I am currently applying for several PhD programs (in mathematics) and for many of them, it is required to write a short (approx. 2 pages; no more than 10.000 characters) summary of my Master's thesis. It should contain the motivations of the thesis and research, the methods used as well as the results obtained in my research.

Now, the application commitee is probably less interested in the precise topic of my research or in the project itself, but I guess that the aim of this writing in my application is more for them to examine my ability of writing and explaining my research to others, as the latter is one of the key abilities a scientist should probably have, in my opinion.

My questions are now the following:

(1) How detailed should such a writing be? In my specific case, I am appliying for a math PhD and many things which I did in my thesis, which lied in the border of math and physics, are very abstract, so it not always easy to explain them in simple, non-technical, terms (and I guess, this applies for most of the projects done in pure mathematics). So, should I aim in writing this text in a more "popular" science way, or should I "confront" them with full technical details (the middle way is, as written above, hardly possible, as the things are kind of abstract).

(2) Should I aim in writing this stuff more formally, or more from a personal point of view? So, should I, for example, write about my personal reasons for chosing this particular problem, or should I more concentrate about the scientific reasons of why this type of questions are interesting?

I am currently applying for several PhD programs (in mathematics) and for many of them, it is required to write a short (approx. 2 pages; no more than 10.000 characters) summary of my Master's thesis. It should contain the motivations of the thesis and research, the methods used as well as the results obtained in my research.

Now, the application commitee is probably less interested in the precise topic of my research or in the project itself, but I guess that the aim of this writing in my application is more for them to examine my ability of writing and explaining my research to others, as the latter is one of the key abilities a scientist should probably have, in my opinion.

My questions are now the following:

(1) How detailed should such a writing be? In my specific case, I am appliying for a math PhD and many things which I did in my thesis, which lied in the border of math and physics, are very abstract, so it not always easy to explain them in simple, non-technical, terms (and I guess, this applies for most of the projects done in pure mathematics). So, should I aim in writing this text in a more "popular" science way, or should I "confront" them with full technical details (the middle way is, as written above, hardly possible, as the things are kind of abstract).

(2) Should I aim in writing this stuff more formally, or more from a personal point of view? So, should I, for example, write about my personal reasons for chosing this particular problem, or should I more concentrate on the scientific reasons of why this type of questions are interesting?