we've already talked about how Classical Greece

has had an immeasurable impact

not just on Western civilization,

but on civilization as a whole.

In order to understand the period

that we call Classical Greece,

it's valuable to place it in context on a timeline,

so I have significant conflicts or events

that happened to the Greek world on this timeline,

especially in the fifth and fourth centuries BCE

In the beginning of the fifth century BCE,

you have the Greco-Persian Wars,

where the Greek city states are able to fend off attack

from the great Persian Empire,

and then they go on the offensive.

But as we exit the fifth century BCE,

the city states start fighting amongst themselves.

You have Athens leading the Delian League

in a fight against Sparta and their allies,

which significantly weakens the city states.

It ends with Athens losing,

but all of the city states have been weakened,

and it leaves them open to be conquered by the Macedonians,

in particular Phillip of Macedonia,

and then his son Alexander the Great

is able to not just keep control

of Greece, of the city states,

but conquer Egypt and Persia

and get all the way to modern day Afghanistan and Pakistan,

but after his death,

you then have his successors,

and Greece falls under the Antigonid dynasty.

But eventually as we get into the second

and first century BCE,

it goes under Roman control,

and we've talked about this Classical period,

all of the various contributions.

We've talked about the contributions in philosophy,

from people like Socrates,

and Socrates's student Plato,

and Plato's student Aristotle,

but there were also significant contributions

in mathematics.

You have Pythagoras,

who actually predates these philosophers,

and he's most famous, especially to many of us,

for his Pythagorean Theorem

and a lot of mathematics

and the foundations of a lot of geometry.

But he and his followers,

they were actually creating something of a mysticism,

of a religion around mathematics,

and even a philosophy that would later influence

some of the other philosophers that we talk about,

especially this ideal of ideal platonic forms.

You can imagine, if you're studying perfect right triangles,

there's no such thing as a perfect right triangle

in the universe.

These are ideas that we use in geometry,

and other things in the universe

are really just approximations of these,

but to appreciate the philosophical side of Pythagoras,

here are some quotes from him,

or quotes ascribed to him.

"There is geometry in the humming of the strings.

"There is music in the spacing of the spheres.

"Reason is immortal, all else mortal."

And you see even in the sixth century BCE

this thread of Greek thinking,

putting reason at a very high level,

not just trying to explain everything

with pure mysticism,

although Pythagoras definitely was,

and Pythagoreanism was definitely about mysticism,

but it was mysticism that at the core

had mathematics and geometry.

But continuing on with significant

mathematical contributions from ancient Greece,

we have Euclid.

We don't know all of the exact details

of his birth and his death,

but he is the Father of Modern Geometry,

and as you can see in this map here,

he didn't live in what we call Greece proper today.

He lived in Alexandria,

a city established by Alexander the Great,

and this is during the Hellenistic Period

where all of the territory,

or most of the territory that had been conquered

by Alexander the Great was still ruled by his successors.

Egypt was ruled by Ptolemy,

establishing the Ptolemaic dynasty

in the time of Euclid,

and Euclid lived in that great center

of learning and the arts, Alexandria,

which even exists today,

and he is most famous for his Elements.

This is a much later printing of his Elements,

of Euclid's eEements,

but you would be amazed how much of modern geometry

has been described by Euclid.

Even your geometry textbook can trace it back

directly to Euclid's Elements.

Abraham Lincoln famously learned every proof

in Euclid's Elements in order to fine tune his mind.

So you can really view Euclid

as the Father of Geometry,

but that's not all.

There are many other contributors in philosophy and math,

and this is just, once again, a sample

of all of the folks who contributed.

On the side of philosophy,

you have Xenophon,

who was another one of Socrates' students

in addition to Plato,

and in fact, the life of Socrates

we learn from the writings of Plato and Xenophon.

Xenophon was also a historian

who gave us some accounts of the later Peloponnesian War.

You have the famous cynics,

Antisthenes and his student Diogenes,

Diogenes, famous for living in a barrel in Athens,

and somewhat insulting Alexander the Great.

But these cynics, which the word is derived

from being dog like,

these are people who were philosophers

who gave up the trappings of materialism

and caring, frankly, what other people thought.

As we go a little bit out of our timeline right over here,

you have Archimedes,

one of the greatest mathematicians

and scientists of all time,

but you also have contributions in the arts,

some of the most famous playwrights of the ancient time,

Aeschylus, Sophocles, Euripides.

Aristophanes, we might remember as being a bit

of a thorn in the side of Socrates.

He wrote about Socrates,

but it was more of a parody.

You have contributions in medicine,

the famous Hippocrates.

The Hippocratic Oath still has an influence

on modern medicine.

You have some of the earliest what we could say historians

that we know of,

Herodotus, famously giving us the accounts we have

of the Greco-Persian Wars,

a lot of what we even know

about the ancient Persian Empire.

You have Thucydides,

who gives us accounts of the Peloponnesian War

along with Xenophon.

And so when you see this density

of arts, sciences, learning

in one place,

a lot of this was centered in Athens.

It makes you wonder what was going on at that time,

and historians do call the period

from when the Athenians were able to fend off the Persians

all the way until the end of the Peloponnesian War

as the Golden Age of Athens,

and for good reason.

Look at this flourishing of the arts and the sciences

that developed during that period.

You might wonder what was happening in terms of government,

and government of this period might be one

of the longest lasting influences.

As we exit the sixth century BCE in 507,

you have Greek Democracy taking root in Athens,

and in fact, the word democracy is a Greek word,

government by the people.

And shortly after that,

during the Golden Age of Athens,

you start having leadership by Pericles.

He was an orator.

He was a statesman.

He was a general.

In this period right over here

that I have in orange,

often known as the Age of Pericles,

he helped Athens invest significantly

in the arts and in architecture.

Some of the most iconic structures

we now associate with Greece or ancient Greece

were built during his time.

They were promoted by him.

Here you have a picture of the Acropolis,

which is this rock outcropping,

which still exists in Athens

as it likely looked during the time of Pericles,

during the Golden Age of Athens,

and you can see here in particular

the most famous structure.

The Parthenon, a lot of which still stands today,

was constructed under the rule of Pericles.

As I mentioned, the Greek city states get conquered

by the Macedonians,

but after the death of Alexander the Great,

falls under the control of the Antigonid dynasty,

but eventually, as we get into the second century BCE,

off of this timeline,

it comes under Roman control,

becomes part of the Roman Empire.

But the Roman Empire is itself significantly influenced

by Greek culture, Greek mathematics,

Greek architecture, Greek philosophy,

and in a lot of ways,

the Romans end up becoming the caretakers

of much of this culture that we talk about in this video,

and once you have the decline of the Roman Empire,

especially the western Roman Empire,

and Europe enters into the Middle Ages,

you have the Islamic world that acts

as a bit of a bridge

of this Greek culture into the European Renaissance

and eventually the Enlightenment.

And so we can trace even our modern views

of science and philosophy

all the way back to these Greeks,

and so I'll leave you with this quote

from the Roman poet Horace

who wrote this around the first century BCE.

"Captive Greece took captive her fierce conqueror

"and instilled her arts in rustic Latium," or Laecium.

And so what he's saying is,

even though Rome had conquered Greece,

Greece's culture took captive her conqueror,

took captive the Roman culture,

instilled Greece's arts in the rustic Latin world.