Origins of algebra | Introduction to algebra | Algebra I | Khan Academy

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

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Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

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What I want to do
in this video is

think about the
origins of algebra.

The origins of
algebra, and the word,

especially in association
with the ideas

that algebra now represents,
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, I believe, it

was in the eighth
or ninth century.

I believe it was actually 820
AD when he wrote this book.

AD.

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 or 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,

and I don't know
Arabic, but I actually

do know some
languages that seems

to have borrowed a
little bit from Arabic,

or maybe it went the
other way around.

But this says Al-kitab,
and I know just enough

Urdu and Hindi to understand
a good India movie,

but Al-kitab, kitab means book.

So this part is book.

Book.

Al-mukhtasar, well, I think
that means compendious,

because I don't know
the word for compendious

and that seems like that.

Fihisab, hisab means
calculation in Hindi or Urdu,

so this is calculation.

Calculation.

Al-gabr, this is the root.

This is the famous algebra,
this is where it shows up.

So this is for completion, you
could view that as completion.

Completion.

And then wa'l-muqabala, and that
means essentially balancing.

Balancing.

Completion and balancing.

So if we wanted
to translate it--

I know this isn't a video
on translating Arabic,

but the book, I guess
this is saying compendious

on calculation by
completion and balancing

is the rough translation
right 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 a
lot of its modern--

took on many of
its modern ideas.

Ideas of balancing an equation.

The abstract problem
itself, not trying

to do one off problems
here or there.

But al-Khwarizmi was
not the first person,

and just to get an idea of
where all this is happening.

So he was hanging
out in Baghdad,

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 eighth
or ninth century.

So let me draw a
time line 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 that is right there.

Maybe I'll put a cross
over there to signify that.

When we want to
be non-religious,

we say the common era.

Before the common era, when
we want to be religious

we say AD, which means
in the year of our lord.

I don't know the Latin,
Anno Domini, I believe,

year of our lord.

And then when we want--
in the religious context,

instead of saying before common
era, we say before Christ, BC.

But 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,

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 there
there are 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 algebra that
they were working on.

And that was, once again,
in this part of the world.

Babylon was right about there.

And Babylon, it's 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
where people were starting

to do what we would
call real, real algebra.

And then you fast forward.

And I'm sure we're
missing-- and I'm sure

even our historians don't know
all of the different instances

of people using algebra, but the
major contributions to algebra,

we saw it here in
Babylon 2000 years ago.

And then if we fast
forward to about 200 to 300

AD, so right over there,
you have a Greek gentleman

who lived in Alexandria.

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 Diophantus.

I don't know how to
pronounce it, Diophantus.

And he is sometimes
credited with being

the father of algebra,
and it's debatable

whether it's Diophantus
or al-Khwarizmi.

al-Khwarizmi, who
kind of started

using these terms of
balancing equations

and talking about
math in a purer 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-Khwarizmi
is sometimes

what other people would argue
as the father of algebra,

so he made significant
contributions.

And if you go to 600 AD-- so
if you go to about 600 AD,

another famous mathematician
in the history of algebra

was Brahmagupta, in India.

Brahmagupta, in India.

So obviously, and
actually, I don't

know where in India he lived.

I should look that
up, but roughly

in that part of the world.

And he also made
significant contributions.

And then you have
al-Khwarizmi, who

shows up right
there, al-Khwarizmi.

And he is 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 people

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 way
a modern mathematician

would start to think
about the field.