Is Physics in principle Mathematics?

I recently had arguments with a couple of friends on whether science, in particular physics, is in principle a continuation of mathematics. They were heated debates and I still stand by my point- physics is in principle different from mathematics. I am aware that my hard-line stance may brand me as a "Physics chauvinist", but I have to do what needs to be done. Before I prove my point, let us first understand what is meant by being "same in principle". To make things more concrete, I will first prove that chemistry is in principle physics (no offense to anyone in chemistry).

Chemists may want to believe that they are unique, but unfortunately they are not. To their credit, they have developed many hand waving arguments that can often lead to approximately the same results as physics will predict (and are observed in experiments). These arguments sometimes tend stretch beyond what a computer can calculate using physical laws, but this is purely a material limitation. Physics can predict exactly how hydrogen molecule is formed. Physics can also explain very nicely the unusual stability of aromatic molecules like benzene. Left alone, chemist will attribute their stability to a bunch of diagrams which can be very misleading! More complicated molecules have been successfully described within the limits of quantum mechanics, but as their complexity increase, more powerful computers are required for calculations. Because of technological limitations, physicists can only go up to a certain level of complexity without having to spend disproportionate amounts of money or time. However, in principle, if one had an infinitely powerful computer, one can predict everything in chemistry using physics. The most striking example to substantiate this claim is that chemists still come to physicists to gain better insight of what they are doing!

I hope we are clear with the meaning of being "same in principle". Now, let me prove that physics is not in principle the same as mathematics. I start with an admission that physics relies heavily on mathematics for any significant numerical prediction. However, these predictions wont come naturally from mathematics unless a leap in understanding is achieved through physics and there is no way this leap can be circumvented. Again, to make things more tangible, let me give you an example. Let's imagine a conversation with a hypothetical mathematician friend.

Me: Hey dude*, can you tell me what this is? d^2(x)/(dt)^2=-(k^2)x

(* I don't know the corresponding word for ladies. This choice of word is purely due to my limited vocabulary. I will appreciate if you don't brand me as a male chauvinist for this!)

Mathematician: Oh! This is a second order linear differential equation.

Me: So?

Mathematician: It can be solved easily. The most general solution will have the form A*sin(kx) + B*cos(kx)

Me: So?

Mathematician: It mean that x has, in general, two oscillating components. You can draw figures... blah blah..

Me: So?

Mathematician: What do mean by so?

Me: Well.. I mean, what now?

Mathematician: What the f**k! Are you playing with me?

Me: No. I just want to know what happens now.

Mathematician: You are nuts dude. Get the f**k out of here! @#$%$#$%..... blah blah.

You get the general idea of how the rest of the conversation must have been. Our mathematician friend is pretty disturbed. So, let's leave him in peace for a while and turn our attention to our hypothetical physicist friend who has been listening quietly.

Me: Hey! Could you believe he got so mad at me for asking such a simple question? What do you think of it?

Physicist: You mean the mathematician or the equation?

Me: Oh! Well... Let's stick to the equation.

Physicist: That equation describes a simple harmonic oscillator like a pendulum. According to Newton's second law, a pendulum oscillates about its mean position. It also says that the time of oscillation is independent of the amplitude. That's why pendulum clocks were so reliably used in the past. Time period depends only on the length of the pendulum, assuming Earth's gravity is fixed.

Me: Oh.... Now that is a lot of stuff.

The large chunk of information about pendulums and clocks, as we see, cannot be naturally derived from the equation unless one had the physical intuition. One may be tempted to argue that every information comes from the same equation after all. There is nothing different in principle. It is just the way one interpretes it. To this, all that I can say is that nature is the same to all, but only a true artist can capture its essence and not every body can claim to be an artist!