What is the nature and purpose of mathematics?

To put a structure to the quantifying and geometric natural world.

Mathematics is the only science where one never knows what one is talking about nor whether what is said is true
Bertrand Russell

I like that quote from Russell. Mathematics is sets of rules that act on themselves. It is useful for modeling the world, and it is fun to explore and learn about, at least for some of us.

Mathematics seeks to find and analyze patterns.

I just started reading Is God a Mathematician? It’s an interesting book, posing the same types of questions.

My take on it so far is that all of mathematics, starting with simple counting and proceeding to more complexity from there, is our human way of introducing (and finding) order into the complex system of our tiny portions of the world to start, and from there to “the Cosmos at large”. The fascinating thing is that the orderliness is there, just waiting for us to find and describe mathematically.

The main philosophical schools of thought I will roughly summarize.
Platonism: mathematics seeks to describe the universe of ‘forms’.
Formalism: pick the axioms you want, derive the results of them from logic.
Intuitionism: mathematical objects are constructs of the human mind.
Logicism: mathematics can be derived from logic.

Each captures an interesting aspect of the subject. None alone are fully satisfying or workable.

Math is truth. When we are able to define the things we see in mathematical formulas, we are able to express truth. We test what we think we know, by using numbers. If our real life numbers fit the hypothetical formulas and give us the answers we suspect, we know that reality is as we think is it. Numbers, Math, is a test that we use to measure reality.

ARITHMETIC (by Carl Sandburg)

Arithmetic is where numbers fly like pigeons in and out of your
head.
Arithmetic tells you how many you lose or win if you know how
many you had before you lost or won.
Arithmetic is seven eleven all good children go to heaven—or five
six bundle of sticks.
Arithmetic is numbers you squeeze from your head to your hand
to your pencil to your paper till you get the answer.
Arithmetic is where the answer is right and everything is nice and
you can look out of the window and see the blue sky—or the
answer is wrong and you have to start all over and try again
and see how it comes out this time.
If you take a number and double it and double it again and then
double it a few more times, the number gets bigger and bigger
and goes higher and higher and only arithmetic can tell you
what the number is when you decide to quit doubling.
Arithmetic is where you have to multiply—and you carry the
multiplication table in your head and hope you won’t lose it.
If you have two animal crackers, one good and one bad, and you
eat one and a striped zebra with streaks all over him eats the
other, how many animal crackers will you have if somebody
offers you five six seven and you say No no no and you say
Nay nay nay and you say Nix nix nix?
If you ask your mother for one fried egg for breakfast and she
gives you two fried eggs and you eat both of them, who is
better in arithmetic, you or your mother?

What sucks is how much people put into their questions and there’s no Lurve. Is Lurve lame?

Mathematics is a game that provides employment for people with Asperger’s Disorder. Keith Devlin’s paper A mathematician reflects on the useful and reliable illusion of reality in mathematics is an interesting glimpse into the nature of mathematics from a mathematician’s point of view.

Math is the only language spoken by the entire world.

This link talks about the real mathematicians and the problems they solved, despite their problems…. http://www.youtube.com/watch?v=d9jubx1gRi0&feature=player_embedded#!
In three parts….

and
http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html
talks about how teaching math needs a makeover because it teaches real world problem solving skills. yes, it does.

@cazzie, We could run a whole new thread on the problem with the way math is taught. I have a little bit experience in this. Years ago, when I was going to college, I did some substitute teaching between the end of the college term and the end of public school term. I was not expected to teach anything, so I gave the students some recreational math problems to give them something to do. Now picture the situation. I am a young substitute teacher with no authority and no experience. It is near summer break. My expectations were low about anybody taking an interest in the problems. Yet, to my surprise, there was quite a bit of interest.

Recreational math problems are much closer to the type of work that mathematicians do than the types of plug-in problems that most students are given. They require a bit of ingenuity. So what are we to conclude? Students want to be challenged. They want the opportunity to explore and discover and mathematics is ideally suited for this, it is taught right.

I apologize for going off topic, but this kind of stuff gets me worked up.

@LostInParadise I think it is very relevant to the question, and replies to some of the answers of the thread (@ratboy) Arguing that mathematics is simply and excuse for people to fulfil their obsessions is simplistic. Applied math helps solve problems in many fields of science, architecture, biology, chemistry, space exploration, computers, economics, (not a science and it’s application of math to it’s theories can be questioned on so many levels…but it’s still an area where math is used..)

Math solves problems. (I’m going to put that on a t-shirt.) The nature of math is to solve problems and explain things in definitive terms. (I don’t have Aspergers, just for the record) and I don’t have a math degree, but I fell in love with math when I started doing accounting and then again when I started doing my lay-man’s chemistry.

Solving problems with math begins with learning to ask the right questions, so it’s also an exercise in logic, which more people could use, in my opinion.

I agree with all that you say. My point relates to your second reference, regarding the way math is taught. This relates to what is commonly referred to as the math wars and, like I said, this is a whole other discussion. I do strongly feel that the only way to get a sense of math is to solve problems that guide students to explore and discover on their own, with the teacher mostly on the sidelines to be used as a resource.