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Who Invented Algebra?

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Who Invented Algebra?

What would the world be without Algebra? It is a subject that is studied all over the world, and it is a discipline within math that is responsible for many discoveries and understandings. The man who invented Algebra was name Al Khwarizmi. He was a Persian mathematician living in 820 AD, and he wrote a book that displayed the beginnings of Algebra through problems and equations. Without his seminal work, algebra may not have been developed as it was.

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Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī or simply Al Khwarizmi was born in 780 AD and died in 850 AD.

Origins of the word ‘Algebra’
Algebra comes from the Arabic word al-jabr. The Latin name for Al Khwarizmi, which was “algoritmi”, roughly translates to “algorithm” or “equation”. This name is fitting because Algebra consists of many equations, algorithms, and problems. Also, it is believed that name was designed to be a dedication to the author of the first work on Algebra, Al Khwarizmi.

Al-Jabr




Al-Jabr is also the name of Al Khwarizmi’s book. The book is often referred to, alternately, by a longer title that translates closely to the English phrase, “The Book of Summary Concerning Calculating by Transposition and Reduction”. This translation captures the essence of what is found in his book, and his techniques involving algebraic equations are still taught and learned today.


A major change



Al Khwarizmi’s book brought major changes to the math world. Before his book, Greeks were responsible for most of the world’s understanding of math. The world was used to learning about math in terms of geometry, so Khwarizimi’s algebra was significant change at first. His work would influence later mathematicians including, Isaac Newton. It is believed that Al Khwarizimi was very proud and confident in his work that he successfully sold it to Roman travelers and conquerors, which in turn not only helped the Romans improve their understanding of math, but also helped Khwarizmi to spread his work beyond the Muslim world. Next time you complete an algebraic equation, be sure to thank Al Khwarizmi for his work and book about Algebra!



Who Invented Algebra?
 
Saying that “The man who invented Algebra was Al Khwarizmi “ is like saying that America was invented by Columbus.

The word algebra is a Latin variant of the Arabic word al-jabr, and came from the title of a book, Hidab al-jabr wal-muqubala, written in Baghdad about 825 A.D. by the Arab mathematician Mohammed ibn-Musa al-Khowarizmi. Al-jabr refers to operations described in the book by al-hwārizmī.

The words jabr (JAH-ber) and muqubalah (moo-KAH-ba-lah) were used by al-Khowarizmi to designate two basic operations in solving equations. Jabr was to transpose subtracted terms to the other side of the equation. Muqubalah was to cancel like terms on opposite sides of the equation. In fact, the title has been translated to mean "science of restoration (or reunion) and opposition" or "science of transposition and cancellation" and "The Book of Completion and Cancellation" or "The Book of Restoration and Balancing."

Jabr is used in the step where x - 2 = 12 becomes x = 14. The left-side of the first equation, where x is lessened by 2, is "restored" or "completed" back to x in the second equation. Muqabalah takes us from x + y = y + 7 to x = 7 by "cancelling" or "balancing" the two sides of the equation. See Origin of the Word Algebra

Al-Khowarizmi’s contribution was to use the words al-jabr and muqubalah to designate two basic operations in solving equations. His predecessors ( see the timeline below) were intrinsically (intuitively) performing such operations but did not give a name to such operations. And of course, Al-Khowarizmi may also have expanded the study of such operations.

Algebra may divided into "classical algebra" (equation solving or "find the unknown number" problems) and "abstract algebra", also called "modern algebra" (the study of groups, rings, and fields). Classical algebra developed over a period of 4000 years, while abstract algebra had its origins only during the last two or three centuries.
Chronologically, developments in algebra went through stages: Egyptian, Babylonian, Greek, Hindu, Arabic, European ( since 1500) , and modern algebra. Since algebra grew out of arithmetic, its development was preceded by concepts in numbers such as - irrationals, zero, negative numbers – by Hindu mathematicians, and complex numbers. As a science, Algebra progressed through three stages: first - the rhetorical (or verbal), second - the syncopated (in which abbreviated words were used), and third - the symbolic (modern).

