WEBVTT

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What I want to do
in this video is

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think about the
origins of algebra.

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The origins of
algebra, and the word,

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especially in association
with the ideas

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that algebra now represents,
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

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is the "Compendious
Book on Calculation

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by Completion and Balancing."

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And it was written by a
Persian mathematician who

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lived in Baghdad
in, I believe, it

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was in the eighth
or ninth century.

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

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AD.

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And algebra is the Arabic word,
that here is the actual title

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that he gave to it, which
is the Arabic title.

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Algebra means restoration
or completion.

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Restoration or 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,

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and I don't know
Arabic, but I actually

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do know some
languages that seems

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to have borrowed a
little bit from Arabic,

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or maybe it went the
other way around.

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

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Urdu and Hindi to understand
a good India movie,

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but Al-kitab, kitab means book.

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So this part is book.

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Book.

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

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because I don't know
the word for compendious

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and that seems like that.

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Fihisab, hisab means
calculation in Hindi or Urdu,

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so this is calculation.

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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, you
could view that as completion.

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Completion.

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

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Balancing.

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Completion and balancing.

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So if we wanted
to translate it--

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

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but the book, I guess
this is saying compendious

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on calculation by
completion and balancing

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

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took on many of
its modern ideas.

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Ideas of balancing an equation.

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The abstract problem
itself, not trying

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to do one off problems
here or there.

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But al-Khwarizmi 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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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

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in around the eighth
or ninth century.

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So let me draw a
time line here, just

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so we can appreciate everything.

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So that is timeline,
and then whether or not

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you are religious, most
of our modern dates

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are dependent on the birth of
Jesus, so that is right there.

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

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When we want to
be non-religious,

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we say the common era.

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Before the common era, when
we want to be religious

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

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

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year of our lord.

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

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

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But either way, so this
is 1000 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 when

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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,

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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 stumbling

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on many of the ideas in algebra.

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But our first records of
people really exploring

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the ideas that are
hit upon in algebra

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come from ancient
Babylon around 2000 years

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before the common
era, before Christ.

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So right around there
there are 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 algebra that
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 there.

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And Babylon, it's 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

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that we know of that
where people were starting

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to do what we would
call real, real algebra.

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And then you fast forward.

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

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

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of people using algebra, but 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 to 300

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

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who lived in Alexandria.

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So this is Greece
right over here,

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but he lived in Alexandria,
which at the time

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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 Diophantus,

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or Diophantus.

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

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And he is sometimes
credited with being

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the father of algebra,
and it's debatable

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whether it's Diophantus
or al-Khwarizmi.

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al-Khwarizmi, who
kind of started

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using these terms of
balancing equations

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and talking about
math in a purer 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

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by the Babylonians,
although they all

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did contribute in their own way.

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It's not like they
were just copying

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

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another famous mathematician
in the history of algebra

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was Brahmagupta, in India.

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Brahmagupta, in India.

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So obviously, and
actually, I don't

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know where in India he lived.

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I should look that
up, but roughly

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in that part of the world.

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And he also made
significant contributions.

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And then you have
al-Khwarizmi, who

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shows up right
there, al-Khwarizmi.

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And he is the gentleman
that definitely

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we credit with the name
algebra, comes from Arabic

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for restoration, and some
people also consider him to be,

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if not the father of
algebra, although some people

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say he is the father, he is
one of the fathers of algebra

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because he really started
to think about algebra

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in the abstract sense, devoid
of some specific problems

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and a lot of the way
a modern mathematician

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would start to think
about the field.