Persistence
Success as a mathematician requires a great deal of persistence through failure. However, it is often the case that our successes are highlighted for public consumption--in our polished research papers, or on a website like this one, for example--while our many failures are hidden from view. Showcasing our accomplishments and burying our failures is natural, but it gives a misleading impression of the bumpy road we travel on our way to success.
In 2020, I received my first NSF research grant. NSF grants are highly selective and, in addition to providing financial support for your research, receiving one is validation that your work is valued and important. Receiving that grant was a huge success for me, and I am very proud of that particular line on my CV. What you don't see on my CV, however, are the three consecutive rejections I received in 2017, 2018, and 2019. What you certainly don't see on my CV is the review from 2019 that said "I have ranked this proposal #11 out of 11 proposals reviewed."
Not getting discouraged by repeated rejections is difficult, to say the least. Upon receiving the 2019 reviews, I decided it would be a waste of time to submit another proposal. When I mentioned this decision to the chair of my department, he requested that we go through all of the reviews together. After discussing the reviews, he told me that he believed my work was worthy of an NSF grant and he insisted that I apply just one more time, despite my dejected unwillingness to do so. Thanks to his wisdom and encouragement, that would be the year that my proposal was awarded. (Thanks, Serkan!)
I share this story in hopes that it might encourage others in similar positions. Academia can be a cruel world with rejections around every corner, and far too many promising mathematicians are prematurely discouraged before they have the opportunity to realize their potential. If you're feeling discouraged and ready to give up, I urge you to apply just one more time.
I learned a great deal from my rejections and, in the end, this helped me write a stronger proposal. It would be hard to summarize everything I learned from those failures, but in hopes of supporting other early-career researchers applying for grants, I am linking all four of my NSF proposals and panel reviews below.
Summer 2023 update: In July 2022, I submitted a proposal for an NSF CAREER award, and then I submitted (essentially) the same proposal for an NSF standard grant in October 2022. The CAREER award is one of the most selective research award in the United States for pre-tenure researchers: 500 awards are given each year across all scientific fields. As this was my one and only opportunity to apply for the CAREER award before I earned tenure (I had intended to submit a proposal in 2021, but the deadline coincided with the birth of my daughter...), I put a great deal of thought and effort into this proposal, including early submission for an external review from a leading researcher in the field. Unfortunately, I was not awarded the CAREER award; however, I was very excited to learn that the proposal was funded for a standard grant! I am including the proposal and both sets of reviews below. The critical reviews for the CAREER award, in particular, include some helpful tips for those planning to apply for this award.