Here is a partial timeline of key algebraic discoveries and developments from Wikipedia:


[TABLE="class: MsoNormalTable, width: 100"]
[TR]
[TD="width: 20%"]
Year
[/TD]
[TD="width: 78%"]
Event
[/TD]
[/TR]
[TR]
[TD="width: 20%"] Circa 1800 BC[/TD]
[TD="width: 78%"] The Old Babylonian Strassburg tablet seeks the solution of a quadratic elliptic equation. [/TD]
[/TR]
[TR]
[TD="width: 20%"] Circa 1800 BC[/TD]
[TD="width: 78%"] The Plimpton 322 tablet gives a table of Pythagorean triples in Babylonian Cuneiform script. [/TD]
[/TR]
[TR]
[TD="width: 20%"] 1800 BC[/TD]
[TD="width: 78%"] Berlin papyrus 6619 (19th dynasty) contains a quadratic equation and its solution. [/TD]
[/TR]
[TR]
[TD="width: 20%"] 800 BC[/TD]
[TD="width: 78%"] Baudhayana, author of the Baudhayana Sulba Sutra, a Vedic Sanskrit geometric text, contains quadratic equations, and calculates the square root of 2 correct to five decimal places[/TD]
[/TR]
[TR]
[TD="width: 20%"] Circa 300 BC[/TD]
[TD="width: 78%"] Euclid's Elements gives a geometric construction with Euclidean tools for the solution of the quadratic equation for positive real roots. The construction is due to the Pythagorean School of geometry. [/TD]
[/TR]
[TR]
[TD="width: 20%"] Circa 300 BC[/TD]
[TD="width: 78%"] A geometric construction for the solution of the cubic is sought (doubling the cube problem). It is now well known that the general cubic has no such solution using Euclidean tools. [/TD]
[/TR]
[TR]
[TD="width: 20%"] 150 BC[/TD]
[TD="width: 78%"] Jain mathematicians in India write the “Sthananga Sutra”, which contains work on the theory of numbers, arithmetical operations, geometry, operations with fractions, simple equations, cubic equations, quartic equations, and permutations and combinations[/TD]
[/TR]
[TR]
[TD="width: 20%"] Circa 100 BC[/TD]
[TD="width: 78%"] Algebraic equations are treated in the Chinese mathematics book Jiuzhang suanshu (The Nine Chapters on the Mathematical Art), which contains solutions of linear equations solved using the rule of double false position, geometric solutions of quadratic equations, and the solutions of matrices equivalent to the modern method, to solve systems of simultaneous linear equations. [/TD]
[/TR]
[TR]
[TD="width: 20%"] 1st century[/TD]
[TD="width: 78%"] Heron of Alexandria, the earliest fleeting reference to square roots of negative numbers.[/TD]
[/TR]
[TR]
[TD="width: 20%"] Circa 150[/TD]
[TD="width: 78%"] Greek mathematician Hero of Alexandria, treats algebraic equations in three volumes of mathematics. [/TD]
[/TR]
[TR]
[TD="width: 20%"] Circa 200[/TD]
[TD="width: 78%"] Hellenistic mathematician Diophantus lived in Alexandria and is often considered to be the "father of algebra", writes his famous Arithmetica, a work featuring solutions of algebraic equations and on the theory of numbers. [/TD]
[/TR]
[TR]
[TD="width: 20%"] 499[/TD]
[TD="width: 78%"] Indian mathematician Aryabhata, in his treatise Aryabhatiya, obtains whole-number solutions to linear equations by a method equivalent to the modern one, describes the general integral solution of the indeterminate linear equation, gives integral solutions of simultaneous indeterminate linear equations, and describes a differential equation. [/TD]
[/TR]
[TR]
[TD="width: 20%"] Circa 625[/TD]
[TD="width: 78%"] Chinese mathematician Wang Xiaotong finds numerical solutions to certain cubic equations. [/TD]
[/TR]
[TR]
[TD="width: 20%"] Circa 7th century
Dates vary from the 3rd to the 12th centuries.[SUP][7][/SUP]
[/TD]
[TD="width: 78%"] The Bakhshali Manuscript written in ancient India uses a form of algebraic notation using letters of the alphabet and other signs, and contains cubic and quartic equations, algebraic solutions of linear equations with up to five unknowns, the general algebraic formula for the quadratic equation, and solutions of indeterminate quadratic equations and simultaneous equations. [/TD]
[/TR]
[TR]
[TD="width: 20%"] 7th century[/TD]
[TD="width: 78%"] Brahmagupta invents the method of solving indeterminate equations of the second degree and is the first to use algebra to solve astronomical problems. He also develops methods for calculations of the motions and places of various planets, their rising and setting, conjunctions, and the calculation of eclipses of the sun and the moon[/TD]
[/TR]
[TR]
[TD="width: 20%"] 628[/TD]
[TD="width: 78%"] Brahmagupta writes the Brahmasphuta-siddhanta, where zero is clearly explained, and where the modern place-value Indian numeral system is fully developed. It also gives rules for manipulating both negative and positive numbers, methods for computing square roots, methods of solving linear and quadratic equations, and rules for summing series, Brahmagupta's identity, and the Brahmagupta theorem[/TD]
[/TR]
[TR]
[TD="width: 20%"] 700s[/TD]
[TD="width: 78%"] Virasena gives explicit rules for the Fibonacci sequence, gives the derivation of the volume of a frustum using an infinite procedure, and also deals with the logarithm to base 2 and knows its laws[/TD]
[/TR]
[TR]
[TD="width: 20%"] Circa 800[/TD]
[TD="width: 78%"] The Abbasid patrons of learning, al-Mansur, Haroun al-Raschid, and al-Mamun, had Greek, Babylonian, and Indian mathematical and scientific works translated into Arabic and began a cultural, scientific and mathematical awakening after a century devoid of mathematical achievements. [/TD]
[/TR]
[TR]
[TD="width: 20%"] 820[/TD]
[TD="width: 78%"] The word algebra is derived from operations described in the treatise written by the Persian mathematician, Muammad ibn Mūsā al-hwārizmī, titled Al-Kitab al-Jabr wa-l-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing") on the systematic solution of linear and quadratic equations. Al-Khwarizmi is often considered the "father of algebra", for founding algebra as an independent discipline and for introducing the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation) which was what he originally used the term al-jabr to refer to.[SUP][9][/SUP] His algebra was also no longer concerned "with a series of problems to be resolved, but 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." He also studied an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems. [/TD]
[/TR]
[/TABLE]
 
