What “Mathematical Finance” means in academia

I've been reading a lot of financial mathematics books, and I wanted to point out an interesting trend.

These two books …

• The Concepts and Practice of Mathematical Finance (Mark Joshi)
• A Course in Derivative Securities (Kerry Back)

… are almost exactly the same. And I bet there are more books like them.

They start with a few chapters on Brownian Motion, Ito Calculus, and No-arbitrage theory, then derive the Black-Scholes equation a few different ways, then spend the remaining 80% of the book applying this knowledge to obscure and typically non-existent financial instruments. The books came out in 2003 and 2005 respectively.

This isn't a criticism. I just want to open up a discussion for those familiar with the material.

What is or what was the utility of this field of study? Is it still relevant? Or have the analytical methods been completely replaced by the empirical methods?

I'm aware that the concept of Implied Volatility has everything to do with the deviation from the expected output of the Black-Scholes equation. Are there other examples of esoteric mathematical finance equations having a profound impact on the way we think about financial markets?