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Abraham Seidenberg (1916 – 1988) India ~ Sulbasutras
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Old 03-04-2019
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Abraham Seidenberg (1916 – 1988) India ~ Sulbasutras


AMERICAN HISTORIAN OF MATHEMATCS:

Abraham Seidenberg (1916 – 1988) said: “Ancient Egyptian, Babylonian and Greek geometries derive from the mathematics recorded in the Sulbasutras.”
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The distinguished mathematician and historian of mathematics Abraham Seidenberg, who taught at Berkeley for 42 years, died in Milan, Italy, on May 3, 1988. He had been born in Washington, D.C., on June 2, 1916 and received his B.A. degree at the University of Maryland in 1937 and his Ph.D. at Johns Hopkins in 1943 before joining the Department of Mathematics at Berkeley as Instructor in 1945. He became Professor in 1958 and Professor, Emeritus in 1987. His career included a Guggenheim Fellowship, Visiting Professorships at Harvard and at the University of Milan, and numerous invited addresses, including several series of lectures at the University of Milan, the National University of Mexico, and at the Accademia Nazionale dei Lincei in Rome. At the time of his death, he was in the midst of another series of lectures at the University of Milan.

Seidenberg's writings, as were his lectures, are noted for their meticulous clarity of expression. His publications in pure mathematics include some very influential work in commutative algebra, notably his joint paper with I.S. Cohen that greatly simplified the existing proofs of the so-called going-up and going-down theorems of ideal theory, and a recent series of papers on finiteness results and constructive methods in algebra. His articles on algebraic geometry include a much-quoted one on the normality of the general hyperplane section of a normal projective variety. His papers on differential algebra include several on the foundations of differential algebra, for any number of differentiations and for any field characteristic, on the Picard-Vessiot theory of homogeneous linear differential equations, and on the so-called Lefschetz-Seidenberg principle of differential algebra, an analog of the Lefschetz principle for algebraic geometry, which says, very roughly, that algebraic geometry of characteristic zero is the same as algebraic geometry over the field of complex numbers. Another famous result is the Tarski-Seidenberg theorem, to the effect that there is a decision procedure for algebra over the real number field and for elementary geometry, first proved by Tarski using complicated logical machinery, then restated more simply by Seidenberg and given a much simpler mathematical proof. Among Seidenberg's publications are a large number of articles on the mathematics of primitive peoples and on the history of mathematics, in particular on ancient mathematics. Most of these articles are in support of his thesis that both arithmetic and geometry have their origins in ritual. His sources are the anthropological literature and Egyptian, Babylonian, Greek, Indian and Chinese documents. Although this work was a center of some controversy, in large part because of the general aversion among anthropologists to diffusion theories of culture, important aspects of it have received striking vindication. Thus the eminent mathematician and historian of mathematics B.L. van der Waerden starts the introduction to his 1983 monograph “Geometry and Algebra in Ancient Civilizations” with the words

Until quite recently, we all thought that the history of mathematics begins with Babylonian and Egyptian arithmetic, algebra, and geometry. However, three recent discoveries have changed the picture entirely.
The first of these discoveries was made by A. Seidenberg. He studied the altar constructions in the Indian Sulvasutras and found that in these relatively ancient texts the “Theorem of Pythagoras” was used to construct a square equal in area to a given rectangle, and that this construction is just that of Euclid. From this and other facts he concluded that Babylonian algebra and geometry and Greek “geometrical algebra” and Hindu geometry are all derived from a common origin, in which altar constructions and the “Theorem of Pythagoras” played a central role. Those who knew Seidenberg well, including many students, remember his warmth, compassion and integrity. He had a number of very dear friends.

He is survived by his widow, Ebe. M. A. Rosenlicht G. P. Hochschild P. Lieber Written by: 1916-1988 Professor Emeritus

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POSTED ON FB: 18th January 2016: https://www.facebook.com/47266792277...575839/?type=3

Source: http://users.uoa.gr/~apgiannop/Sourc...semicircle.pdf


ABRAHAM SEIDENBERG,
An Eminent Algebraist And Historian Of Mathematics Traced The Origin Of Sophisticated Mathematics To The Originators Of The Rigvedic Rituals.
https://bluefieldstate.edu/sites/def...f%20Shaikh.pdf



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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