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Source: https://writers.stackexchange.com/a/29036
License name: CC BY-SA 3.0
License URL: https://creativecommons.org/licenses/by-sa/3.0/

I'm a mathematician and physicist who's routinely annoyed when fiction gets mathematical and/or physical details wrong, even in works that are meant to be about geniuses in the field, such as Good Will Hunting or A Beautiful Mind. You can easily Google examples of people pointing out where either the facts were wrong or their difficulty for people at a given level of expertise was exaggerated. In The Big Bang Theory (among others), I even object to the implications of specific details to characterization. (For example, in S8E2 a character who refers to a technique by a name only a physicist would use later admits struggling with something every physicist understands well.)

But I'm also a writer, and I know the most important thing is doing what's right for most of your audience. And whether the specific problems Will solved on the blackboard are as hard as claimed in-universe, or whether John Nash's "if we all go for the blonde" thought experiment properly exemplifies Nash equilibria, isn't the point. The point is, do the work's consumers develop the inferences about and attitudes toward the work and its characters that you intended, and are they glad they did?

If you want to try harder than those successful scriptwriters and don't gave much time in which to do so, try searching for people discussing the topics' use (well or badly) in fiction. Futurama uses group theory occasionally; one episode was even written by a PhD in the subject, with the mathematics being integral to the plot. You'll learn more about how to use group theory in fiction from The Prisoner of Benda than from a group theory textbook.

Good luck!

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