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### Why Is Math Important?

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Date: 01/02/2002 at 15:30:23
From: Amanda Dalton
Subject: Why math is important

Why is math so important? Some of it we don't need to know in the
real world so why do they teach us things we won't need to know?
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Date: 01/02/2002 at 16:57:46
From: Doctor Achilles
Subject: Re: Why math is important

Hi Amanda,

Thanks for writing to Dr. Math.

This is a really hard question to answer well. I can think of a few
reasons.

The first is that it's often surprising how many places strange math
ideas pop up. We have an FAQ page dedicated to this, and it links to a
lot of archives that show how math is used in a lot of different
professions (from physics and medicine to law and just your everyday
life):

Why Study Math?
http://www.mathforum.org/dr.math/faq/faq.why.math.html

But there are two really important reasons for learning math that
don't directly link to how you will use it in your daily life.

The first is basically "the more you know, the more options you have
available." I'm 21 years old. Almost everyone I know who is my age
either had no idea what he or she wanted to do 5 years ago, or they
thought they knew but then changed their minds later. (Actually, a
fair number of my friends STILL don't know what they want to do.) I
have one close friend who wanted to be a computer scientist until he
got to college, and then he changed his mind and he's now studying
politics. But all the math that he learned for computer science has
helped him with the statistical analysis and economics he has to study
as part of his politics work. Fractions, geometry, algebra, and trig
will all be integrated into just about anything you ever want to
study, and having practiced those things in high school will allow
you to not have to worry about relearning them later. Slope-intercept
form for economic graphs or for population models in biology should be
second nature, so that you don't have to worry about math later and
can focus on what you really do want to study.

For example, let's say you want to be an ecologist. Ecologists often
study population size. Let's say that you're studying a population
whose size increases like this: size = 2 * time + 100. This is a
standard slope-intercept equation. A lot of people don't want to learn
slope-intercept because it doesn't seem to have any point. But if you
understand it enough that you don't have to think about it, then when
you see an equation like that, you won't have to worry about the math
at all and you can just think about the ecology.

So basically, the idea here is that if you learn math now, then when
you're confronted with math later in life, you won't have to worry
about it at all and instead you can just pay attention to what you
want to.

The alternative strategy is to not learn math now. You can wait and
see what math you end up needing for your job or your future education
and just learn that. That's okay in principle, but you'll end up
playing "catch-up" all the time.

When I finished the math requirements at college, I was really happy
at the time because I didn't like math then and I was glad to be done
with it. These past couple of years, I've gotten interested in
computer science as a hobby. However, not having any advanced math I
can't go very far with it, so if I wanted to do anything with it, I'd
have to go back and take a lot of math classes that would've been
easier for me to take a couple of years ago.

Since you don't know for sure what you're going to do with your life,
it's best to keep your options open. Of course, you can't learn
everything, and sooner or later you have to decide what you do want to
study. But, whatever it is, having a good background in math will put

The second reason to study math is that it gives you a different
perspective on things. I think that most people hate math because it
is taught just as an exercise in memorization. You get the impression
that all there is to math is just a bunch of formulas that you can
look up in a book. I think of math as something totally different.

What is Mathematics?
http://www.mathforum.org/dr.math/problems/erum.09.22.00.html

Philosophy of the Truths of Mathematics
http://www.mathforum.org/dr.math/problems/lauren.02.28.01.html

The way to be good at math is not to memorize a whole lot of different
things, it's just to memorize a few small things and then play around
with them and see what else you get.

multiplication, division, addition, and subtraction. One day (a long,
long time ago) somebody who knew all of those things was sitting
around and thinking. Below is my own cartoonish recreation of what
might have happened.

This person (we'll call him or her "Pat") was sitting around thinking

Pat knew that 3 + 4 = 7

Then Pat thought "what would happen to the equation if I added one to
both sides?" Pat tried it and got:  3 + 4 + 1 = 7 + 1

Pat realized right away that this new equation was also true. So then
Pat went back to the original equation: 3 + 4 = 7 and decided to
subtract 3 from both sides and got: 3 + 4 - 3 = 7 - 3.

