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[46th Thread: Was al-Khwarizmi a plagiarist of 
Mathematics?]
1.
The aim of the thread is to refute the claim that al-Khwarizmi was a plagiarist & thief of Mathematicians without discarding their contributions.
I've refuted @BharadwajSpeaks earlier https://twitter.com/Burairss/status/1275104370384756740?s=20
Mathematics?]1.
The aim of the thread is to refute the claim that al-Khwarizmi was a plagiarist & thief of
Mathematicians without discarding their contributions.I've refuted @BharadwajSpeaks earlier https://twitter.com/Burairss/status/1275104370384756740?s=20
2.(i).
I. "It is an algebraic treatise" is a wrong claim. He didn't even read nor any research on it.
The Bakhshali manuscript is in a very damaged state & some of the pages we've are themselves broken up into fragments & large parts are missing; https://twitter.com/BharadwajSpeaks/status/1343142908224917505?s=20
I. "It is an algebraic treatise" is a wrong claim. He didn't even read nor any research on it.
The Bakhshali manuscript is in a very damaged state & some of the pages we've are themselves broken up into fragments & large parts are missing; https://twitter.com/BharadwajSpeaks/status/1343142908224917505?s=20
Even the exact order of the pages has been a matter of conjecture since the state in which it first came didn't have original order.
II. Indians were mostly concerned with Astronomy & astrology though they made significant contributions but in algebra, it wasn't that case.
II. Indians were mostly concerned with Astronomy & astrology though they made significant contributions but in algebra, it wasn't that case.
III.Both Diophantus & Indians lack practicality like reduction & restoration unlike al-Khwarizmi.
IV. According to Swiss-American Cajori, al-Khwarizmi work was neither purely Indian nor Greek.
This itself refutes the claim that it's theft or complete plagiarism
5. He's born
IV. According to Swiss-American Cajori, al-Khwarizmi work was neither purely Indian nor Greek.
This itself refutes the claim that it's theft or complete plagiarism
5. He's born
in Khwarizm, not Arabian desert. So this is a bigoted remark.
(ii).The date of this Bakhshali MS given by @BharadwajSpeaks is also wrong.
The Bodleian’s radiocarbon dating project took 3 samples of bark, avoiding areas containing ink, from fragments identified as belonging to
(ii).The date of this Bakhshali MS given by @BharadwajSpeaks is also wrong.
The Bodleian’s radiocarbon dating project took 3 samples of bark, avoiding areas containing ink, from fragments identified as belonging to
folios 16, 17
& 33. The date ranges found for these samples are
224–383,680–779 & 885–993 respectively.
@BharadwajSpeaks deliberately chose the earliest one to prove his point which is incorrect. This is a dishonest move coupled with his biased reading of Bakhshali MS research.
& 33. The date ranges found for these samples are
224–383,680–779 & 885–993 respectively.
@BharadwajSpeaks deliberately chose the earliest one to prove his point which is incorrect. This is a dishonest move coupled with his biased reading of Bakhshali MS research.
3.(i). Bodleian date was refuted by a team of researchers including Hayashi who'd done the most comprehensive work on Bakhshali MS.
Their conclusion fits well to 2nd half of 1st Millennium CE(ie from 500-1000 CE which means 6th-10th century).
https://twitter.com/BharadwajSpeaks/status/1343143545255784452?s=20
Their conclusion fits well to 2nd half of 1st Millennium CE(ie from 500-1000 CE which means 6th-10th century).
https://twitter.com/BharadwajSpeaks/status/1343143545255784452?s=20
(ii). "ancient Hindu treatise..."
Hindu is a wrong notion to such work.
Saidan who wrote a paper on "Kitab al-Fusul fi al-Hisab al-Hindi" rejected the short name. He states that it should be understood as arithmetic done in the Indian way" with Hindu-Arabic numerals,rather than
Hindu is a wrong notion to such work.
Saidan who wrote a paper on "Kitab al-Fusul fi al-Hisab al-Hindi" rejected the short name. He states that it should be understood as arithmetic done in the Indian way" with Hindu-Arabic numerals,rather than
simply as Indian arithmetic.
The numbering system should rather be called as Indo-Arabic system, which is both semantically & linguistically correct.
(iii). "Arithmetic & Algebra"
When it comes to arithmetic, Bakhshali MS only mentioned fraction multiplication as shown below
The numbering system should rather be called as Indo-Arabic system, which is both semantically & linguistically correct.
(iii). "Arithmetic & Algebra"
When it comes to arithmetic, Bakhshali MS only mentioned fraction multiplication as shown below
In modern view, it'll look like below 1st image(from left).
