- A common complaint that math teachers hear
is when am I gonna need this in the real world?
I get it.
When I was in high school,
I felt like algebra class was pointless.
A bunch of imaginary numbers and rules
dreamed up by philosophers trying to prove to each other
how smart they were.
- But the origins of math are deeply practical.
Many mathematical innovations were invented to solve
very real world problems--problems of resource distribution,
of labor compensation, trade, property,
of determining the very value of things.
In other words, finance.
- And even though we, modern humans, have calculators
and accountants to crunch the big numbers for us,
it still takes an understanding of math to really know
what your money is doing and what risks are worth taking.
(bright music)
To help explain how money influenced
the development of mathematics, we invited Naiomi Israel,
a program director with the nonprofit organization FiCycle,
which teaches high school kids math through finance.
- Since the beginning of the species,
Homo sapiens have had to learn how to work together
and share the results of that work.
If two families of early people managed
to bring down a wooly mammoth,
how should they split the meat so that no one gets angry?
The idea of fairness was essential to a cooperative society,
which required methods to measure and count things.
One of the earliest numbering systems
was known as a tally stick,
a piece of wood or bone with notches carved into it.
Some date back over 10,000 years!
The people who used them probably didn't have words
or even concepts for numbers.
Each notch likely corresponded to an item,
so they could keep track of their possessions.
- Once humans developed agriculture,
this concept was refined with the invention of the bullae.
Instead of notches in wood,
Sumerian farmers used small clay tokens
to represent their goods.
For instance, if several farmers were going to store
their grain together, they'd use little sack tokens
with markings to identify who's were whose.
These tokens might be said to represent
the first form of math and money.
- To prevent any funny business, the tokens were sealed
in a hollow clay ball called a bulla and baked,
so it would have to be broken open to validate the contents.
Eventually, they started pressing impressions of the token
on the outside of the ball,
so it would only have to be cracked in case of a dispute.
It wasn't a big leap from here to realize
that they could press the tokens
into a separate clay tablet,
and then save room with new symbols
that represented numbers known as cuneiform script,
and thus the accounting ledger was born.
- Over the next few thousand years,
Babylonian mathematics, as it's known today,
made many important discoveries,
most of which were inspired by financial needs.
If a toolmaker and a shepherd wanted to trade,
they could use conversion ratios to find out
how much each one's goods were worth in a standardized unit,
like of sacks of grain.
For tax purposes, the government had to know
how much land someone owned,
so they developed sophisticated ways
of measuring irregular areas.
The resulting discipline,
Geometry, literally means earth measurement.
And if you needed to split 20 loaves of bread
amongst nine workers, you can't do it evenly
without inventing fractions.
- By about 2000 BC, the people of Mesopotamia
had started using precious metals as currency
instead of cumbersome cows and sacks of grain.
But metals can't be counted like cows or measured by area
like land or volume like grain.
Their value is determined by weight,
which means they had to devise methods
to accurately weigh things and create standardized units.
- As trade exploded across Europe, Asia, and Africa,
many different civilizations began striking their own coins
of different metals and levels of purity.
This may have simplified the transportation of currency,
but it was a mathematical headache.
For instance, if you have a four gram silver coin
at 70% purity, a 2 gram coin at 90% purity,
and a 5 gram coin at 60% purity,
and you melt them all down and combine them,
how pure is the resulting lump of silver?
- Problems like these spurred the development
of Hindu-Arabic mathematics
around the 9th or 10th century.
The scholar al-Khwarizmi provided equations
or sets of step-by-step instructions
to discover unknown values from known values.
Algebra is derived from the Arabic term al-jabr.
And the name al-Khwarizmi
eventually gave us the term algorithm
to describe a set of instructions
that provide an answer from an input.
Hindu scholars may also have invented the concept
of negative numbers to represent debt.
- A couple hundred years later,
the son of an Italian merchant named Leonardo Pisano,
advocated Hindu-Arabic mathematics
for many financial purposes.
Thanks to his book, "Liber Abaci",
Algebra spread throughout the mercantile class in Italy
used for things like establishing currency exchange rates
and calculating compound interest on loans.
Fibonacci, as he is more widely known,
is also credited with developing present value:
the notion that theoretical money
in the future is worth less
than the same amount of money in your hand.
- Some fields of applied mathematics
also derive from financial needs.
Mathematicians like Girolamo Cardano, Blaise Pascal,
and Pierre De Fermat developed gambling strategies
that became the foundation of probability theory,
and the science of statistics was greatly advanced
by the needs of the insurance industry
looking to minimize risk.
- Even calculus owes a bit of debt to finance.
To save money on wine for his wedding,
Johannes Kepler came up with new equations
to find the exact volumes of barrel shapes,
which contributed to the development of integral calculus.
- Today, virtually, everyone has access to the innovations
of these mathematical pioneers,
but it wasn't always this way.
Through much of ancient history,
the secrets of math were closely guarded,
and the elite who knew them
enjoyed special power and privilege.
Math was the magic that moved money,
and money made the world go round.
- I suppose that's kind of true today.
The "Wizards of Wall Street" use advanced math
to influence the flow of trillions of dollars
that affect people on every corner of the globe.
But you don't have to understand derivative pricing formulas
to benefit financially from math.
- The math you learn in high school algebra
is all you need to make many of the financial decisions
you'll face in life like investing,
budgeting, and managing risk.
- Sure, you can have a financial advisor
do a lot of that work for you, but at the end of the day,
if you really wanna translate your life goals
into financial results,
it helps to speak the language of math.
- [Julia and Philip] And that's our Two Cents.
- Thanks to our patrons for keeping Two Cents
financially healthy.
Click the link in the description
to become a Two Cents patron.
- For more on the historical legacy of money,
check out our video, "The History of the US Dollar".
(bright music)