One thing I learned from Calculus, this time around

Turns out that this story actually doesn’t have anything to do with anything Erdos or Darwin said.
Erdos Photo by Topsy Kretts – Own work, CC BY 3.0,

Darwin photo from Public Domain,











This blog post is about how I gave an assignment that I regret and am embarrassed about. It all starts four years ago, when I gave my Calculus II students a review assignment in which they were supposed to solve calculus problems to earn letters for a key to decipher some quotes, which had been encrypted using a simple substitution. I looked for math-relevant quotes on the internet and had found the following:

“A mathematician is a device for turning coffee into theorems.”

“A mathematician is a blind man in a dark room looking for a black cat that isn’t there.”

The first was credited to Paul Erdös, the second to Charles Darwin.

This spring, I dusted off my old assignment.  At first I couldn’t find my original key, so I had to solve the cryptoquips myself.  I recognized the first quote as soon as I got the word ‘mathematician’.  The second I didn’t remember at all, and had to work out again.  As I remembered the second quote, I felt uncomfortable.  I realized that since the first time I gave this assignment, I had read a lot more about the idea of ableism—bias against people with disabilities.  I was not sure that it was okay with me (or with others) to use the word ‘blind’ in this way.  I have read that the term blind is correct and not offensive in referring to the condition of not possessing vision.  It is potentially offensive to use the term to indicate a condition of ignorance. Some people point out that the word blind has many meanings, only one of which is sightlessness; I can see what they’re saying, but my rule is to try to avoid any words in my own speech and writing in a way that I know could hurt someone, even if other people think the words should be okay.  In my interpretation of the quote, the man is supposed to be blind, as in physically not able to see.  However, the man does not actually exist; the quote in its larger structure is a metaphor, which uses blindness to describe something else entirely.

As I said, I felt slightly uneasy when I read the quote again, but at the time I didn’t fully work this reasoning through. I was in a hurry, and I trusted my past self, so I decided that this use was okay. I wanted to make sure that the quotes were actually correctly phrased, though, so I did a (very) little Googling. I learned that the coffee quote probably wasn’t from Erdös at all, but his fellow Hungarian mathematician Alfréd Rényi.  Ha, I thought, I will make that part of the assignment!  I will ask the students to do some research and figure out if these are real quotes and are correctly attributed!  This will be good practice in always carefully sourcing any quote you use. (I cringe now reading this thought.)

After I passed out the assignment, I started thinking even more about the second quote. I did my own assignment and started investigating more.  It turns out, the second quote was also misattributed. On Quote Investigator, I learned that the second quote has a long history, and is descended from one that involves racist language/images. The Quote Investigator entry has a trigger warning at the beginning. I thought, wow, this quote was a terrible mistake.  I didn’t make this assignment so that the class could discuss the power of language for good and ill, racism, ableism, or the problematic history and culture of mathematics. My Calculus II students are not likely to have been at all interested in ‘mathematician’ as an identity, and there was no reason at all to use either of these quotes to begin with.  What was I doing, sending my students into this complex terrain, when all I wanted them to do was practice their anti-derivatives? Especially when I had no idea how to unpack the whole thing? I now really regret using the second quote in class, this time and four years ago.

In some ways, this was a “teachable moment”—a real-life example of how mathematical culture is (obviously) every bit as problematic as culture at large, how innocuous-seeming assignments and utterances can carry enormous baggage, and how well-meaning people can make potentially hurtful mistakes, especially if they try to hurry through and never question their past judgments. As I mentioned, I don’t feel that I have the tools and background knowledge to lead the best discussion on all of this.  But I felt that, tools or not, I needed to say something about the assignment in class. I messed up, and I needed to acknowledge that.

I gave this assignment out on Monday.  On Wednesday, the last day of class, I told my students that I was sorry and why.  They didn’t have anything to say about it. Except one student who asked, “Are we still going to get credit for doing the assignment?”  I said yes, and after waiting a while to see if anyone wanted to talk more, we moved on to Lagrange Multipliers.  From the response, it seems possible that none of the students found the assignment offensive or distracting, and probably nobody would have brought it up with me if I had just kept quiet. However, I don’t think that would have been the right thing to do. In my classroom, I have power. I am the expert, I give the grades, I get to decide what is okay, and I choose what I/we talk about.  I could tell myself, “If nobody brings it up with me, nobody was hurt, no harm done.” But that ignores the real power imbalance in the classroom. Since I am in the professor, students would likely not feel comfortable telling me that something I said hurt them. It is hard to speak up. If I can’t bring myself to admit mistakes and speak frankly about difficult things, how can I hope that my students will find the courage to do this, or to tell me when I am wrong?

