My name is Galvin and I am a university Freshman.
As part of my university's curriculum, I have been tasked to prepare a popular science article on a mathematics research paper. The target audience of the popular science article is the general public. I would like to write a science article based on a topic from Quantitative Finance/ Mathematical Finance.
I think your best shot it to drop the Finance part.
There are annual popularizations of what's been going on in Mathematics generally:
"The best writing on Mathematics in 19nn" (edited) by M. Pitici
"What's happening in the Mathematical Sciences", vol n, by D. Mackenzie.
To write or edit this kind of thing, you have to be a PhD mathematician and a good writer or a sense for it. However, your task can be to start with Pitici or Mackenzie, and then dumb it down even further. That should be doable. But you'll find very little finance in those sources -- although I do see an article 'Mathematics and the Financial Crisis' in Mackenzie vol 8, copyright 2011.