[mechMA]

Well this is a tough one.

Whats your philosophy on this one?
If you have no standard, try this:

look at something in the room that there is more than one of, and try to describe how many there are with out using numbers, and you can only use words.
hard to do isn't it?

[mafiaparty303]

there is a paper clip infront of me...there is another next to it,....and another....and another....

[Borek]

About 3yo daughter of my friend have seen sheeps for the first time of her life. "Mom, see, sheep! Second! second! second! ..."

[constant thinker]

1 word: Necessity.

[Mitch]

The two ways to count numbers is by the typical numerical digits and also by recognizing patterns. If you are using your brain to count numbers, but also need to count an other set of numbers the only way to do it is to block the second set of numbers into patterns and group them. Oddly enough, I know this because I've done it for recreation and in the lab.

[Yggdrasil]

From the point of view of pure mathematics:

Numbers are parts of an algebra which we have adopted to describe physical phenomena quantitatively.  In mathematics, algebras are sets of elements (numbers) equipped with one or more binary operations (e.g. addition and multiplication) and a set of axioms which completely define the properties of the algebra.  These abstract algebras can then be applied to describe the quantitative aspects of physical phenomena.  For example, the natural numbers (1,2,3,...) are a good algebra to describe counting (e.g. how many fingers am I holding up, how many apples are on the tree).  Similarly, the real numbers are a good algebra for describing continuous measurements and the complex numbers are good for describing waves (e.g. electromagnetic radiation).  Algebras can also be used to describe phenomena that we do not normally associate with "numbers", for example, we use groups to describe symmetry operations and we use vector spaces to describe quantum mechanical operators.

Of course, here's a good philosophical question:  did mathematicians invent these algebras to describe physical phenomena, or did these algebras exist a priori and mathematicians discovered them?

[Mitch]

Nobel committees do not consider Mathematics as a discovery science.

[xiankai]

it comes from history, just like language. over time it built up into the gigantic numeral system that wraps itself around virtually everything today

[Yggdrasil]

Nobel committees do not consider Mathematics as a discovery science.

I would disagree.  For example, a lot of work has been done to elucidate the structure of prime numbers.  Of course, mathematicians have had to invent various tools to probe the structure of primes (such as the Riemann zeta function), but I would argue that the information obtained through these methods have been discoveries.  Mathematicians did not invent these properties of prime numbers; rather, they discovered them.  As an analogy, chemists study the structure of natural products.  They use tools that they have invented (organic synthesis, NMR, crystallography), but these tools just help to aid in the elucidation of the structures of their compounds of interest.

[constant thinker]

Yggdrasil, you have a very good point. I agree with you.

[Borek]

I think what Mitch refers to is simply the fact that there is no Nobel in math.

[Donaldson Tan]

I think what Mitch refers to is simply the fact that there is no Nobel in math.

I think they call it the Fields Medal.

It is quite hard to justify numbers or mathematics is really a science in its own right because unlike the physical sciences, there is no physical effect. In fact, mathematics has evolved a long time to describe physical phenomena and financial accounting such that it is a tool that we can no longer live without. An extension of mathematics would be Computer Science. Is Computer Science a science in its own right or is it a systematic experiment to automate logic on a machine?