Doing theoretical/pure mathematics

[jimgavagan]

Do u think theoretical/pure mathematics is possible BEFORE (or, without ever) observing the natural world, or do you think that observations of concrete physical phenomenon (the natural world) HAVE to come first?

 

[micromass]

I think pure mathematics doesn't care about physicial observations. You may have them, or you may not have them. It doesn't matter.

 

[Oriako]

That is actually an extremely good question jimgavagan.

There is a debate going on over whether mathematics are contrived or discovered. If mathematics is contrived, then it is entirely based off of our raw sense data or 'qualia' and have it seems to exhibit an emergent nature due only to human interaction. If mathematics is discovered, then it is somehow woven into metaphysical reality in a way that is accessible by human consciousness. The realm of abstract ideas and principles is very intriguing and depending on your perspective, these concepts could have existed before the universe or anything existed. It just all depends on if they are a priori in nature or are a sort of intellectual structure conjured up solely by human beings.

 

[disregardthat]

That is actually an extremely good question jimgavagan.

There is a debate going on over whether mathematics are contrived or discovered. If mathematics is contrived, then it is entirely based off of our raw sense data or 'qualia' and have it seems to exhibit an emergent nature due only to human interaction. If mathematics is discovered, then it is somehow woven into metaphysical reality in a way that is accessible by human consciousness. The realm of abstract ideas and principles is very intriguing and depending on your perspective, these concepts could have existed before the universe or anything existed. It just all depends on if they are a priori in nature or are a sort of intellectual structure conjured up solely by human beings.

I don't think he was getting at this issue at all. He is talking about whether physical motivation is necessary for development of mathematics. It's not however, just think about number theory.

 

[chiro]

I don't think he was getting at this issue at all. He is talking about whether physical motivation is necessary for development of mathematics. It's not however, just think about number theory.

While I agree with you that it isn't necessary, I find that many areas of mathematics are motivated by natural sciences such as physics and computer science. Typically we get something of that sort in nature, and then take what's in nature and try to codify it into some kind of framework so that we can analyze it.

 

[disregardthat]

While I agree with you that it isn't necessary, I find that many areas of mathematics are motivated by natural sciences such as physics and computer science. Typically we get something of that sort in nature, and then take what's in nature and try to codify it into some kind of framework so that we can analyze it.

No doubt about that, but Jim went out a little strong perhaps.

 

[jhooper3581]

I think theoretical/pure mathematics is an important tool before observing physical world. For example, calculus and analysis are important to understand quantum mechanics.

 

[Vahsek]

I don't think he was getting at this issue at all. He is talking about whether physical motivation is necessary for development of mathematics. It's not however, just think about number theory.

Sorry but I seriously think that even number theory originated from observing the physical world. For instance, it's completely logical to deduce that numbers were invented in the first place only to quantify things that we can see. All the other theories simply added up to that main basic idea.

 

[rbj]

so let's get really basic:

we have this mathematical operation called "addition" and it has definition without referring to physical quantity. but there are so many different physical quantities that are conserved within some boundary. when that is the case, addition has physical significance and the math reflects the natural world intrinsically.

 

[coolul007]

I think mathematics was invented to explain the physical world, first counting and then the rest follows. if there were no humans in the forest would we see numbers?