I am currently doing master's in mathematics and am applying for summer research projects in various institutes where they ask a particular question: What is your topic of interest and why? I asked a few people( professors, mostly) and Google, and they suggested I should tell my story. How and when I became interested in a topic? What caused me to choose it over others?
I don't have such a story. I never had a fancy dream about my career. (I can't say that without people judging that I am not a serious candidate.)
I am devoted to pursue a career in research. My field of interest is Topology, Cosmology and Geometry. Also, I read Algebra for fun. I want to study about the universe from a mathematical point of view, see what it looks like and if possible explore why it looks like that. If there is a possibility of multi universe, do all of them have the same structure and components? Is our knowledge of mathematics vast enough to be able to formulate or model the topology of the universe? I know the answer to that one is no, but then what sort of advancements are required to achieve that goal and how do we go about that? Finding answers to such questions is why I want to study cosmic topology. Unfortunately, I keep getting rejected due to "lack of passion" in my statement of purpose. And also because I come from a mathematics background and I don't have sufficient theoretical knowledge about cosmology (I am doing my self study for that).
How do I convince the institutes that I am thoroughly interested in working in such projects? If asked directly, my answer is that it is an interesting and challenging field where I will be able to work with two of my favourite fields, astronomy and pure mathematics, but that isn't sufficient anymore. What more could I add to my answer that would make me a suitable candid ate?