Mathematics from arts?

Last Halloween I found myself the lone math student at a party, wearing a Springer Yellow Book costume. While I do not claim to be good at making costume decisions, to my relief people enjoyed a good “textbook costume” pun. Most of all, I was happy that nobody found my costume scary1.

After a while I started a conversation with a couple of people about our jobs and what we enjoy about it. I told them about the research and teaching aspects of my graduate program. This semester I was a teaching assistant for a lower-division Linear Algebra and Differential Equations course. I find this course to be quite fun to teach, because I get to help students develop a geometric intuition for abstract mathematics and point to wonderful applications of that abstraction.

As it turned out, one of the people in our group was a graphics design student. He told me about a project involving linear algebra, and how he wished that he had taken more math courses. He also mentioned using the Bézier curves in his classes. I had never heard of that name, so I wrote a note to look into it later. This conversation reminded me of something I had read in Jordan Ellenberg pitch for Outward-Facing Mathematics:

“Those of us who teach spend a lot of hours talking about math in front of students who have been forced to be there. That makes it easy to forget that people out in the world generally admire math and are excited to learn about it, if we give them a way in!”

Back at home, I looked up Bézier curves, which lead me down a delightful rabbit hole of computer fonts and automobile design2, and in the process I learned new math. In this post (and hopefully others) I am going to write about the wonderful mathematics that I learn inspired by people in other professions.

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A Defense of Diversity Statements in Hiring

Recently, Abigail Thompson, a Vice President of the AMS and Professor at UC Davis, wrote a short opinion piece coming out against the use of diversity statements in hiring. As I read her piece, I found myself troubled by some of the assertions and decided to do a bit of research to confirm my suspicions.

Before I dive into the gist of Professor Thompson’s argument, I think it is important to reiterate why diversity matters in mathematics. Here, I risk making Professor Thompson into a strawman; she’s not asserting diversity in mathematics is unwelcome, just that diversity statements should be removed from hiring. But humor me so I can climb on this soapbox.

First, creating a more equitable society and correcting past injustices that have disadvantaged underrepresented minorities is the most obvious reason diversity should matter. Of course, I have heard the rebuttal, “Yes, but why is it a responsibility of mathematicians to facilitate this change in our field?” Well, mathematicians have the power to enact substantial change by incorporating diversity initiatives into hiring, extracurricular programs, and candid reassessments of the academic climate. Sure, mathematicians may not cause systemic change in society at large, but undoubtedly academics have the power to influence climate and advocate for their values at their own universities.

More selfishly, collaborative environments benefit from diversity. A Tufts study on collaboration efforts of mock jurors found that diverse groups “deliberated longer, raised more facts about the case, and conducted broader deliberations” (6). While the Tufts study focused only on racial diversity, it is emblematic of a larger trend in social psychology which has demonstrated positive effects of diversity in a variety of collaborative environments (7). Crucially, mathematics is more collaborative now than it has ever been and, unfortunately, is not much more diverse (5). Through this lens, if we care about the advancement of our field, we should value diversity for its practical use in addition to its moral imperative.

Now, to the substance of Professor Thompson’s argument:

One of Thompson’s major planks is that a diversity statement is “a political test with teeth.” Thompson likens diversity statements to McCarthy-era loyalty oaths (back in the 1950s, the UC system forced faculty to sign pledges that they were loyal to America and not the Communist party, infamously firing those who refused to comply). Gently put, this is an odd comparison. Even if we accept Thompson’s claim that diversity statements are “political,” they hardly seem comparable to McCarthy-era extremism with respect to harm and disruptiveness. People didn’t sign the loyalty oath, likely because it aimed to exclude, isolate, or punish individuals for their political beliefs. A diversity statement’s entire purpose is to include historically excluded, silenced, or isolated minorities and allow them space in the academic community.

