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What I wanna do in this video

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is think about the origins of Algebra,

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the origins of Algebra.

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And the word

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especially an association with the ideas

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that Algebra now represents.

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comes from, comes from, this book

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or actually this is a page of the book right over there.

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The English translation for the title of this book is,

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"The Compendious book on Calculation by Completion and Balancing."

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And it was written by a Persian mathematician

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who lived in Baghdad, in, in...

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I believe it was in the 8th or 9th century

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I believe it was actually 820 A.D.

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when he wrote this book.

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A.D.

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And Algebra is the Arabic word

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that here is the actual title that he gave to it

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which is the Arabic title

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"Algebra means restoration or completion"

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restoration... restoration or completion... completion

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And he associated it in his book with a very specific operation,

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really taking something from one side of an equation

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to another side of an equation.

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But we can actually see it right over here. I don't know Arabic

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but I actually do know some languages that seem to have borrowed a little bit from Arabic

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or maybe went the other way around.

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But this says Al Kitab and

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I know just enough Urdu or Hindi to understand a good Indian movie.

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But Al Kitab 'Kitab' means "book".

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So this part is 'book'.

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Al-Muhktasar I think that means 'compendious'

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because I don't know the word for compendious and that seems like that.

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Fi Hisab, 'Hisab' means 'calculation' in Hindi or Urdu so this is calculation.

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Al-Gabr this is the root.

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This is the famous Algebra. This is where it shows up.

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So this is for 'completion'.

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You can view that as completion...completion

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and then Wa...Al-Muqabala

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that means essentially 'balancing'

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completion and balancing.

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So if we wanted to translate it

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and I know this is not a video on translating Arabic.

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but the book... the book

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I guess this is saying 'compendious on calculation by completion and balancing'

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is the rough translation over there.

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But that is the source of the word 'Algebra'.

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And this is a very very very important book.

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Not just because it was the first use of the word Algebra.

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But many people viewed this book as the first time

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that Algebra took on many of its modern ideas,

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ideas of balancing an equation,

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the abstract problem itself,

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not trying to do one-off problems here and there.

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But Al-Khwārizmī was not the first person.

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And just to get an idea of where all this is happening,

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so he was hanging out in Baghdad.

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So this is, and this part of the world shows up

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a lot in the history of algebra.

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But he was hanging out right there in around the 8th or 9th century.

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So let me draw a little timeline here,

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just so we can appreciate everything.

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So that is... timeline.

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And then whether or not you are religious,

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most of our modern dates are dependent on the birth of Jesus.

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So I will put, so that is right there.

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Maybe we'll put a cross over there

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to signify that, when we wanna be non-religious,

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we say 'common era' 'before the common era';

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when we wanna be religious,

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we say A.D.

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which means 'the year of our lord'.

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Anno...I don't know the latin...'Anno Domini', I believe

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'the year of our lord'

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And then when we want to ... in the religious context,

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instead of saying 'before common era',

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we say 'Before Christ', B.C.

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But either way, either way, so this is 1000

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in the common era.

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This is 2000 in the common era.

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And obviously we are sitting at least

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when I'm making this video, I'm sitting right about there.

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And then... this is 1000 before the common era.

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And this is 2000 before the common era.

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So the first traces, and I'm skipping out in

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and really it's just what we can find.

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I'm sure if we were able to dig more.

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We might be able to find other evidence

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of different civilizations and different people,

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stumbling on many of the ideas in Algebra.

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But our first records of people

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really exploring the ideas that are hit upon in Algebra

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come from ancient Babylon,

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around 2000 years before the common era,

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before Christ. So right around, right around there

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where there were stone tablets

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where it looks like people were exploring

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some of the fundamental ideas of Algebra.

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They weren't using the same symbols.

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They weren't using the same ways of representing the numbers.

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But it was Algrebra they were working on

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and that was once again in this part of the world.

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Babylon was right about... right about there.

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And Babylon has kind of kept the tradition of Sumeria.

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This whole region was called Mesopotamia

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-- Greek for 'between two rivers' --

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But that's the first traces of people that we know of

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that were people who were starting to do

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what we would call real real Algebra.

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And then you fast forward

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and I am sure even our historians don't know

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all the different instances of people using Algebra.

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But kind of the major contributions to Algebra

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we saw it here in Babylon 2000 years ago.

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And then if we fast forward to about 200-300 A.D.,

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so right over there,

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you have a Greek gentleman who lived in Alexanderia.

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So this is Greece right over here, but he lived in Alexandria

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which at the time was part of the Roman Empire.

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So Alexandria is right over here.

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And he was a gentleman by the name of

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Diophantus or Diaphantus

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or I don't know how to pronounce it.

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Dio... Diophantus.

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and he is sometimes credited with being the father of Algebra.

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And it's debatable whether it's Diophantus or whether it's Al-Khwārizmī',

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Al-Khwārizmī' who kinda started using these these terms of balancing equations

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and talking about math in a pure way

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while Diophantus was more focused on particular problems.

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And both of them were kind of beat to the punch by the Babylonians

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although they all did contribute in their own way.

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It's not like they were just copying what the Babylonians did.

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They had their own unique contributions

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to what we now consider 'Algebra'.

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But many, especially western historians,

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associate Diophantus as the father of Algebra.

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And now Al-Khwārizmī' is sometimes

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what other people would argue as the father of Algebra.

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So he made significant contributions.

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So if you go to about 600 A.D.

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So if you go to about 600 A.D.

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another famous mathematician in the history of Algebra

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was Brahma Gupta in India

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Brahma Gupta... in India.

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So... obviously and actually I don't know

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where in India he lived. I should look that up.

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But it's roughly... roughly in that part of the world

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And he also made a significant contributions.

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And then of course you have Al-Khwārizmī'

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who shows up right about there.

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Al-Khwārizmī' and he's the gentleman

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that definitely we credit with the name Algebra,

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comes from Arabic for 'Restoration'

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and some people also consider him to be, if not the father of Algebra,

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although some say he is the father,

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he is one of the fathers of Algebra,

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because he really started to think about Algebra in the abstract sense,

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devoid of some specific problems,

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and a lot of the ways

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that a modern mathematician would start to think about the field.