Fractions were already known to Egyptians, Babylonians & Rome before Indians.
Egyptians used to write fractions like 2nd image. Their num system was a base 10 idea & they've symbols for 1,10,100 etc
Babylonians came
Fractions were already known to Egyptians, Babylonians & Rome before Indians.
Egyptians used to write fractions like 2nd image. Their num system was a base 10 idea & they've symbols for 1,10,100 etc
Babylonians came
up with a num system of base 60(image)but their representation of fractions was more sensible.
Romans came up with words to describe a part of a whole, like 1/12 was called uncia or 6/12 as semis etc.
So arithmetic isn't unique to Indians only.
But the Harappans had developed
Romans came up with words to describe a part of a whole, like 1/12 was called uncia or 6/12 as semis etc.
So arithmetic isn't unique to Indians only.
But the Harappans had developed
the decimal system with scales of weights & lengths discovered during excavations.
So, Bakhshali MS covers arithmetic
progressions of various types & rational approximations of square roots.
When it comes to Algebra & Quadratic equations, the contribution goes to Diphomatus
So, Bakhshali MS covers arithmetic
progressions of various types & rational approximations of square roots.
When it comes to Algebra & Quadratic equations, the contribution goes to Diphomatus
& it seems as if the author copied it from his work as his date of work ranges ~250AD.
However, al-Khwarizmi work was quite distinct from Diophantus in the sense that an exposition which starts with primitive terms in which the combinations must give all possible prototypes for
However, al-Khwarizmi work was quite distinct from Diophantus in the sense that an exposition which starts with primitive terms in which the combinations must give all possible prototypes for
equations which henceforward explicitly constitute the true object of study.
Carl Boyer mentioned al-Khwarizmi work shows dissimilarity from Diophantus with none of the syncopation found in his Arithmetica or in Brahmagupta's work.
Al-jabr comes closer to the elementary
Carl Boyer
mentioned al-Khwarizmi work shows dissimilarity from Diophantus with none of the syncopation found in his Arithmetica or in Brahmagupta's work.Al-jabr comes closer to the elementary
algebra of today than the works of either Diophantus or Brahmagupta.
4.(i). "Isnt the earliest Indian algebraic treatise"
1. Yes, this MS is not the earliest {Hayashi says, it belongs to 7th cen.}nor it's the original work but a copy as Hayashi noted
https://twitter.com/BharadwajSpeaks/status/1343144585694855168?s=20
4.(i). "Isnt the earliest Indian algebraic treatise"
1. Yes, this MS is not the earliest {Hayashi says, it belongs to 7th cen.}nor it's the original work but a copy as Hayashi noted
https://twitter.com/BharadwajSpeaks/status/1343144585694855168?s=20
(ii). "Early Algebra is found in Shulba Sutras dating back to at least 800 BC"
(sulba, not shulba)
The dude is completely clueless about 'Sulba Sutras'.
These were appendices to the Vedas giving rules for constructing altars. They contained quite an amount of
(sulba, not shulba)
The dude is completely clueless about 'Sulba Sutras'.
These were appendices to the Vedas giving rules for constructing altars. They contained quite an amount of
geometrical knowledge but the mathematics was being developed, not for its own sake, but purely for practical religious purposes.
Composed by 4 men over a period of 600 yrs, these individuals were priests & scholars & not mathematicians.
The mathematics given in the Sulbasutras
Composed by 4 men over a period of 600 yrs, these individuals were priests & scholars & not mathematicians.
The mathematics given in the Sulbasutras
is there to enable the accurate construction of altars needed for sacrifices. It's clear from the writing that Baudhayana, being a priest, must have been a skilled craftsman.
For ex - Sulba sutra of Baudhayana contains geometric solutions(not algebraic ones)of a linear equation
For ex - Sulba sutra of Baudhayana contains geometric solutions(not algebraic ones)of a linear equation
in a single unknown.
(ii). "Traditional algebra Traditional Algebra reached its pinnacle in the works of Aryabhata & Bhaskara".
Fancy words with no substance.
Bhaskara I had made contributions in Number theory & Sine functions, particularly wrote commentaries on Aryabhatta
(ii). "Traditional algebra Traditional Algebra reached its pinnacle in the works of Aryabhata & Bhaskara".
Fancy words with no substance.
Bhaskara I had made contributions in Number theory & Sine functions, particularly wrote commentaries on Aryabhatta
works. Bhaskara I significant contribution was to apply the Brahmi numerals into practice. These numerals are 1st direct ancestor of modern Indo-Arabic numberals[0-9] as can be seen in below image
But he wasn't related to Algebra, not even remotely or at rudimentary level.