Moreover, is assessing whether job candidates treat people as individuals really a political statement as Thompson asserts? A person’s background influences the way they interact with most things–the classroom is no exception. Consider a student who can’t afford school supplies. Likely, that student will encounter challenges many others won’t: working a job outside class, distracting financial concerns, or even how to take notes each day. I’m not arguing that the instructor should give preferential treatment to this student; just that an inclusive instructor should strive to work with each student to help them realize their academic goals, being sensitive to the backgrounds different students bring into the classroom.

Studies also support the notion that individual identity influences performance in the classroom. For instance, two different studies (one conducted in Florida, one in Tennessee) found that having a teacher of the same race contributed positively to academic success (1, 2). Other studies reiterate that representation matters and that even math classrooms aren’t immune from the effect one’s background brings. For instance, a University of Massachusetts Amherst study found that “increasing the visibility of female scientists, engineers and mathematicians […] profoundly benefits [young women’s] self perception in STEM” (8).

While I agree with Thompson that treating people as individuals is an assertion of how society “ought to be organized,” I believe characterizing this sentiment as “political” misconstrues the meaning by associating it with partisan politics.

All of this is to say: it’s not political to treat people as individuals. It’s human and it’s logical.

Then, Professor Thompson criticizes the fact that “the diversity ‘score’ is becoming central in the hiring process.” Thompson’s language implies that other factors like caliber of research take a backseat to diversity which, when looking at the faculty of any R1 University, seems misleading. The New York Times rebutts this point best:

“The ethos [of mathematics] is characterized as meritocracy [and] is often wielded as a seemingly unassailable excuse for screening out promising minority job candidates who lack a name-brand alma mater or an illustrious mentor. Hiring committees that reflect the mostly white and Asian makeup of most math departments say they are compelled to “choose the ‘best’” […] even though there’s no guideline about what ‘best’ is.”

To paraphrase, hiring committees are just like the rest of us: subject to implicit bias. Certainly, the diversity statement plays a crucial role in patching “the leaky pipeline.”

Moreover, the diversity statement also communicates to underrepresented minorities that a math program cares about creating an inclusive research community. The University of Michigan recently conducted a study on academic attrition and found that, for underrepresented minorities, academic climate was a major factor in their decision to leave (4). In other words, stressing a department’s belief in the value of diversity helps positively shape department norms and combat attrition. The same Times article wrote about Edray Goins, a black mathematician who left a “better” position in a hostile academic environment for a department which emphasized inclusivity (3). Fortunately, Professor Goins chose to remain in academia, but his story is the exception, not the rule.

To her credit, Thompson ends by asserting that “mathematics must be open and welcoming to everyone, to those who have traditionally been excluded, and to those holding unpopular viewpoints.” Unfortunately, the substance of her previous argument makes these words feel empty.

If we truly care about increasing diverse representation in mathematics, we should pursue every available avenue. Diversity statements are only one piece of the puzzle, but they are important nonetheless.

1. Long Run Impacts of Same Race Teachers
2. Representation in the classroom: the effect of own race teachers on student achievement
3. For a black mathematician, what it’s like to be the only one
4. Exit Interview Study: Executive Summary, University of Michigan
5. Women, Minorities, and Persons with Disabilities in Science and Engineering
6. Racial diversity improves group decision making in unexpected ways
7. More sources on the value of diversity in performance
8. Female Scientists Act like a Social Vaccine to Protect Young Women’s Interest and Motivation in the Sciences, UMass Amherst Study Shows


Disclaimer: The opinions expressed on this blog are the views of the writer(s) and do not necessarily reflect the views and opinions of the American Mathematical Society.

Comments Guidelines: The AMS encourages your comments, and hopes you will join the discussions. We review comments before they are posted, and those that are offensive, abusive, off-topic or promoting a commercial product, person or website will not be posted. Expressing disagreement is fine, but mutual respect is required.

