- Mathematical world?

I have had this discussion with several people now, and it seems this is one of those never-ending debates where no one party will accept they are wrong and the other one is right. Now I share it with you, let's see what you think:

My claim is that Physics is independent of Mathematics. Yes, yes... I know when you take physics in school it's always mathematics or at the very least full of mathematics, but that is understandable because Mathematics is just another language and it turns out to be one which everyone is suppose to know plus it allow us to calculate numeric answers for Physics problems. I know all of these, but I still think that Physics exists whether or not I can put them in an equation, or whether or not you can put numbers to it.

Let's just think of a child. S/he knows that to reach the top of the kitchen counter he needs to jump higher than he needs to reach the top of the couch (where he might not even need to jump), and therefore the initial upward velocity needs to be large enough. He goes through all this process and eventually gets it right. Now, I think the kid learned Physics by trial and error, however some people think the child unconsciously solved a complicated (or not so complicated) mathematical model. Some of the advocates of a mathematical world believe that we are born with the mathematical abstraction, some others believe that we subconsciously learn it as we go. Also, some people are not amazed by the fact that relatively simple (by simple I mean something that at least 1 person in this world can do) mathematical models can "describe" the universe. Why should they be? After all, Physics is Mathematics, or so they claim.

Here is the list of (some) points I have heard in favor of Physics being independent of Math:
1) If Mathematics is just another language, I should be able to say the same things in English, or Spanish or Chinese or whatever. Mathematics is then not special at all and there is no reason the world should be mathematical.
2) It's hard to believe that a kid or an animal have a subconscious mathematical machinery that solves some kind of equation for every single world situation. It would be easier to just learn by experience where left or right, up or down are.
3) Before Newton, people could also tell things fell to the ground. They just didn't make much of it.
4) This is similar to 3 - Physical phenomena exist whether or not we have a mathematical theory for it.

Now, for Math is basically just the negation of every point above mentioned:
1) Mathematics is NOT just another language, it is THE language.
2) Whether or not you believe it, we all have the mathematical machine inside our heads.
3) We don't know new Physics until we can explain them with a mathematical model.

There are probably more, and better points to consider. However, usually these points are defended with examples which makes it hard to convince anyone. Like I said at the beginning, I don't think this battle will ever end but if you have a good argument for either one (or maybe a different option) please share it.