![works. Bhaskara I significant contribution was to apply the Brahmi numerals into practice. These numerals are 1st direct ancestor of modern Indo-Arabic numberals[0-9] as can be seen in below image But he wasn't related to Algebra, not even remotely or at rudimentary level.](https://pbs.twimg.com/media/Er9DK5aUcAEKivv.jpg "works. Bhaskara I significant contribution was to apply the Brahmi numerals into practice. These numerals are 1st direct ancestor of modern Indo-Arabic numberals[0-9] as can be seen in below image But he wasn't related to Algebra, not even remotely or at rudimentary level.")
But he wasn't related to Algebra, not even remotely or at rudimentary level.
As for Aryabhatta, from his extended work - Aryabhatiya- we came to know that he's involved in solving Diophantus equations rather than exposition or founding Algebra, which is seen in al-Khwarizmi work-الكتاب المختصر في حساب الجبر والمقابلة- in which he discussed the fundamental
methods of reduction & balancing. He also provided an exhaustive account of solving polynomial equations & a systematic approach to solve linear & quadratic equations build the foundation of Algebra.
(iii). "offers mathematical proof to its theories"
There is no evidence that
(iii). "offers mathematical proof to its theories"
There is no evidence that
the MS provides proof for his theories especially on "sqaure root" as they're no iterations given in the MS.
The theorem is that "Bakhshali square root is quartically convergent".
Interestingly, it's mathematically equivalent to performing 2 consecutive iterations of the
The theorem is that "Bakhshali square root is quartically convergent".
Interestingly, it's mathematically equivalent to performing 2 consecutive iterations of the
Newton-Raphson iteration(also called Heron formula). So, does Bakhshali copied it from Heron?
In short, this claim of demonstrating proofs for its theories is baseless.
5.(i). "carbon dated to 3rd century CE by Oxford"
The carbon-dating by Bodleian https://twitter.com/BharadwajSpeaks/status/1343145953683881984?s=20
In short, this claim of demonstrating proofs for its theories is baseless.
5.(i). "carbon dated to 3rd century CE by Oxford"
The carbon-dating by Bodleian https://twitter.com/BharadwajSpeaks/status/1343145953683881984?s=20
has been refuted by a team of Kim, Keller, Hayashi, Montelle, Dominik as I mentioned above.
Even if we accept Bodleian claim, then they gave 3 separate dates but @BharadwajSpeaks being intellectually dishonest & ignorant only mentioned the earliest date to fool ppl.
*Sigh* !
Even if we accept Bodleian claim, then they gave 3 separate dates but @BharadwajSpeaks being intellectually dishonest & ignorant only mentioned the earliest date to fool ppl.
*Sigh* !
(ii). "oh we invented Algebra. It is Halal"
Ad-homniem & Red-herring at best.
This bigoted comment exposes typical sanghi attitude of @BharadwajSpeaks here who's biased & nit-picking in his thread.
al-Khwarizmi laid the foundation of Algebra at rudimentary level which is very
Ad-homniem & Red-herring at best.
This bigoted comment exposes typical sanghi attitude of @BharadwajSpeaks here who's biased & nit-picking in his thread.
al-Khwarizmi laid the foundation of Algebra at rudimentary level which is very
crucial & provided a systematic approach to solutions, not just difficult equations mentioned by his Predecessors.
The word 'halal' is unnecessary here as we're not talking of practical life but a science to understand the world & mechanism of it.
Further analysis by him is
The word 'halal' is unnecessary here as we're not talking of practical life but a science to understand the world & mechanism of it.
Further analysis by him is
unfounded.
6.(i). "Visited India"
There is no evidence that al-Khwarizmi visited India in any historical records.
@BharadwajSpeaks fabricated this statement in order to support his so-called plagiarism claim.
It's more probable that the work https://twitter.com/BharadwajSpeaks/status/1343146273814167552?s=20
6.(i). "Visited India"
There is no evidence that al-Khwarizmi visited India in any historical records.
@BharadwajSpeaks fabricated this statement in order to support his so-called plagiarism claim.
It's more probable that the work https://twitter.com/BharadwajSpeaks/status/1343146273814167552?s=20
was gifted by Indian traders to al-Ma'mun.
