At what point does math begin to describe the world in depth?

[Niaboc67]

I am taking Finite mathematics we learn things such as annuities and interest rates as well as matrices. Anyways i have taking math my entire life. And i do see the physical parts with things such as 1+1=2 but not in say y=5x+6 graphed out, or with isolating variables with functions like 8x+3=2x-4. At what point in mathematics does it start describing the physical world like the velocity of things, the rate/force a ball will hit and bounce against a floor and just nature in general. At what point does math begin describing these things?

 

[Stephen Tashi]

. At what point in mathematics does it start describing the physical world like the velocity of things, the rate/force a ball will hit and bounce against a floor and just nature in general.

It's physics that describes those things, not math per se. The physics that describes those things uses some of the math called calculus.

 

[Number Nine]

Strictly speaking, never. You can study applied mathematics if you want, and many of your math courses may feature examples of mathematics being used to describe the real world, but modern mathematics tries to abstract away from the real world, not towards it. If you want to model velocity, then calculus is the best tool you have, but it's just a tool; calculus is not "about" velocity or anything else in the real world.

 

[Vodkacannon]

-Calculus is a good tool because the universe is constatly changing. Our planet is constantly changing, that animal population near the lake is continuously changing. Calculus is probably the best at rates of change.

-One specific type of calculus, stochastic calculus works on sporadic things and seemingly random statistical things.

-Even more specifically, Brownian motion. It describes the random movement of a given particle.

-And finally, chaos theory. The study of dynamical systems that are sensitive to conditions.

All of these things are compatable with studying nature.

 

[coolul007]

Mathematics is the language of science. It is a concise way to describe the behavior of what is observed and then extended to describe behavior that has not been observed. The difficult part of learning mathematics is learning the fundamentals and not seeing an application. It is the "we must learn to crawl before we can walk, learn to walk before we can run" This may take some time until it "clicks".

 

[micromass]

modern mathematics tries to abstract away from the real world, not towards it.

How does mathematics abstract away from the real world?? Mathematics is heavily influenced by physics, so to some degree mathematicians care about the real world. True, some areas of research have no applications at all in the real world, but that's a minority.

 

[homeomorphic]

Calculus and differential equations are probably the most powerful tools for use in science and engineering. Fourier series are also very useful, for things like signal processing--radios, TVs, communication.

Fairly serious math was involving in unraveling the mysteries of quantum mechanics, which lead to the invention of the transistor, which I consider to be one of the greatest triumphs of math and physics, since the concepts involved are so deep and sophisticated, involving many insights that you wouldn't get until graduate school. It's easy to think that they might not be practical, yet they have completely changed the world. Modern computers and the whole internet would not have been possible without it.

Strictly speaking, never. You can study applied mathematics if you want, and many of your math courses may feature examples of mathematics being used to describe the real world, but modern mathematics tries to abstract away from the real world, not towards it.

It should abstract FROM the real world, not abstract away from it. To the extent that it pursues abstraction for its own sake, it is misguided. I think it's high time for the pendulum to swing the other way and for mathematicians to go back to the real world that they have been neglecting a bit lately.

If you want to model velocity, then calculus is the best tool you have, but it's just a tool; calculus is not "about" velocity or anything else in the real world.

I think that's, at best, a half-truth. If you forget about the inspiration for the mathematics, it becomes empty and lifeless. So, yes, it's about velocity. To me, that IS part of it. Not logically speaking, but morally speaking. It's not a good idea to try to separate the math from all the things that make it meaningful and to act like the subject can really stand up on its own without supporting examples, many of which can be drawn for the real world. Maybe if you are a robot, but not if you are a human being. Of course, it is abstract, so that it can apply equal well to any other rate of change, aside from velocity, which is rate of change of position. That much is true. But acting math can really stand on its own psychologically speaking is what leads to classes like the one I took on PDE, where the concepts were completely obscured because it was "not a physics class", and therefore, it ought to be studied abstractly, without the aid of physical insight, despite the fact that physical insight heavily influenced the historical development of the subject. Then, I read Arnold's PDE book, and because Arnold does not believe in separating math from physics, magically, the light was turned on and it was possible to understand many things conceptually that were needlessly obscured because of insisting that PDE is not "about" physics.

How does mathematics abstract away from the real world?? Mathematics is heavily influenced by physics, so to some degree mathematicians care about the real world. True, some areas of research have no applications at all in the real world, but that's a minority.

Judging by the papers I have seen and the talks I have been to, it's not really a minority.