If her research had applications, it would've turned her pure math into applied math, which sounds less cool. But an application in string theory isn't always considered a "serious" application. String theory was popular in the 80s, as a model to unify quantum physics and relativity, but experiments since then haven't really confirmed supersymmetry, which is one of it's key hypothesis. Some still think string theory can be saved and make new versions of it to account for modern discoveries, but they're very marginal.
Ok, so there's a problem in physics. General relativity and quantum mechanics both beautifully describe the universe at very large and very small scales respectively. However, they disagree with each other (general relativity breaks down when applied to quantum objects).
Many physicists since a long time have been believing that string theory would be the theory that would unify quantum mechanics and general relativity to get the theory of everything.
Why do so many ppl believe this? It's because the math of string theory is very elegant. Why is it elegant? It's because it strongly hints at unification.
But this is the problem - there is zero experimental evidence for string theory. In fact, certain requirements for string theory to be true have not been proven to be true yet (and have started to become less and less likely as experiments have progressed). This is why, string theory is just this incredibly complicated and mathematically intense theory without any practical applications.
The mathematician here hates her math to be practically applied. However, when she's told that it's being applied in string theory, she's relieved as she knows that it won't ever be practically applied. That's the joke lmao
The string theory bit aside, the implications of being an applied mathematics professor is pretty grim: you're going to be known as the one responsible for the application, good or bad, and it's also a pretty different profession from theoretical mathematics. Like, a worse profession.