(ii). "His book is a plagiarism from Indian Mathematics"
Unfounded claim with no evidence. In fact, the Indians had no rules like the ''restoration'' & ''reduction" unlike al-Khwarizmi as Cajori mentioned
(ii). "His book is a plagiarism from Indian Mathematics"
Unfounded claim with no evidence. In fact, the Indians had no rules like the ''restoration'' & ''reduction" unlike al-Khwarizmi as Cajori mentioned
7. "the derivation of PI given in his book 'al-Jabr"'
The derivation of π(pi) is irrelevant to Algebra but @BharadwajSpeaks
brought it in his thread to discard al-Khwarizmi by 'changing goalposts'.
Firstly, pi has a long history before Aryabhatta. https://twitter.com/BharadwajSpeaks/status/1343148153168531456?s=20
The derivation of π(pi) is irrelevant to Algebra but @BharadwajSpeaks
brought it in his thread to discard al-Khwarizmi by 'changing goalposts'.
Firstly, pi has a long history before Aryabhatta. https://twitter.com/BharadwajSpeaks/status/1343148153168531456?s=20
Both Egyptians & Mesopotamians have derived the value of pi close to 3.125 or 3.162
In the Egyptian Rhind Papyrus, which is dated about 1650 BC, there is good evidence for 3.16 as value of pi.
Secondly, Archimedes derived the value of pi by purely geometrical means
In the Egyptian Rhind Papyrus, which is dated about 1650 BC, there is good evidence for 3.16 as value of pi.
Secondly, Archimedes derived the value of pi by purely geometrical means
Thirdly, Ptolemy came up with 3.1416 & Zu Chongzhi with 355/113 before Aryabhatta.
Now, when it comes to Aryabhatta, he mentioned his calculation & value in Aryabhatiyam - gaṇitapāda 10 - as given below
But this is just one method as this is what al-Khwarizmi mentioned.
Now, when it comes to Aryabhatta, he mentioned his calculation & value in Aryabhatiyam - gaṇitapāda 10 - as given below
But this is just one method as this is what al-Khwarizmi mentioned.
So the source used by @BharadwajSpeaks exactly mentioned just 1 method as can be understood from the words, "the other method is used by astronomers among them"...
So al-Khwarizmi considered Aryabhatta as an Astronomer & not even Mathematician.
The other 2 values given by him
So al-Khwarizmi considered Aryabhatta as an Astronomer & not even Mathematician.
The other 2 values given by him
are Ö10(~3.1622), 3 1/7.
The first value was given by Zhang Heng & the second was by Archimedes but Banu Musa considered Archimedes’ method to be incomplete & not arriving at the truth. As mentioned by Suter, Banu Musa method was different from Archimedes.
So this is all on pi.
The first value was given by Zhang Heng & the second was by Archimedes but Banu Musa considered Archimedes’ method to be incomplete & not arriving at the truth. As mentioned by Suter, Banu Musa method was different from Archimedes.
So this is all on pi.
8.(i). "heavily plagiarised from Indian Mathematicians"
Still there is no evidence that al-Khwarizmi plagiarized from Indian Mathematicians.
The most we can say is that he developed his own approach by studying it though we don't see it in al-Jabr. https://twitter.com/BharadwajSpeaks/status/1343149266022195201?s=20
Still there is no evidence that al-Khwarizmi plagiarized from Indian Mathematicians.
The most we can say is that he developed his own approach by studying it though we don't see it in al-Jabr. https://twitter.com/BharadwajSpeaks/status/1343149266022195201?s=20
(ii). Henry only translated Brahmasphutasiddhānta in whose chapter 18, we witness that Brahmagupta gave solution to linear equation & 2 solutions to quadratic equation. But al-Khwarizmi solved 6 different kinds of equations with a straight forward & elementary exposition of the
solution of equations,especially that of 2nd degree which is different from Diophantus & Brahmagupta works as mentioned by Boyer
If al-Khawarizmi plagiarized it all from Indians then why he didn't make use of syncopation or of negative numbers?!
Moreover, the Brahmagupta work
If al-Khawarizmi plagiarized it all from Indians then why he didn't make use of syncopation or of negative numbers?!
Moreover, the Brahmagupta work
seems to be influenced by Diophantus bcz he used some of the same examples of Diophantus. For al-Khwarizmi, he didn't seem to be aware of Diophantus work as mentioned by Boyer.
9. @BharadwajSpeaks used the same screenshot to highlight the point of Henry https://twitter.com/BharadwajSpeaks/status/1343150578940092417?s=20
9. @BharadwajSpeaks used the same screenshot to highlight the point of Henry https://twitter.com/BharadwajSpeaks/status/1343150578940092417?s=20
that al-Khwarizmi plagiarized it from Hindus, despite the fact that the name "Hindus" didn't come in application until 12th cen. & the name itself was given by Persian Aryans or was derived from old Persian.