Pat then did some arithmetic, and ended up with: 4 = 4.

Right away, Pat realized that this was something that could be applied
to new, different things. What Pat thought next was "what if I didn't
know one of the numbers?"

Pat was already familiar with equations like this: 3 + 4 = ?, and knew
that you could solve those equations.

What Pat decided to try was something a little different: ? - 4 = 7.
Pat knew from before that you can add or subtract the same number from
both sides of an equation (see above) and you'll still have a true
equation. So what Pat did was to add 4 to both sides of this equation
and got:

? - 4 + 4 = 7 + 4

After a little bit more arithmetic, Pat ended up with ? = 11.

So math is not just a bunch of memorization. If it's taught well, math
is just an extension of a few basic ideas to more and more complicated
applications. Algebra is not something new to learn, it's just another
way to do addition and subtraction and multiplication and division,
only with numbers and letters instead of just with numbers.

For a look at how complicated mathematical formulas are really just a
new way to look at old formulas you already know, check out:

Remembering Area Formulas
http://www.mathforum.org/dr.math/problems/summer.12.23.01.html

A classic example for me of how math is an exciting exploration of
simple ideas that leads you to interesting results is the "golden
ratio."  The golden ratio is a number (about 1.62). If you make a
rectangle where one side is equal to some number (whatever number you
like) and the other is equal to that number times the golden ratio, it
turns out to be a really pretty rectangle (at least as pretty as
rectangles get). In fact, if I told you to just draw a rectangle on a
piece of paper, you'd probably draw one that came pretty close to the
golden ratio.

Also, if you then take that rectangle and cut it up into a square and
another rectangle, the new rectangle that you make will also have the
golden ratio. You can then take the new rectangle and do the same
thing to that, on down forever, and each rectangle you make doing that
will have the golden ratio. You can then connect the corners of these
rectangles you've made and it makes a really pretty spiral (called the
golden spiral) which has other neat mathematical properties.

So one day there was some guy named Fibonacci. And he thought of an
interesting way to make a sequence of numbers. You start with the
sequence {1, 1}.  Then to get the next number of the sequence, you
just add the last two numbers in it together. So you get {1, 1, 2}.
Then you add the last two number of that sequence together to make a
new sequence {1, 1, 2, 3}. After a couple of more times, you'll end up
with {1, 1, 2, 3, 5, 8, 13}.

Now here's the cool part: One day someone asked themself what the
ratio is between each number in the Fibonacci sequence and the number
before it. So what that person did was take a number and divide it by
the one before. At first it didn't look too interesting, but the
person kept at it for a little while. As he got to bigger and bigger
numbers, he realized that the ratio of numbers in the Fibonacci
sequence gets closer and closer to the golden ratio. He then went on
to prove using calculus that as the numbers go on to infinity, the
ratio will EXACTLY approach the golden ratio.

Just imagine how exciting that must have been. To start with a simple
pattern like the Fibonacci sequence that anyone can understand and to
end up finding a ratio that has really cool mathematical properties
when you look at rectangles and spirals!

All of math is, as far as I see it, an exploration of what happens
when we assume certain basic "axioms" about the world and then see
what we get from that. There have been some very surprising results
that have opened the door to new questions about what our simple
assumptions and trivial starting places will take us next.

If you want to learn a bit more about the golden ratio and the
Fibonacci sequence, check out the Dr. Math FAQ:

Golden Ratio, Fibonacci Sequence
http://mathforum.org/dr.math/faq/faq.golden.ratio.html

So math really is important for your daily life, no matter what you
want to do. It's true that not everything you learn will be needed
later, but you never know what you'll want to do, and the more you
know and have to build on, the better off you'll be. Also, if you look
at it the right way, math is not a chore of memorization, it's a game
where you start with a few simple rules and see what more complicated
rules you can come up with using those simple tools.

If you have other questions, please feel free to write back.

- Doctor Achilles, The Math Forum
http://mathforum.org/dr.math/
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