Originally Posted by avito009 Well then you mean mathematical dimensions are length breadth and depth whereas physical dimensions are latitude, longitude and height above sea level. Is that right? 
No. There's no distinction between mathematical dimensions and physical dimensions. Dimensions are just names for the orthogonal bases in coordinate systems.
Well another thing I noticed was that when the spacial dimensions of length breadth and depth are taken then the material is irrelevant as these dimensions remain same when we immerse a body in water as oposed to when placed in air.Why so?

They're not irrelevant. The object can still be described using the 3D Cartesian coordinate system you adopted.
There are physical phenomena that we can model using the laws of physics. Those laws of physics are framed using well known coordinate systems, like Cartesian, cylindrical and spherical polar coordinates, but there's nothing stopping you from defining your own coordinate systems and using those. For example, solid state physics makes use of reciprocal space, relativity can be framed using time as a dimension. Nuclear physicists sometimes use complex forms for things that are not complex, which can sort of be seen as a new 'dimension'.
Yes, most of nature can be described by using three spatial dimensions in your coordinate system, but that's not a fundamental property of the Universe. You could, for example, use a 1D or 2D system of coordinates if you want to describe a certain situation, which might be fine. However, there are other situations where one or two dimensions are not good enough. Similarly, some scientists find it easier to describe certain phenomena using many dimensions, but that doesn't mean that they are 'real'.
Now if we consider the dimensions of length breadth and space as woody says it is the interaction where space is defined. Now then this makes sense as to how Einstein discovered his new gravity. Since we can now imagine space to be a rubber sheet and the massive object causing a deviation in space.
Look at it this way just as when you have a cube so this cube if we consider space to be a rubber sheet has to displace some of the space it interacts. Is this how Einstein knew gravity?

I'm not very good at relativity, but from what I understand, I think the answer is no. Einstein developed his theories by investigating the properties of objects as they approach the speed of light and never assumed or treated space as a material that can be warped and bent.