Is Math a Tool for Understanding Our World?

[matt010nj]

Math "language"

Is mathematics a science that was created in order to describe our physical world and its phenomenons or independent science that simply co-exists with others?

 

[Char. Limit]

Mathematics is the root and basis of all sciences, from physics to sociology. They are dependent on it, and it depends on only itself.

 

[HallsofIvy]

From a very strict point of view, however, mathematics is NOT a "science" itself. By "very strict" I mean defining a science as based on the "scientific method":
1. Observe and experiment
2. From the observations, develop as many theories as possible
3. From the theory predict results of additional experiments
4. Do the experiments to eliminate those theories that predicted incorrect results
5. Repeat

(Mathematics is only really used in part (3) of that.)

Mathematics is not a science in that it does not depend upon the results of experiments. More simply put, science depends upon inductive logic while mathematics depends upon deductive logic.

In fact, I would go further. Science, because of its insistence upon correspondence with the result of experimentation, is necessarily based on a "Realistic" philosophy while mathematics, insisting on a logical progression from axioms, is necessarily based on an "Idealistic" philosophy.

 

[Redbelly98]

Is mathematics a science that was created in order to describe our physical world and its phenomenons or independent science that simply co-exists with others?

You might be interested in these other discussions:

https://www.physicsforums.com/showthread.php?t=215118
https://www.physicsforums.com/showthread.php?t=237609

Also, this paper by Eugene Wigner:
http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

 

[matt010nj]

You might be interested in these other discussions:

https://www.physicsforums.com/showthread.php?t=215118
https://www.physicsforums.com/showthread.php?t=237609

Also, this paper by Eugene Wigner:
http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

before it immerse into Mathematical Platonism subject - Thanks for the link.

 

[Tac-Tics]

Science tends to work on the principles of deduction and experiment.

Math tends to work on the principles of induction and proof.

There's no hard line, though. Actual math requires a lot of experimenting. "If I take this set and apply this operation, the result looks like this. What if I apply the operation twice? Three times? Oh hey, a pattern! Now let's find a proof for the general case." Good science is always supported by good math, and great theories are often based on the simplest mathematical model that fits the evidence.