Origins of Algebra

Where did the word "Algebra" and its underlying ideas come from?

What I wanna do in this video

is think about the origins of Algebra,

the origins of Algebra.

And the word

especially an association with the ideas

that Algebra now represents.

comes from, comes from, this book

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

The English translation for the title of this book is,

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

And it was written by a Persian mathematician

who lived in Baghdad, in, in...

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

I believe it was actually 820 A.D.

when he wrote this book.

A.D.

And Algebra is the Arabic word

that here is the actual title that he gave to it

which is the Arabic title

"Algebra means restoration or completion"

restoration... restoration or completion... completion

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

really taking something from one side of an equation

to another side of an equation.

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

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

or maybe went the other way around.

But this says Al Kitab and

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

But Al Kitab 'Kitab' means "book".

So this part is 'book'.

Al-Muhktasar I think that means 'compendious'

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

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

Al-Gabr this is the root.

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

So this is for 'completion'.

You can view that as completion...completion

and then Wa...Al-Muqabala

that means essentially 'balancing'

completion and balancing.

So if we wanted to translate it

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

but the book... the book

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

is the rough translation over there.

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

And this is a very very very important book.

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

But many people viewed this book as the first time

that Algebra took on many of its modern ideas,

ideas of balancing an equation,

the abstract problem itself,

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

But Al-Khwārizmī was not the first person.

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

so he was hanging out in Baghdad.

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

a lot in the history of algebra.

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

So let me draw a little timeline here,

just so we can appreciate everything.

So that is... timeline.

And then whether or not you are religious,

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

So I will put, so that is right there.

Maybe we'll put a cross over there

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

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

when we wanna be religious,

we say A.D.

which means 'the year of our lord'.

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

'the year of our lord'

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

instead of saying 'before common era',

we say 'Before Christ', B.C.

But either way, either way, so this is 1000

in the common era.

This is 2000 in the common era.

And obviously we are sitting at least

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

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

And this is 2000 before the common era.

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

and really it's just what we can find.

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

We might be able to find other evidence

of different civilizations and different people,

stumbling on many of the ideas in Algebra.

But our first records of people

really exploring the ideas that are hit upon in Algebra

come from ancient Babylon,

around 2000 years before the common era,

before Christ. So right around, right around there

where there were stone tablets

where it looks like people were exploring

some of the fundamental ideas of Algebra.

They weren't using the same symbols.

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

But it was Algrebra they were working on

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

Babylon was right about... right about there.

And Babylon has kind of kept the tradition of Sumeria.

This whole region was called Mesopotamia

-- Greek for 'between two rivers' --

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

that were people who were starting to do

what we would call real real Algebra.

And then you fast forward

and I am sure even our historians don't know

all the different instances of people using Algebra.

But kind of the major contributions to Algebra

we saw it here in Babylon 2000 years ago.

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

so right over there,

you have a Greek gentleman who lived in Alexanderia.

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

which at the time was part of the Roman Empire.

So Alexandria is right over here.

And he was a gentleman by the name of

Diophantus or Diaphantus

or I don't know how to pronounce it.

Dio... Diophantus.

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

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

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

and talking about math in a pure way

while Diophantus was more focused on particular problems.

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

although they all did contribute in their own way.

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

They had their own unique contributions

to what we now consider 'Algebra'.

But many, especially western historians,

associate Diophantus as the father of Algebra.

And now Al-Khwārizmī' is sometimes

what other people would argue as the father of Algebra.

So he made significant contributions.

So if you go to about 600 A.D.

So if you go to about 600 A.D.

another famous mathematician in the history of Algebra

was Brahma Gupta in India

Brahma Gupta... in India.

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

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

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

And he also made a significant contributions.

And then of course you have Al-Khwārizmī'

who shows up right about there.

Al-Khwārizmī' and he's the gentleman

that definitely we credit with the name Algebra,

comes from Arabic for 'Restoration'

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

although some say he is the father,

he is one of the fathers of Algebra,

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

devoid of some specific problems,

and a lot of the ways

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