- #1
jimgavagan
- 24
- 0
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?
Oriako said: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.
Jarle said: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 said: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 said: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.
Theoretical or pure mathematics is the branch of mathematics that deals with abstract concepts and theories rather than practical applications. It involves the study of fundamental principles and structures, such as numbers, shapes, and patterns, and their relationships and properties.
Theoretical mathematics is concerned with developing and proving abstract theories and concepts, while applied mathematics applies these theories to real-world problems and situations. Theoretical mathematics is often seen as the foundation for applied mathematics.
To excel in theoretical mathematics, one needs a strong foundation in mathematical concepts and theories, critical thinking and problem-solving skills, and the ability to think abstractly and logically. Strong mathematical intuition and creativity are also important for developing new theories and proofs.
Some common areas of research in theoretical mathematics include number theory, algebra, geometry, topology, and analysis. These areas involve the study of fundamental mathematical structures and their properties, as well as the development of new theories and proofs.
Although theoretical mathematics may not have immediate practical applications, it provides the foundation for applied mathematics and other fields such as physics, engineering, and computer science. The knowledge and skills gained from studying theoretical mathematics can also be applied in problem-solving and critical thinking in various industries and disciplines.