I feel that it is my job to manage the classroom climate and call out disrespect. If a student said something I viewed as potentially hurtful in my classroom, even/especially to another student, it would be my job to identify that as unacceptable, whether the other student spoke up or not.  This is actually my number one job, as a person, much more important to me than teaching mathematics: in any situation where I have power, I must use that power responsibly.  Whether or not any student in this particular classroom was bothered by the assignment, I was bothered by the assignment, which is proof that it had the power to hurt. Therefore it was my job to speak up.

I have told a couple people about this experience since it happened.  Honestly, nobody really seems to know how to respond to me. I can’t tell if people are appalled that I ever thought that quote was okay, or if they think I’m being ridiculously politically correct, or if they think I am moralizing about what they should do in their classroom. I guess the fact that the same thing could provoke any of these reactions shows how complicated this terrain is. After thinking about it for a long time, I came to the conclusion that using the quote was not right. Now that I see it that way, I can only respond from that place. I am not saying that everybody has to see it that way or else be a bad person.  I am just doing my best to do what I think is right.

That assignment wasn’t what I wanted my students to remember about Calculus II.  But it is one thing that I will not forget about this class. The math classroom does not exist in a vacuum, and of course we need to reckon with the same issues as the larger culture.  For me, right now, that means re-examining everything—including old calculus assignments.

Thoughts? Ideas? Please share in the comments.

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7 Responses to One thing I learned from Calculus, this time around

  1. Avatar Steven G says:

    Really, can we keep this SJW language-policing nonsense out of mathematics. Thanks.

    • Avatar Beth Malmskog says:

      The thing that I relearned here is that every classroom, mathematics included, is full of language and cultural artifacts. Ignoring that can lead to alienating or hurting students, though hopefully it didn’t here. I also want to point out that nobody censored or policed me. This is about me using language that I feel good about using, and giving assignments that I’ve fully examined. This is not me telling anybody else what they shouldn’t or can’t say.

  2. Avatar Jeremy says:

    Definitely the right thing to do. Even if no one is bothered by it now, they might remember your reaction years down the road, and it will hopefully send the message that words do have the power to hurt, even unintentionally. While I might not find the quote is “bad”, to me the situation is simple: there are many words in our language, so why use ones that some people dislike? I know this can be taken to an extreme, but I find as a general practice it’s a good way to go. Thanks for the thoughtful post!

    • Avatar Steven G says:

      Yes, let’s take a poll of everyone in the world and censor any word that at least one person dislikes. Maybe we should just ban language altogether.

      • Avatar Jeremy says:

        Hi Steven,

        As I mentioned, this idea can be taken to an extreme. Of course, I agree with you that there needs to be a limit. All I was trying to express was the fact that if someone finds that they don’t care what words they use, then it seems reasonable to ask them to use words others don’t find offensive (since the person doesn’t care anyway). I think banning language isn’t a great idea, but I was just trying to say that we need to consider the reactions of others.

        Have a good day!

  3. Avatar David Roberts says:

    A better quote would be the longer one from Andrew Wiles about groping around in a dark room and slowly learning the shape of the furniture etc. This isn’t a metaphor from a non-mathematician with all kinds of historical baggage (and I’m not sure it’s actually that good a quote to illustrate the idea), but one from an eloquent mathematician about their own experience in what is generally seen as a high point of 20th century mathematics. Showing the video of that quote, up to and including when Wiles struggles to speak through his emotion would be a way to better explain the idea, but also open up for other teachable moments. Also, it makes for a better overall practice: substitute a good example that conveys the intended meaning more closely, and no unintended messages.

    • Avatar Dierk Bormann says:

      Very good suggestion David, I fully agree. Especially since Wiles’ metaphor also contains the positive “finding the light switch” experience (or something like that, I don’t recall the exact wording), in contrast to the above quote where the black cat will never be found.

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