Posted in AMS, Diversity, General, Interview, Jobs, Mathematics in Society, News | 2 Comments

CROSSWORD! (or: Diversion as a vehicle for conversation on power and usage)

There is so much that is peculiar, irregular, silly, or downright twisted in mathematical verbiage that, certainly, we could all benefit from some soul-searching on the language of our culture. Some of mathematics usage is confusing (e. g. overuse of “normal” and “regular”) and some irritating (personal peeve: persistent classroom use of “guy” to refer to mathematical expressions – I know anthropomorphization makes things friendly and all, but I’m not sure that thinking of all mathematical objects as “guys” is good for our ongoing gender problem). And then there are other things that just floored me the first time I heard them (um, “clopen,” anyone?), not to mention our obsession/affliction with eponymy and its discontents. There is a dissertation in linguistic anthropology waiting to be written on mathematical usage, and perhaps several that already have been.

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Mathematics at 2019 SACNAS

Below I share some details about SACNAS and some of the mathematical events that happened at this year’s SACNAS National Conference.  I hope that this may also serve as an invitation/motivation for anyone interested in diversity and mathematics to participate in SACNAS at any level.


The Society for Advancement of Chicanos/Hispanics and Native Americans in Science (SACNAS) is a society that aims to further the success of Hispanic and Native American students in obtaining advanced degrees, careers, leadership positions, and equality in STEM.  SACNAS was founded in 1973 by underrepresented scientists to address the representation of Chicanos/Hispanics and Native Americans in STEM.  Diverse voices can expand scientific and mathematical knowledge as well as bring creative solutions to scientific problems.  This is one of SACNAS’s motivations for building an inclusive, innovative, and powerful national network of scientists, which now includes over 6,000 society members, over 115 student and professional chapters, and over 20,000 supporters of SACNAS throughout the USA.  Contrary to the name, the society is welcoming of people from all backgrounds, identities, fields of study, and professions. SACNAS is the largest multicultural STEM diversity organization in the US.

SACNAS has programs and events that train and support the diverse STEM talent that is found in this country.  This is done in partnership with the student and professional chapters, the leadership programs, Native American programs, regional meetings, and policy and advocacy initiatives.  SACNAS also hosts THE National Diversity in STEM Conference.  This year’s 2019 SACNAS National Conference in Honolulu, Hawai’i brought in over 5,000 participants!  Next year the 2020 SACNAS National Conference is in Long Beach, California!

Math at SACNAS:

Mathematicians and mathematics have always been a strong part of SACNAS.  In fact some of the founders of SACNAS include mathematicians, such as Dr. Richard Tapia (Rice University) and Dr. William Vélez (University of Arizona). I am fortunate to have met these two great mathematicians, who at different times in my academic journey have shared their wisdom and thoughtful advice.

Dr. Richard Tapia and I at the 2011 National SACNAS Conference.

My first SACNAS conference was in 2011 in San José, California.  I was a second-year undergraduate student attending his first scientific conference.  I was eager to learn and excited for all the opportunities that would be presented at this conference, but I did not know what to expect.  Fortunately, I found a community of mathematicians who share similar goals for diversifying mathematics and who genuinely care in supporting the success of students.  I trace my interest in combinatorics to the 2011 SACNAS National Conference, where I had the opportunity to attended the NSF Mathematics Institutes’ Modern Math Workshop.  That year’s keynote lecture on “Counting Lattice Points in Polytopes” was presented by Dr. Federico Ardila (San Francisco State University).  As an example of the power of networking, community, and mathematics at SACNAS, four years later Federico became one of my master’s thesis co-advisors.  More than that, I found an unconditional mentor, friend, and research collaborator and I owe part of this to SACNAS for providing a space for a student like me to grow academically and professionally.

Students from the UC Berkeley Cal NERDS program (including me)  with Federico Ardila at the 2011 SACNAS National Conference.

The Modern Math Workshop is a two-day workshop that takes place in conjunction with the national meeting of the SACNAS conference and showcases the contemporary research happening at NSF-funded mathematical sciences institutes around the country.  It became a collaboration with SACNAS in 2006 and has been jointly organized by the Mathematical Sciences Institutes since 2008. Since 2011 this event has been funded by the NSF through the Mathematical Sciences Institute Diversity Initiative. The workshop is a mix of activities including research expositions aimed at graduate students and researchers, mini-courses aimed at undergraduates, a keynote lecture by a distinguished scientist, and a reception where participants can learn more information about the Mathematical Sciences Institutes.

