Dear,

Pure mathematicians try to generalize and make more abstract the pre-existing concepts , they delve deeper into seemingly simplistic mathematics.
There are two things that can be done with a concept or an idea, you can go uphill or you can go downhill ( look deeper into the concepts).Pure mathematics goes downhill.
Lets say that we have the Cartesian co-ordinate system. A pure mathematician defines a field of numbers, develops the concept of vectors , define vector spaces,find some of the properties of vector spaces ,generalise to functional spaces, define hilbert spaces and so on.
On the other hand an applied mathematician would find how to use this concept of Cartesian co-ordinate system to solve some problems, in other words how can this mathematical concept be applied.
In the light of the above example, they may realise that quantum mechanics is having some sort of link with linear algebra, incorporate the concept of hilbert spaces , get more result out of the equations (as those concepts have already been developed in pure mathematics )
Applied mathematics like pure mathematics plays a crucial role in science. In physics many concepts of pure mathematics are now applied ( so in a sense physics is applied mathematics) .

Hope this helps!

Dear,

Pure mathematicians try to generalize and make more abstract the pre-existing concepts , they delve deeper into seemingly simplistic mathematics.
There are two things that can be done with a concept or an idea, you can go uphill or you can go downhill ( look deeper into the concepts).Pure mathematics goes downhill.
Lets say that we have the Cartesian co-ordinate system. A pure mathematician defines a field of numbers, develops the concept of vectors , define vector spaces,find some of the properties of vector spaces ,generalise to functional spaces, define hilbert spaces and so on.
On the other hand an applied mathematician would find how to use this concept of Cartesian co-ordinate system to solve some problems, in other words how can this mathematical concept be applied.
In the light of the above example, they may realise that quantum mechanics is having some sort of link with linear algebra, incorporate the concept of hilbert spaces , get more result out of the equations (as those concepts have already been developed in pure mathematics )
Applied mathematics like pure mathematics plays a crucial role in science. In physics many concepts of pure mathematics are now applied ( so in a sense physics is applied mathematics) .

Hope this helps!