Still as mentioned above, it's unlikely that Henry has studied
Still as mentioned above, it's unlikely that Henry has studied
that al-Khwarizmi plagiarized it from Hindus, despite the fact that the name "Hindus" didn't come in application until 12th cen. & the name itself was given by Persian Aryans or was derived from old Persian.
Still as mentioned above, it's unlikely that Henry has studied
Still as mentioned above, it's unlikely that Henry has studied
al-Khawarizmi work to make such conclusion. Also, there is nothing elementary in Indian mathematics as opposed to al-Khwarizmi.
10.(i). "came to the same conclusion after diligent research"
Interestingly Cossali couldn't decide whether al-Khwarizmi https://twitter.com/BharadwajSpeaks/status/1343153229920522240?s=20
10.(i). "came to the same conclusion after diligent research"
Interestingly Cossali couldn't decide whether al-Khwarizmi https://twitter.com/BharadwajSpeaks/status/1343153229920522240?s=20
took Algebra from Greeks or Indians.
But other scholars don't agree with Cossali like Sarton, Gandz, Boyer, Cajori, Rashed etc.
Sarton(image 1) Rashed(image 2)
Gandz(image 3)- who wrote the work, "The sources of al-Khwarizmi algebra".
Cossali despite doing diligent research
But other scholars don't agree with Cossali like Sarton, Gandz, Boyer, Cajori, Rashed etc.
Sarton(image 1) Rashed(image 2)
Gandz(image 3)- who wrote the work, "The sources of al-Khwarizmi algebra".
Cossali despite doing diligent research
failed to explain the differences in Diophantus, Brahmagupta & al-Khwarizmi works.
(ii). "skilled in Indian tongue and fond of Indian matters"
How come al-Khwarizmi was fond of Indian matters yet didn't travel there even once!!!
The proficiency in Sanskrit still doesn't
(ii). "skilled in Indian tongue and fond of Indian matters"
How come al-Khwarizmi was fond of Indian matters yet didn't travel there even once!!!
The proficiency in Sanskrit still doesn't
give the idea of plagiarism when there are glaring distinctions.
10.This is quite intriguing that Cossali made a comment like that with no evidence whatsoever.
Other historians of mathematics & those who wrote works in this regard found it very different https://twitter.com/BharadwajSpeaks/status/1343153852279791618?s=20
10.This is quite intriguing that Cossali made a comment like that with no evidence whatsoever.
Other historians of mathematics & those who wrote works in this regard found it very different https://twitter.com/BharadwajSpeaks/status/1343153852279791618?s=20
For ex- Rashed said that al-Jabr concerns the theory of linear & quadratic equations with a single unknown & the elementary arithmetic of relative binomials & trinomials...That is,the elementary & foundational pillar was given by al-Khawarizmi which isn't observed in other works.
My CONCLUSIONS:---
1. As mentioned during the whole thread, there is no evidence of plagiarism by al-Khwarizmi, rather Brahmagupta copied some same examples as of Diophantus & Aryabhatta didn't contributed much.
But al-Khwarizmi did build the elementary level of Algebra.
1. As mentioned during the whole thread, there is no evidence of plagiarism by al-Khwarizmi, rather Brahmagupta copied some same examples as of Diophantus & Aryabhatta didn't contributed much.
But al-Khwarizmi did build the elementary level of Algebra.
2. The appreciations showered by sanghis & others on @BharadwajSpeaks thread despite having intellectual dishonesty, ignorance & persistent red-herring with biased understanding suggest us how anti-intellectualism & ignorance are prevalent in India & we're still blinded by hate
& prejudice of others. He for sure is an Islamophobic bigot.
3. Lastly, in my humble opinion, we'd stop calling Islamic Mathematics or Islamic medicine etc. Islam wasn't revealed to guide us in Science but rather opens our intellects & hearts to pursue it to comprehend the
3. Lastly, in my humble opinion, we'd stop calling Islamic Mathematics or Islamic medicine etc. Islam wasn't revealed to guide us in Science but rather opens our intellects & hearts to pursue it to comprehend the
magnificent & unbelievable complex creations of God.
We'd separate the purpose of religion of Islam from the utility of Science.
Though, we can use mathematical arguments to prove existence of God...
END!!!!
We'd separate the purpose of religion of Islam from the utility of Science.
Though, we can use mathematical arguments to prove existence of God...
END!!!!
This is a thoroughly researched refutation on al-Khwarizmi which took me 2 days to finish. Give it a read & RT...
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