: Writing about a subject on which you have no expertise? So I signed up for a novel workshop, and within a month the first chapter will be due. Problem is I that want to use characters who

It is not unusual for writers to consult outside sources (both books and people) to describe details and dialogue about little known things.

One thing Stephen King describes in his book On Writing is to do a lot of research, but avoid including too much of the information you learned. Purely out of insecurity, newbie writers tend to include too much specialized information in their stories. But doing that is unnatural and distracting for the reader. It is far better to resist the temptation to include too much information -- and try to include as little info as possible. Not merely because you are a nonexpert, but because an expert probably wouldn't explain things in such a dense fashion.

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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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It would have been incredibly off-topic to ask this on Math.SE -- you're in the write place.

So here's the most important thing:

Your readers, on the whole, know little to nothing about technical subjects, and will not catch fabrications or errors. The portion of readers who do know will respect you for trying if you do it well enough, and respect you even more if you get anything right.

LaurenIpsum provides in her answer an excellent example of literary sleight-of-hand, but it's easy to miss the point of her answer. While you can sidestep technical terminology using her demonstrated method, you don't do it just because you don't know anything about your subject. You do it because it's not the point of the scene.

Think about great scenes in a range of movies and books involving technical imagery and conversation. What made the scene great? It wasn't the complexity of the terminology. It was the circumstances underlying the scene.

If a character reveals that -- oh my god -- using SHA1 on the password wasn't enough -- they used a rainbow table -- we should have used bcrypt, thus thwarting brute-force attacks! -- that's great. That's really great. Nobody knows what anyone just said. But if the compromised password means citadel security is likewise broken, we have a powerful tool to move the plot forward, and the tension just went up a notch. It went up a notch not because of bcrypt, rainbow tables, and SHA1, but because the enemy is coming, and our defenses are down.

What I'm saying is that technical terminology should embellish a scene and add a sense of authenticity, but it's not necessary, and you can make great scenes without it. The success of your scene should not be dependent upon the professor demonstrating Perelman's proof of the Poincaré conjecture.

BUT, all that being said, authenticity is a lot like salt -- if used sparingly in the right places, it adds flavor. Put in too much, and people turn up their noses. Unless you're a master chef, of course.

So -- the ultimate question -- where do you get authenticity when you know nothing? You do what all fiction writers must do -- hybridize learning and invention.

For example, go learn topological basics. Spend a few days on it. If it's a major character, maybe longer. As much as you can stand. Find good sources that you can learn from easily.

Instead search youtube for beginner's topology. Rearrange the words and search them elsewhere -- "learn topology" "basics of topology" "fundamental topology" "how to learn topology" "where to start with topology". Find nice beginner-friendly sites that have colorful diagrams with arrows. Search for topology animations. As you learn some basic terms, search those terms and see if you can get more detailed information on them, and through that, learn other terms. You'll quickly start building out a mental map that you can take as far as you wish. If you're a good or experienced writer, you'll know when you've gone far enough. If not, you'll learn as you go, and next time you'll know understanding Perelman's proof of the Poincaré conjecture was way, way, too far.

Usually it only takes basic terms to lend authenticity. You don't need to throw around anything heavy, because even beginner's terms are foreign to those who know nothing. Yet, inversely, beginner's terms are the most important, because they are the most commonly used terms in technical conversations. Just like learning a language-- sure, a fluent English speaker can use words like "defenestrate" and "categorical", but in common conversation, the words you see most are "the" and "a" and "hello" and "please/thank you" and so on, and that's an authentic English conversation, and anybody who sees those words knows it very quickly. Don't make the mistake of thinking the character will sound smarter or more real if he uses more arcane words-- that only makes him more likely to be wrong, and harder to understand.

Once you know enough to fool a fool, fill in the gaps with your imagination, with healthy use of LaurenIpsum's hand-waving method. I mean, I don't really understand cryptography at all, but don't you think that little clip would have fooled someone who knew nothing whatsoever?

Always remember it's only embroidery. The core of the story will not depend on the technical terminology, and ultimately the readers will forget it as soon as they read it -- unless you come up with something catchy, e.g. flux capacitor. And the catchiest terms are almost always the imagined ones.

Last tip-- consult someone who does know!

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Writing a story in which math plays a pivotal role when you know little about mathematics would probably be a mistake. There is, unfortunately, no way to fake knowing something. You either have to do the research, or write the story anyway, hoping your guesses are right. Guessing wrong will make you look foolish.

Of course, the question of how much research you need to do is one without a good answer. But a story about math will probably attract readers who are interested in math. And those readers may well know a lot of math themselves.

If you do choose to write this story anyway, run it past some beta readers who are mathematicians or math teachers. They may be able to tell you where you've made mistakes.

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I've done a bit of research on social studies, since a character of mine starts studying that at university. I had to make the lectures/assignments realistic, so am lucky to already be doing a different course, so just went to the social studies area to see what it involves.
A bit of time spent researching could make the scenes believable.

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Many years ago, I studied German with a teacher who did not believe in sugar coating his comments. One piece of advice that has stayed with me was "If you don't know the word for picnic, don't try to write about eating outside!"

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For a first draft, you can use placeholders. XXX, TK (publication shorthand for "to come"), TECH, literally the word [placeholder] in square brackets — anything to indicate that you'll fill in the mathguffin details later. Also, feel free to gloss or summarize. The point of the scene is not going to be the math anyway, right?

The professor pointed to the blackboard.
"You see? If you [TK math thing], you get this result. But if you do this — " He changed some variables and added a new line to the equation. " — then you get [different result]!"
Ben gasped. "Of course! It makes perfect sense! How could I never have seen this before?"
"Because I'm a genius," said the professor smugly.
"And because you had me helping you," came the tart voice of the professor's wife from behind them. Ben winced. "I was the one who pointed out XXX to you," she continued. "You never would have gotten to TKTK if I hadn't pushed you halfway there."

If the point of the scene is the math, then you're going to have to do a lot of research very fast.

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