men doubtless required much time and imagination, and above all a great ability for abstract thinking. These major discoveries took place within an environment which was at once mystical, philosophical, religious, cosmological, mythological and metaphysical."

"In India, an aptitude for the study of numbers and arithmetical research was often combined with a surprising tendency towards metaphysical abstractions; in fact, the latter is so deeply ingrained in Indian thought and tradition that one meets it in all fields of study, from the most advanced mathematical ideas to disciplines completely unrelated to 'exact sciences.

In short, Indian science was born out of a mystical and religious culture and the etymology of the Sanskrit words used to describe numbers and the science of numbers bears witness to this fact. "

"Sanskrit means “complete”, “perfect” and “definitive”. In fact, this language is extremely elaborate, almost artificial, and is capable of describing multiple levels of meditation, states of consciousness and psychic, spiritual and even intellectual processes. As for vocabulary, its richness is considerable and highly diversified. Sanskrit has for centuries lent itself admirably to the diverse rules of prosody and versification. Thus we can see why poetry has played such a preponderant role in all of Indian culture and Sanskrit literature. "

(source: The Universal History of Numbers - By Georges Ifrah p 365 - 441). For more refer to chapter on GlimpsesIX and Hindu Culture1).



Yaad Kuch Aata Nahin, Yeh Hua Kab Se...Ho Gaya Mushkil Chhupaana Raaz Yeh Sab Se...Tum Kaho To Maang Loon Main Aaj Kuch Rab Se Rabba mere rabba rabba, rabba mere rabba,Is pyaar ko main kya naam doon Roshni se bhare bhare..Bhare bhare naina tere..Chhooke bole na chhoona mujhe Suraj hua maddham, chaand jalne laga..Aasmaan yeh haai kyoon pighalne laga..Main thehra raha, zameen chalne lagi.. Bheeghi Bheeghi Raaton Mein, Phir Tum Aao Na...Asi Barsaton Mein Aao Na.. Humko Humise Chura Lo, Dil Mein Kahin Tum Chhupa Lo,Hum Akele Kho Naa Jaaye, Door Tumse Ho Naa Jaaye,Paas Aao Gale Se Lagaa Lo Toota Toota ek parinda...Jo bhi kaal hua kal bhi phir aayaga Hai...Tumse milke dil ka hai jo haal kya kahe..Ho gaya hai kaisa yeh kamaal kya kahe Ruka Ja, Oh Jaana Wali Ruka Ja...Nazara Mein To Tera Bhura Sa Sahi..Adami Mein Bhura Nahi Dil Ka Aja Re, Aja Re Oh Mere Dilbar Aja..Dil Ki Pyaas Buja Ja Re...Oh Noorie kabhie kabhie mere dil mein khayaal aata hai...ke jaise tujh ko banaya gaya hai mere liye..ke jaise tujh ko banaya gaya haiKitna bechain hoke tumse mila...Tumko kya tha khabar tha main kitna akela ..Ke kitna mohabbat hai tumse...Hai...Tumse milke dil ka hai jo haal kya kahe..Ho gaya hai kaisa yeh kamaal kya kaheTujhe dekha to yeh jaana sanam..Pyaar hota hai deewana sanam..Tujhe dekha to yeh jaana sanam.Tujhe dekha to yeh jaana sanam..Pyaar hota hai deewana sanam.Ab ahan se kahan jaaye hum..Teri bahon mein mar jaaye hum Aksar is duniya mein anjaane milte hain,Anjaani raahon mein milke kho jaate hain,Lekin hamesha voh yaad aate hain Na kajre ki dhaar, na motiyon ke haar,Na koi kiya singaar phir bhi kitni sundar ho,Tum kitni sundar ho Na jaane mere dil ko kya ho gaya..Abhi to yahin tha, abhi kho gaya..Ho gaya hai tujhko to pyaar sajna..Lakh kar le tu inkaar sajna..Dildaar sajna, hai yeh pyaar sajna



Dil Dooba Dil Dooba...Neela Akho Mein Yeh Dil Dooba.. Neela Neela Amber Per Chand Jab Aye...Aisa Koi Saathi Ho ..Aisa Koi Premi Hoi Jaanam Dekh Lo Mit Gayeen Dooriyaan..Main Yahaan Hoon Yahaan Hoon..Yahaan Hoon..Yahaan...Kaisi Sarhadein...Kaisi Majbooriyaan..Main Yahaan Hoon Yahaan Hoon..Yahaan Hoon..Yahaan...Tum Chhupaa Na Sakogi Main Vo Raaz Hoon...Tum Bhulaa Na Sakogi Vo Andaaz Hoon...Goonjtaa Hoon Jo Dil Mein To Hairaan Ho Kyon...Main Tumhaare Hi Dil Ki To Aavaaz Hoon...Main Yahaan Hoon Yahaan Hoon..Yahaan Hoon..Yahaan... Aisa muhje tu na dehka na...seeena se laga loonga, tum ko tumse chura loonga...dil mein chupa loonga Gila Gila Dil Gila.. Mila mila mila koi mila ...Teri Ha Adaar Laga sab se judaa hai dil tuje per fida hai... Dhoom Dhoom let ya body do the talking..Dhoom Dhoom be the fire thats buring..Dhoom machaalay dhoom machaalay dhoom Tere Liye Hum Hai Jiye..Hota ke siya...Dil mein Magar chalte reha chaahat ke Diya... Zara zara bahekta hai, mahekta hai,Aaj to mera tan badan, main pyaasi hoon,Mujhe bhar le apni baahon mein Dheera dheera se mera zindagi mein ana...tumsi pyar huma hai kitna jaana jaana Pyar ke isa khel mein..do dil aur mehl mein, tera peecha na chodunga soniya Mera mehboob sanam, tera ashiq hogaya hum...milaka nazaaro se nazaar tera pyaar mein kogaya hum... Wada Raha Pyar Se Pyar Ka, Hum Na Hoga Juda, Dil Ke Dhadkhan Sunrha Hai Mera Khudda Dheera Dheera Se Mera Zindagi Mein Ana...Tumsi Pyar Huma Hai Kitna Jaana JaanaSaamne hain raastein, hum guzar jaaye...Ya kisi ke vaaste hum thaher jaaye...Ab yahan tak aa gaye hain, ab kidhar jaaye...Jaaduuuuuuu teri nazar...Kushboo tera baadan..tu har kar, ya nah kar...Kali nagin ke jaise..Zulfe teri kali kali..Sagar ko moti aur..Suraj ko tu dati hai lali..Kali nagin ke jaise..Zulfe teri kali kaliYeh din yeh mahine saal guzar jaayenge mere yaar..Magar itna rakhna khayaal..Jeena sirf mere liye, jeena sirf mere liye..Kasam se jeena sirf mere liye, jeena sirf mere liye Banno ki saheli resham ki dori..Chhup chhupke sharmaaye dekhe chori chori..Yeh maane ya na maane main to ispe mar gaya..Yeh ladki haai allah, haai haai re allah Tum paas aaye, yun muskuraaye,Tumne na jaane kya sapne dikhaaye,Tum paas aaye, yun muskuraaye,Tumne na jaane kya sapne dikhaaye,Ab to mera dil jaage na sota hai,Kya karoon haaye, kuch kuch hota hai
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