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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?

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    That second paragraph is about as good a story as one typically hears on graduate applications. Mar 26, 2023 at 22:46

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"Lack of passion" can be difficult to interpret when it's the feedback you receive. Still, your question is a bit difficult to answer without reading your actual statement of purpose - especially since I think you do write down elements that could be the ingredients for conveying that "passion", which apparently is somehow missing from the materials you send in when you apply. As a reader (and perhaps host lab?) you want to see a bit of genuine excitement and intrinsic motivation shine through in the applicant's writing.

Are you certain that it is not the second reason (i.e. your lack of cosmology background) that is the main reason you are getting rejected?

In either case, I would go over your statement again and ask for feedback from someone who knows you and the field you're interested in: Are you telling the reader WHY you are devoted to a career in research? WHY you want to apply your mathematics skills and background in this new area?

Good luck!

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  • I agree that I don't have expert level knowledge of cosmology but I have done physics courses in undergraduate and a lot of researchers I know have taken up astronomy and astrophysics after doing their master's in mathematics. This is my primary source of inspiration. I also agree that I am not very clear about how to proceed for research in cosmology after studying mathematics. This is why I want to take up a research project. I believed it would be my starting point. It will help me develop a better understanding of the subject. That was my plan. Now, it seems like its failing.
    – user519535
    Mar 26, 2023 at 17:16
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If you don't have such a story -- develop it.

Along with reading top-notch research on the chosen topics, dedicate some of your time to reading books on the history of mathematics and physics. This investment will pay off, not only at the interview.

Speaking of the history of math, this masterpiece is the first that comes to my mind: "Prime Obsession. Bernhard Riemann and the Greatest Unsolved Problem in Mathematics" by Derbishire.

Speaking of cosmology and relativity, one good book out of many is "Seven Brief Lessons on Physics" by Carlo Rovelli. Professional cosmologist, Rovelli is also a prolific writer, and his other books may be of interest to you.

Also the popular (and not so popular) books by Roger Penrose.

While this sort of reading is only a supplement to working with serious texts and papers, it helps one to develop a broader vision of things.

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    Might it be better to read some things closer to current research in the area? This isn't my area of research, but I'd worry about an application that looks like an interested lay person rather than a serious researcher.
    – Bryan Krause
    Mar 26, 2023 at 18:34
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    No I think you were clear, but you're recommending what seems to me to be very light reading: books targeted to a general audience that don't have much to do with what it means to do research in those fields (not having actually read those specific books, though I'm familiar with similar books in other areas). It's probably okay to refer to them as something that first sparked interest, but that's not where OP is, it seems like they need to show they know something about what current research is like and what work is done towards the available problems.
    – Bryan Krause
    Mar 26, 2023 at 22:31
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    @BryanKrause If you feel that my advise is misleading, I shall remove it. Mar 26, 2023 at 22:44
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    You can keep it or not but it might be helpful to explain where the advice is coming from or clarify if you're recommending just this or something in addition.
    – Bryan Krause
    Mar 26, 2023 at 22:46
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    @BryanKrause Bettwr now? Mar 26, 2023 at 23:09

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