Dear Dr Ross

There is a big difference between a 'discovery' and an 'invention' . So, from where did you get this
concept of Columbus having INVENTED America !!!??? !!

If it was meant to sound more hilarious than PJ's OP, then the purpose was well achieved.

While it might make a good point for debate / discussion [ whether the Persian mathematician
in question actually discovered / invented Algebra ] , I think it has more to do with a Lady's
undergarment - designed [ invented / discovered - your choice ] in ALGERIA - long long long long before
Bhaskara or Aryabhatta .

Also that part about - "Classical / Abstract" - take your pick - We'll call it Dr Ross's Secret , before
MSK Sir 'discovers' anything - Classical / Abstract .

Feels nice to see some humor in an otherwise drab ' copy-paste ' Forum.

Yay Yem
 
Dear Dr Ross

There is a big difference between a 'discovery' and an 'invention' . So, from where did you get this
concept of Columbus having INVENTED America !!!??? !!

If it was meant to sound more hilarious than PJ's OP, then the purpose was well achieved.
.....
Yay Yem

Captain Turtle: Did you have a few drinks before reading my post? Or a few sleepless nights? Go back and re-read the first sentence of my post a bit more carefully. Think it over calmly. Talk it over with someone for the hidden sacrcasm in that sentence. Your post sounds more hilarious than your perceived hilariousness of my post!

Since, more likely, you may be a victim of ADHD, here is the significance of the first sentence:

Al K did not invent algebra. It was already there. Maybe we could say that he discovered it from his exposure to Hindu/Greek mathematics. He compiled the literature, may be worked on some new algebraic problems, wrote a book and passed it on to the Europeans.. From the Europeans' point of view, what Al K passed on was so totally new to them - they were just emerging from the Dark Ages - that they thought (erroneously) that he invented the subject.

If, what was a discovery of algebra is attributed as 'invented', it is rhetorically equivalent to stating that Columbus invented (not discovered) America - Just to drive home the point that one statement is as ridiculous as the other. Something like reductio ad absurdum.
 
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Dr Ross

ADHD / NPD /OCD/ whatever - I'll look forward to the book : " Invention of India " by Dr Ross
- as a sequel to Nehru's ' The Discovery of India '.

Yay Yem
 
Dr Ross

ADHD / NPD /OCD/ whatever - I'll look forward to the book : " Invention of India " by Dr Ross
- as a sequel to Nehru's ' The Discovery of India '.

Yay Yem

If you are so hung up on invention/discovery dichotomy, I will title the book,
"India, re-invented through re-discovery" !
 
In our college days we know 'Algebra' is a 'cobra' which makes us 'kaabra'.

Alwan
 
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