1On the Importance of Humanizing Math Communication
Cole Leis——————————————————————————————————————————————————————————————————————————————
When I first heard about the Steven H. Strogatz Prize for Math Communication from mymath teacher, I admittedly knew relatively little about math communication. I had communicatedmathematical ideas in my schoolwork, of course, but seldom had I thought about the art of mathcommunication itself. I soon found myself noticing a disconnect between the way math is typicallyportrayed and the way that it is actually done. My curiosity surrounding this topic made figuring out
what I wanted to do for MoMath’s contest rather simple: rather than just creating an example ofeffective math communication, I would write a piece describing my thoughts on this issue and, moregenerally, on the importance of communicating mathematical ideas in a manner that humanizes them.
In the remainder of this paper, I will discuss my discoveries about the disconnect I noticed
as well as some thoughts from individuals who interact with the discipline of mathematicians on aprofessional level. I will also address what I believe to be one of the most abstract questions
related to the topic at hand: Why does mathematical communication even matter?
* * *While textbooks and research typically make mathematics appear to be a discipline that is
devoid of mistakes and that only has room for pristine, perfect work and answers, real math ismessy. When the final product has yet to be reached, pages of mathematical work are covered in
missteps, dead ends, and crossed-out numbers. Among the “wrong” numbers, however, are theones that reflect growth and new understanding. This type of scratch work acts as proof of thestruggle and perseverance that went into solving a problem. When the process of reaching theanswer is omitted and only the final answer is kept, the messiness that is so crucial to thediscipline of mathematics is allowed to be forgotten and kept hidden.
To me, the gap between the perfect math that gets published and the messier math thatallows such pristine-looking work to exist seemed substantial when I first noticed it: substantial
enough to explore further. Before I began the process of writing this paper, I discussed thedirection of my project with my math teacher, Mr. Chris Bolognese, with whom I shared aninterest in the dichotomy between the way math is so often perceived and presented and the way
math truly looks most of the time. With Mr. Bolognese’s assistance, I arranged virtual meetings
with several mathematicians in the hope of discovering answers to some of my questions about
the aforementioned gap.

2Soon enough, I learned that I was not the only one who had noticed the disconnect. In myvirtual conversation with Dr. Brendan Sullivan, who teaches mathematics at Emmanuel College,Dr. Sullivan revealed that while he appreciates the fact that a textbook must serve as a reference
for students, he disapproves of the way in which many textbooks portray mathematics, for they
make students believe that their own mathematical work should appear as pristine as the mathwithin their textbooks. In reality, mistakes are a natural part of the process when doing
mathematical work.
I later learned that research mathematician James Tanton has a similar view. When I
spoke with Dr. Tanton, he explained that the papers of mathematicians in the realm of researchalways omit the missteps and keep only the pristine answer. This can be problematic, as it leaves
the organic process of problem-solving out of the work that is published. This also contributes tothe perception that, simply put, math is hard; leaving out the errors makes people believe thatmissteps must be anomalies and that something must be wrong with them if they make mistakes
when doing math. According to Dr. Tanton, some formal math writing ends up making people
feel like they cannot do math, which is a disservice to such people. Dr. Tanton also mentionedthat math is often presented in a way that makes it seem to be devoid of humanity; this, he said,
is the opposite effect of what math communication should have, which is to keep the humanity ofmath intact.
The fact that so many of my thoughts on the gap and math communication as a whole had
been considered by professional mathematicians as well brought me a great deal of excitement
during my virtual conversations. However, I was still curious about something else: How can webridge the gap? Partway through each of my virtual meetings, I described a certain type ofassignment that Mr. Bolognese gives his students for every unit in his math courses: the problem
set. For these assignments, students must write about the process of completing a set ofproblems. Mr. Bolognese encourages students to include their mistakes and revisions in theirproblem sets, helping them to focus on their growth and learning. I have included an excerpt
from one of my older problem sets in which missteps and revisions are clearly shown. In thiswork, it is apparent that I got stuck and reached out for help during the process of solving theproblem (note that I am addressing Mr. Bolognese when using the word “you” in the pagesbelow), and it is evident that my work is nonlinear and, to put it simply, anything but pristine.

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In my view, problem sets are perhaps the most valuable assignments that Mr. Bolognese’s
students complete, for they enable students to practice communicating math without having toremove the humanity from their work. In fact, I would argue that the style Mr. Bologneseencourages his students to use when writing about math problems from problem sets is one thathas a place in the world of published mathematical writing, as it allows the work to retain thehumanity that went into it. Math is not glossy or perfect, so why should formal mathematical
writing have to appear so sterile?
When I described problem sets to the mathematicians I spoke with, they responded
extremely positively. Dr. Hortensia Soto, a mathematics professor at Colorado State University,
explained that Mr. Bolognese’s problem sets prompt his students to engage in metacognition,
which is hugely beneficial when it comes to learning. Dr. Tanton mentioned metacognition as
well. Dr. Tanton also made a connection between problem sets and a paper that Euler wrote thatemphasized false leads, adding that including mistakes in mathematical work can be useful andcan inspire new thought. Meanwhile, Dr. Sullivan discussed a textbook that he wrote in which heoffers examples of what does not work and provides an explanation of how those potential
missteps can lead to learning and the correct solution. According to Dr. Sullivan, incorporating
mistakes in textbooks may benefit students.
While the perfect math of textbooks and research papers certainly has its place, it would
be remiss not to recognize that humanized mathematical writing has value as well. By publishingwork that acknowledges the human process of solving problems, math can be portrayed in amore positive light. This would help to remove the fear of making mistakes from students’minds, and it would make the discipline of mathematics seem more accessible in general. Theretruly is much to gain from reading and writing explanations of math that do not hide the mistakes
and messiness that are so important to the subject, so I would be overjoyed to witness a transition
to a more human style of mathematical writing within the mathematical community.
* * *I will close by offering a few possible answers to the question I raised at the beginning of
this paper: Why does mathematical communication even matter? For Dr. Sullivan, math is thestudy of ideas. Without effective math communication, mathematical ideas, which are essential
for progress as a species in many ways, will die with the people who have them. For Dr. Tanton,
math is in itself a language. A calculation is a sentence with punctuation and structure: one thatconveys ideas in a beautiful way. In his conversation with me, Dr. Tanton discussed the fact thatmath communication is hard because a person has to find a way to put their ideas in a context
that another person will be able to grasp. This, he noted, is true of writing overall, and it isexceedingly important. As for myself, I would say that math communication matters because it
has the potential to make math human. By making math human, we preserve knowledge, reveal
the discipline’s beauty, make it more accessible, and so much more. As a result, I cannot imagine
a more important role for mathematical communication to play.