Why Does Mathematics Need Physics?

[matt grime]

Moderator's note: the first few posts in this thread were split from another thread

What you did in your example was show that mathematics' rules are consistent with the model you proposed. This is a plus point for mathematics, and the model. It doesn't prove that (-1)*(-1)=1. Whether or not such a view of mathematics as divorced from what it is modelling is a good thing is a whole other philosophical kettle of fish. They each have their flaws - yours because it presupposes physical intuition, and the acceptance of signed quantities in the first place.

 

[Dr. Proof]

What you did in your example was show that mathematics' rules are consistent with the model you proposed. This is a plus point for mathematics, and the model. It doesn't prove that (-1)*(-1)=1. Whether or not such a view of mathematics as divorced from what it is modelling is a good thing is a whole other philosophical kettle of fish. They each have their flaws - yours because it presupposes physical intuition, and the acceptance of signed quantities in the first place.

I agree, matt grime. By participating in this forum, I have found a little more understanding of how mathematicians think, that is, what mathematicians think mathematics is. All my life, I have viewed Mathematics and Physics as inseparable subjects; now I know that mathematicians view Mathematics as being a subject in and of itself, without regards to applications. Even though I disagree with this view, because my mind needs real-world applications in order to process information, at least I understand what the view is now.

I think it is interesting to note, however, that Isaac Newton came up with Calculus in order to solve real-world Physics problems. What is the reasoning behind mathematical rules if they do not need real-world applications?

 

[Kurdt]

I agree, matt grime. By participating in this forum, I have found a little more understanding of how mathematicians think, that is, what mathematicians think mathematics is. All my life, I have viewed Mathematics and Physics as inseparable subjects; now I know that mathematicians view Mathematics as being a subject in and of itself, without regards to applications. Even though I disagree with this view, because my mind needs real-world applications in order to process information, at least I understand what the view is now.

I think it is interesting to note, however, that Isaac Newton came up with Calculus in order to solve real-world Physics problems. What is the reasoning behind mathematical rules if they do not need real-world applications?

If you're interested in learning more about that then I recommend reading the first few chapters of Roger Penrose's Road To Reality. It will hopefully answer all your questions and more. It also has plenty of references for more in depth reading.

 

[Office_Shredder]

I agree, matt grime. By participating in this forum, I have found a little more understanding of how mathematicians think, that is, what mathematicians think mathematics is. All my life, I have viewed Mathematics and Physics as inseparable subjects; now I know that mathematicians view Mathematics as being a subject in and of itself, without regards to applications. Even though I disagree with this view, because my mind needs real-world applications in order to process information, at least I understand what the view is now.

I think it is interesting to note, however, that Isaac Newton came up with Calculus in order to solve real-world Physics problems. What is the reasoning behind mathematical rules if they do not need real-world applications?

And number theory was started in 1943 in an attempt to create uncrackable codes. Fascinating stuff, the history of math. :tongue2:

 

[morphism]

I think it is interesting to note, however, that Isaac Newton came up with Calculus in order to solve real-world Physics problems. What is the reasoning behind mathematical rules if they do not need real-world applications?

The view that mathematics is created purely for some "real-world application" is short-sighted, in my opinion. While it is true that a lot of good mathematics was created to solve "real-world" problems, sometimes we can reap great rewards by ditching "reality" and generalizing and focusing on the ideas instead of the applications. Incidentally, such pursuits might actually give rise to more fascinating applications down the road. For a famous example, think about how differential geometry started out, and what Einstein did with it decades later.

I could go on, but instead I'll direct you to a series of videos where Cambridge Fields medalist Timothy Gowers shares his opinion:
(Part 1)
(Part 2)
(Part 3)
(Part 4)
(Part 5)
(Part 6)
(Part 7)
(Part 8)

Enjoy!

 

[matt grime]

my mind needs real-world applications in order to process information, at least I understand what the view is now.

That is OK for your mind, but a physical intuition is no real help for mathematics.

I think it is interesting to note, however, that Isaac Newton came up with Calculus in order to solve real-world Physics problems. What is the reasoning behind mathematical rules if they do not need real-world applications?

When Einstein wanted a curved geometry he found out that mathematicians had invented the subject 30 years before without regard to real life applications. Modern physics is permeated by group theory, the physicists brought that in round about the 1920s. Yet groups were invented in the mid 1800s by Evariste Galois to study completely abstract objects. Euler had been using them before to study other even more abstract things though he didn't formalize it. The language of string theory (which is really just pure mathematics) - derived categories, equivalences of A and B branes - was developed by Grothendieck some 20 years ago before anyone ever thought that particles could perhaps be modeled with vibrating strings.

The histories of the subjects are intertwined, and the better for it, but to say that mathematics needs physics, is definitely getting it the wrong way round if we are to assert one needs the other.

 

[Dr. Proof]

The histories of the subjects are intertwined, and the better for it, but to say that mathematics needs physics, is definitely getting it the wrong way round if we are to assert one needs the other.

Thanks, matt grime, I am beginning to understand this history of math and physics a little better now.