It’s a mentality that I can understand. The way math is taught in school often leaves a lot to be desired and understanding the more advanced and esoteric concepts of higher mathematics requires a certain way of thinking that a lot of people have a hard time with (which is fine; I’ll be the first to say that we shouldn’t be forcing students to take anything beyond Algebra and maybe geometry unless they want to go into a field that will actually require it). Another definite problem is that a lot of mathematicians can get snooty about our discipline.
The argument goes that theoretical mathematics is completely removed from human errors. Everything that mathematics proves it proves through cold, calculating (pun definitely intended) logic, free from the experimental errors and limitations that plague the physical sciences. Mathematics is the one TRUTH of the universe, unimpeachable and unquestionable. And this is true… if we add one little asterisk to that statement.
You see, every branch of mathematics begins with a few assumptions about how things work. These statements usually seem fairly intuitively obvious, like the assertion that given a set of things we can choose one of them (the actual mathematical statement of this is much more convoluted, but that’s what it boils down to). We call these axioms, and they are the structure upon which all mathematics is built. So the more honest statement is that mathematics is truth assuming the axioms are true. And that caveat is not trivial. There has been a lot of interesting work into studying the validity of the axioms and trying to eliminate some of them as necessary starting points. Well, interesting to a mathematician at least.
So what does this have to do with writing?
Whether you consciously realize it or not, there are a whole bunch of assumptions floating around when you set about writing a story. Assumptions about people and how they work, assumptions about what it means to be heroic or villainous, assumptions about what it means to be alive, assumptions about the nature of reality. The list goes on and on. Identifying these assumptions and challenging them can lead to very interesting twists in the direction of your story.
In science fiction, we often seen alien species as being essentially humanoid, if not always in appearance. The thought process goes that if they’ve conquered their planet enough to travel to other worlds, they must have certain qualities, certain social structures, etc. But why? Why couldn’t you have a species that has mastered interstellar FTL drives but not “simpler” technology like gunpowder? What if you had a species of single celled organisms that were able to develop an advanced space-faring civilization? Or you could have a hyper-advanced technological civilization that hasn’t ever been bothered to even invent flight, let alone space travel. What would that mean? How would that shape and be shaped by their history?
Maybe the answer you come up with is that none of that makes any sense, that it couldn’t happen. That’s totally fine. But it’s still good to go through the thought exercise because an assumption questioned is an assumption better understood and armed with that knowledge you can better examine the consequences of its certainty.
You can do this sort of thing with any genre. For fantasy you can examine the assumption that humans are the vanilla ice cream of races: everywhere, pretty mundane by themselves, nothing special, but incredibly versatile in their uses (because you can put all sorts of toppings on top). Another common fantasy assumption is that magic and technology are inherently at odds, that as one waxes the other must wane. You see this all the time.
The battle for balance between magic and technology is a major plot point throughout the Terry Brooks’s Shannara series. But magic and technology don’t have to compete. There have been some really interesting stories that have come about by allowing magic and technology to integrate with each other.
So dig down as deeply as you can into the assumptions that underpin your story and ask yourself if they are really so. And watch as your stories take on a whole new life of their own.