When growing up, I'm sure my fellow students and I were not the only ones get responses to questions like "Why can't one divide by zero?" or "Why is Pi necessary to compute to area of a circle?" answered like "because that's just how things work" or "because it just is."
I'm not going to sit here and act like I was a star student or anything. I was more of a class clown type. I absolutely hate math and all things math. That was, until I went to college. A switch flipped when I was in a Calculus II class.
Our professor asked, "What is a 100 divided by 0?" People in the class responded with, "You can't divide by 0 because it's undefined." To which our professor responded with, "Why?" Then a student took out a calculator and showed the professor that the answer as indeed undefined. To which he responded with, "Ok, how do you that calculator is correct? Do you just believe it because people told you that dividing by zero is undefined? Ok, the answer is undefined... but why?"
Right then and there, a switch flipped in my brain. I realized that I was basically institutionalized to just not question math and to just accept that things work a certain way "just because." It was at that point I actually started to become interested in math, and it completely changed my outlook on math in a positive manner. I love math now (despite being horrible at it).
This reminds me of a lot of what I see in grad school and academia. Something akin to what Tom Wolf talks about here[0]
> I’ve always been a straight-A student.
> if something was not written in a book I could not invent it unless it was a rather useless variation of a known theory. More annoyingly, I found it very hard to challenge the status-quo, to question what I had learned.
I don't think this part is isolated to math, but there's a lot of acceptance for "because" being an answer. Being in an authoritative position and being challenged can be frustrating, but I think a lot of that frustration is self-generated. We stifle creativity when young and it should be no surprise that frequently when people challenge, they don't have the tools to do so (or be receptive) effectively. Truthfully, "I don't know"[1] still shuts down the conversation.
But I think people themselves are uncomfortable with not knowing. I know I am! But that isn't a feeling of shame, it is a feeling that creates drive.
[1] Alternatively, variations like: "That's a good question, I don't know" or "Great question, but we don't have the tools to address that yet". The last one need not undermine your authority either. Truthfully, the common responses resulted in me becoming strongly anti-authoritarian. Which, also has greatly benefited my career as a researcher. So, thanks lol
I remember my high school math teacher responding "that's an interesting question, I don't know" and then coming back with an answer the next lesson after researching the subject.
I'm not going to sit here and act like I was a star student or anything. I was more of a class clown type. I absolutely hate math and all things math. That was, until I went to college. A switch flipped when I was in a Calculus II class.
Our professor asked, "What is a 100 divided by 0?" People in the class responded with, "You can't divide by 0 because it's undefined." To which our professor responded with, "Why?" Then a student took out a calculator and showed the professor that the answer as indeed undefined. To which he responded with, "Ok, how do you that calculator is correct? Do you just believe it because people told you that dividing by zero is undefined? Ok, the answer is undefined... but why?"
Right then and there, a switch flipped in my brain. I realized that I was basically institutionalized to just not question math and to just accept that things work a certain way "just because." It was at that point I actually started to become interested in math, and it completely changed my outlook on math in a positive manner. I love math now (despite being horrible at it).