Two Good Things and One Bad Habit from Studying Mathematics
At various parts of my life and in various contexts, people have asked “What’s the value of a mathematics degree?”.
Usually there’s some vague answer about “learning how to think logically” and “a math degree opens a lot of doors”. Do I agree with these answers, in my personal experience? Sure. Whatever.
What I have realized over the past few while is that thanks to my mathematics training, I’ve learned two good things and one bad habit.
Good Thing: Improving Drawing Skills
I’m not a very good artist. I’ve never really been into drawing or painting, as a kid or an adult. But after excellent courses in linear algebra and multivariate calculus, I feel pretty confident in drawing shapes in two and three dimensions. Given enough exposure to conic sections and integration techniques, my drawing skills have definitely leveled up. It could’ve been a matter of practice, or the context of learning math (which I was good at and did enjoy). Whatever happened, I’m a better artist now.
Good Thing: Defining Terms Upfront
Something that’s pretty common in formal mathematical writing is to define new terms or concepts clearly and early. Many proofs follow a “definition, theorem, proof” format where a concept is defined precisely, a theorem is stated (which is a statement based on the defined concept), and then that theorem is proven. I actually really like math textbooks that follow this format since they flow well.
Often times in technical writing, and even outside of technical writing, concepts or terms are discussed without really defining them clearly. This happens often with acronyms, particularly TLAs (Three Letter Acronyms), where the writer simply assumes the acronyms are known to the reader. While this may allow for some brevity, it can also lead to confusion or even disengagement from the piece of writing. “What does that term actually mean?”, “Am I supposed to know it?”, and even “I don’t think this piece is actually meant for me” may creep into a reader’s mind. Plus it can lead to people getting the wrong idea about the piece of writing in the first place.
I like when things are defined upfront, even if they are not completely well-defined. It creates a common starting point for a piece of writing and for creating an idea. Mathematics does this well, in the written case and in discussion. I’m taking this away as good practice.
Bad Habit: Using The Phrase “I don’t care about that”
In any decent mathematics program, eventually students see some relatively complicated proof. In such a case, there’s several steps to get from the beginning of the proof to the end and each step is discussed and demonstrated. Often at one of these steps, the demonstrator will say something like “Now I don’t care that this value is negative or positive” or “We don’t really care if this function is continuous at point x”. This statement is meant to convey that there is some aspect of the step of the proof that isn’t relevant to how to get to the next step or the problem at hand. However, this statement sometimes comes off as “I, a human, don’t really give a hoot about this thing”.
I sometimes say this in non-math contexts. When I say “I don’t care about that topic”, what I usually mean is “I have no interest in this topic in this particular context”. However, this phrasing can also be interpreted as “I have no interest in this topic at all whatsoever”.
Here’s an example: a coworker may ask me “What ticket should I work on next?”, and I may say “I don’t care which one you take as long as it relates to project X or Y”.
What I mean is “It’s not relevant to me which ticket you decide to take as long as it’s relevant to project X or Y”, but this may be interpreted as “I’m not actually interested in what work you do at all or in your decision making process”. It’s a subtle difference in language, but one that could make a big impact on how people interpret my motivations.
In mathematics, this kind of language makes total sense. Does it matter if x is positive or negative if it’s going to be multiplied by zero? No. And usually this is one step in the process. What is really of interest is the ultimate result. Of course, human beings may care a great deal about how decisions get made or how people feel about their decisions.
Have I learned other things from my mathematics degrees? Absolutely. These two good things and one bad habit are some of the more interesting lessons I received.