Questions that do not require specific technical expertise in order to answer properly. Questions must be of particular interest and usefulness to professionals and academics to qualify as on topic.

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Recommendations for books to understand the math in quantitative finance papers?

Can anyone recommend books that explain the math used in quantitative finance academic papers?
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What papers have progressed the field of quantitative finance in recent years (post 2000)?

My question is pretty simple: what papers do you feel are foundational to quantitative finance? I'm compiling a personal reading list already, drawn from Wilmott forums, papers referenced in ...