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Ph.D. Applications went wrong this year

I am currently a master's student in pure mathematics at a top university in the UK. This year I applied for PhDs across Europe and the US (10 applications), and got rejected from all of them.

I topped in my undergraduate university, which is not very well known, and had good recommendation letters. I think that I was immature in my applications (especially in my statement of purpose), and this is the main reason why they didn't go so well.

I am still interested in doing a Ph.D. in pure math, and so I would like to reapply again next year. However, I am unsure what to do in order to improve my applications. I expect that finishing my Master's with good grades will be good, but I can't just wait a whole year without doing anything.

Tips for reapplying + Filling a gap year

Do you think that doing another Master's will help me improve my applications? My current Master's is just one year, so I think that another Master's will help me get closer to where I need to be in terms of math to start a Ph.D. Plus, it will also give me time to mature a little bit more, and help me fill in this gap year.

However, this feels like a very big commitment. But still, I don't see many more options to continue studying pure math next year otherwise, as there isn't really any possibility of doing research assistantships and the like in pure math. Do you have any other suggestions for how I can fill this gap year?

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    In this day and age, you need to send more than 10 applications, and make sure you don't just apply to the top institutions in your field. Apr 20, 2023 at 11:16

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It seems your concerns are not on your academic preparation, but on your person maturation.

This is a very personal aspect, however if your academic track and your topic knowledge are above the minimum requirements to pursue a PhD (i.e. : you have good marks and you feel confident on tackling the unknown), I would suggest that instead of applying to a Master you look for research positions in big tech/finance companies or universities. It may be not close to pure math, but it will not hurt you.

You can also do something completely unrelated, like taking a part-time job, doing a semester abroad volunteering with some research institution/studente exchange program or some volunteering (since it seems immediate material needs or money are not a concern to you, you may afford that).

Finally, you may thing about pursuing a PhD on your own, looking for grants and applying to them: in many part of the world there are bodies to fund research based on applications, a PhD is then simply a research position with some link to some university professors, rather different than the US system where you get enrolled in a PhD program.

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I had a friend who found a research position at her University (US) during her gap year. She described that experience as the reason why she later pursued a Ph.D. She consequently recommended that to other people thinking about getting into academic research.

Though I can't tell you what to do, I think getting some real research or work experience in your field is more valuable than getting another master's degree. Especially if you get a publication out of that experience.

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