hmmm... here's a question for ya!

[Ma77o]

Is math discovered, or invented?

[Rijnzael]

Mathematics are used to describe the laws of nature and are fundamental to our understanding of nature's laws, but not to the operation of those laws. The laws of physics carry themselves out flawlessly, whereas what mathematics does is attempt to elegantly describe these laws. We discover the laws of nature and we invent mathematics to describe them.

[blackprince491]

Mathematics are used to describe the laws of nature and are fundamental to our understanding of nature's laws, but not to the operation of those laws. The laws of physics carry themselves out flawlessly, whereas what mathematics does is attempt to elegantly describe these laws. We discover the laws of nature and we invent mathematics to describe them.

I couldn't have said it better if i tried excellent answer

[ELorenz]

Math is both discovered and invented. It is discovered in that we find results that are surprising and counter intuitive. For example a mathematician named Rumanujan discovered some interesting properties of infinite series in the first decade of the 1900's that we are only now seeing applications for in string theory. The properties are already there we just haven't figured them out or named them, or made notation for them.

It is invented in that we create the notation and the labels, and in some cases we invent the applications. For example networking makes use of topological properties. We invented the field of networking though, the same thing could be said for cryptography.

[jetbackwards]

I would agree with Rijnzael. Maths is just a method of modelling and abstraction from the real world - we invented it to make expressing the real world more easy!

[Sharmz]

Mathematics are used to describe the laws of nature and are fundamental to our understanding of nature's laws, but not to the operation of those laws. The laws of physics carry themselves out flawlessly, whereas what mathematics does is attempt to elegantly describe these laws. We discover the laws of nature and we invent mathematics to describe them.

I couldn't have said it better if i tried excellent answer

Agree, that was a fantastic answer, gave me new views on math and physics.

[ELorenz]

using the supposition that math is invented to describe the laws of nature, i pose this question.

What does f(x) = x^2 describe in nature.

[JMas]

ELorenz,
I think I know the point you're trying to make. Mathematics is a language that can be used to model nature, though, this is not its sole responsibility/endeavour (this is a huge topic).

As for your f(x) = x^2, well, this relation describes one of the more important natural laws. The Harmonic Potential:

U = 1/2 * k * x^2

where;
U = Harmonic Potential
k = a positive constant
x = displacement

This has been used in a lot of models, for example, an approximation of lattice vibrations in crystals (small amplitude), called the "Harmonic Limit" or "Harmonic Approximation" and the Quantum harmonic oscillator (V. Important) amongst others.

[ELorenz]

I see what you're saying about it being a part of the harmonic function, however U doesn't equal f(x) as I defined f(x) the two are very different functions. Just as x^2 doesnt equal x^3. But you are right in that I am trying to make the point that there are many aspects of mathematics that are completely unrelated to physical laws. Physics uses mathematics, mathematics doesn't use physics.

For example in physics a vector is a quantity and a direction. such as a force vector. In mathematics a vector is an entity that satisfies being an element of a vector space, in fact a point itself could be a vector in mathematics. (I just learned that the other day ).

[JMas]

Elorenz,
Thank you for your reply.

Both U and f show a square relationship on their independent variable. k can be equal to 2.

The concept of a vector was taken directly from physics.

The two vectors you mention in your second paragraph are also different in mathematics as the former is defined in an Euclidean space whereas the latter is defined in Coordinate space. There is no inner product in Coordinate space so you can't have direction or magnitude (which is what I assume you mean by quantity).

That said, you correctly point out that mathematics also studies relations between purely abstract mathematical entities such as number systems, polynomials etc.