This is an interesting question.   From the incisive answers already given, it is apparent that many answers are possible.

From my perspective, there is a positive answer and a negative answer.

Positive answer:  From a Euclidean geometry perspective, the physical structures such as straight edges (e.g., the edge of a distant horizon), rounded edges (e.g., visible edge of the moon), and intersecting twisting lines (e.g., shoreline and tidal water edge) are viewed intuitively.   We have a tendency to ignore the blemishes such as unevenness of edges to arrive at the postulates of plane geometry.   In the intuitive sense, the familiar structures of Euclidean geometry are very much a part of our everyday world.   From this perspective, mathematics is very much a part of our world.

Negative answer:  From a topology perspective, the closure of a nonempty set A in a topological space X is the sets of all points in the space that are near A.   Such points can be infinitesimally near and yet are not in A.   This form of nearness defies intuition but is a very important part of topology.   And this form of nearness is not part of our everyday experience.   Hence, from a topological perspective, mathematics is not part of our world.

My belief is negative. In fact, many things are not mathematical but by hook or crook we try to apply mathematics. That is why most of the scientific study becomes approximations, of course, genuine and useful approximations. A leaf of a tree is neither of any standard mathematical shape such as square, rectangle, etc. The actual noise produced in a signal is neither Gaussian, nor uniform or of any other standard noise model. Much more can be written on this topic. But my one line comment is Science and engineering is a study of approximations. I may not be right. Experts and other genuine researchers may have different opinions.

Yes I think so. Even love is for it is mediated through the nucleus accumbens of the brain.

http://www.science20.com/truth_universally_acknowledged/love_circuit_your_brain_romance

The basic units of the brain are the action potentials which are complicated dynamical systems.

see

http://www.nrbsc.org/csm_sp2010/readings/Week13/hodgkin_lecture.pdf

Then there is transmitter release (also mathematical)

see

http://homepages.inf.ed.ac.uk/mhennig/synaptic_transmission.pdf

Behaviour of groups can be modeled by agent based systems

see http://www.mcs.anl.gov/~leyffer/listn/slides-06/MacalNorth.pdf

The golden ratio is everywhere in nature.

see http://science.howstuffworks.com/math-concepts/fibonacci-nature1.htm

Then Noether’s theorem establishes the link between mathematics and nature

http://www.eftaylor.com/pub/Symmetries%26ConsLaws.pdf

Now, is God mathematical or a universal mathematician that is another question.

Yes! My opinion is positive. Every individual in the world can use numbers as an interal part of our life.  The money we can earn and spend is a number. We will call our friend by mobile using numbers.Number theory is a branch of mathematics. We can compare infinity  with god. Mathematics is universal science. Thinking, reasoning and solving are good exercises for the human brain. So the subject mathematics strengthens our brain indirectly.

This is an interesting question.   From the incisive answers already given, it is apparent that many answers are possible.

From my perspective, there is a positive answer and a negative answer.

Positive answer:  From a Euclidean geometry perspective, the physical structures such as straight edges (e.g., the edge of a distant horizon), rounded edges (e.g., visible edge of the moon), and intersecting twisting lines (e.g., shoreline and tidal water edge) are viewed intuitively.   We have a tendency to ignore the blemishes such as unevenness of edges to arrive at the postulates of plane geometry.   In the intuitive sense, the familiar structures of Euclidean geometry are very much a part of our everyday world.   From this perspective, mathematics is very much a part of our world.

Negative answer:  From a topology perspective, the closure of a nonempty set A in a topological space X is the sets of all points in the space that are near A.   Such points can be infinitesimally near and yet are not in A.   This form of nearness defies intuition but is a very important part of topology.   And this form of nearness is not part of our everyday experience.   Hence, from a topological perspective, mathematics is not part of our world.

We cannot say every thing is mathematical in the world ,but we can say our life is simply mathematics"" suppose when a person get married it is "addition"  and when the person has a baby that is multiplication, when a person die that is subtraction,and finally that is division. ha

To Dear Rajesh Sanghvi and respected others

     Even you taken the leaves of tree. That is also connected with maths. Every tree leaves has got particular shape and it has typical proportionate area. The growing of the plants or crops takes some duration. So the duration, shape and area are related with maths. The color of flowers are also being seen due to the particular wavelength.

And wavelength is related with frequency !!

I teach Mathematics since 20 years. What I wanted to emphasize was that reality is far beyond our understanding. The entire subject of numerical methods is approximations. Even when we try to develop a law of science, we neglect several factors. The common sentence we are familiar with is "Neglecting air resistance...". The exact Fourier series are available for some functions, but when we apply it practically we have to terminate the series after finite number of terms. Often, a nonlinear problem has to be converted into a linear problem.

I never give thoughtless answers. If you do not want to upvote, no problem. But at least do not downvote without carefully understanding the answer. I expect that the researchgate audience is different from Facebook audience where people can like or dislike anything without taking any extra care.

Dear Rajesh Sir

         You are taking it in otherwise. Let me first say sorry if you get bad impact on it.

I want to explain that how the mathematics is involved anywhere in the world. There was not question of upvoting and downvoting of the question. As the question itself has got the two parts. I really thanks to your answer which you have given earlier. Dear Rajesh, every person in the world give their opinion with respect to their perception.

It may go by your way or by my way. It doesn't mean that I am and you are completely wrong. Take it easy and I really once again thanks for about free and frank opinion from your side.

#Dinesh

Mathematics is the Queen of Sciences, and we can always analyse anything or any problem in the world mathematically but this is only one aspect, we can also analyse the same problem from the point of view of others as a chemical Scientist, Physics Scientist, Sociologist, Philosopher etc........

The question is of a philosophical nature, and as such has no definite answer. It doesn't mean that the question is uninteresting, but rather that the interest is in the further questions it raises. For instance, what is "everything"? Assuming that "everything we know is mathematical", does it say anything about what we don't know? Where do you place religious faith? etc.

Some of the science fields are apparently developing independently with respect to mathematics. But if we look to the background and the future (and actual) related results, we see that more and more progress is done thanks to mathematics.

Yes, Everything in world happens mathematically