In addition to the Modern Math Workshop, there are scientific symposia organized by mathematicians, there are oral graduate presentations, and both graduate and undergraduate poster presentations.

Math at 2019 SACNAS:

I do not know if it was because we were in the beautiful city of Honolulu, that the sky was much bluer and the ocean water much clearer, but there was certainly an extra revitalizing energy present at this year’s SACNAS conference.  Below are some of the mathematical events that went on (and that I participated in) at this year’s SACNAS conference.  I am sure there were more that I missed out on.

This year’s Modern Math Workshop was organized by the Mathematical Sciences Research Institute (MSRI)  There were two mini-courses aimed at undergraduate students. One was lead by Dr. Wilfrid Gangbo (UCLA)  and Dr. Anastasia Chavez (UC Davis).   The workshop also included research talks aimed at graduate students and faculty and were delivered by representative mathematicians from each of the NSF Math Institutes.  Additionally, there was a panel which addressed topics such as: imposter syndrome, how to choose a graduate program, how to stay motivated, how to choose a mathematical field, etc.  Below are some of the speakers and panelists.

  • Katherine Breen (Institute of Pure and Applied Mathematics (IPAM))
  • Xinyi Li (SAMSI – Statistical and Applied Mathematical Sciences Institute)
  • Gabriel Martins (California State University, Sacramento)
  • Robin Neumayer (Northwestern University)
  • Marilyn Vazquez (Mathematical Biosciences Institute (Ohio State University)Institute for Computational and Experimental Research in Mathematics (ICERM))

I was able to sit in Dr. Anastasia Chavez’s mini-courses, which was “An introduction to matroid theory.”  My discrete mathematical mind was very happy to hear and learn from my friend on a topic that is incredibly interesting.  You can find her slides here.

Anastasia Chavez delivering her mini-course on matroids.

Apart from the Modern Math Workshop there were three great events/experiences that I would like to share with you all.

  1. Dr. Rebecca Garcia (Sam Houston State University)  and Dr. Kamuela Yong (University of Hawai’i – West O‘ahu) organized the very first “Pacific Islanders in Mathematics” session.  This was a historic event (the organizers are writing a more detailed article to be shared with the public) and it featured amazing speakers including:
    • Kyle Dahlin (Purdue University): Avian Malaria & Hawaiian Honeycreepers – Modeling of the Effectiveness of Vector Control
    • Dr. Marissa Loving (Georgia Tech): Determining Metrics using the Lengths of Curves
    • Ashlee Kalauli (UC Santa Barbara): Solving the Word Problem for Artin Groups
    • Dr. Efren Ruiz (University of Hawai’i – Hilo): Rings Associated to Directed Graphs

      “Pacific Islanders in Mathematics” organizers and speakers (Left to Right): Rebecca Garcia, Efren Ruiz, Kyle Dahlin, Marissa Loving, Ashlee Kalauli, baby Kamuela, and Kamuela Young.

  2. Dr. Pamela Harris and I co-organized, “Latinxs Count!”, an algebraic and geometric combinatorics research talk session at SACNAS. It featured a talk by me and three amazing speakers :
    • Andrés R. Vindas Meléndez (University of Kentucky): An Invitation to Ehrhart Theory
    • Laura Escobar (Washington University in St. Louis): Polytopes and Algebraic Geometry
    • Ryan Moruzzi, Jr. (Ithaca College): Exploring Bases of Modules using Partition overlaid Patterns
    • Rosa Orellana (Dartmouth): The Combinatorics of Multiset Tableaux

      “Latinxs Count!” organizers and speakers (Left to Right): Ryan Moruzzi, Jr., Andrés R. Vindas Meléndez, Pamela Harris, Laura Escobar, and Rosa Orellana.

  3. Dr. Pamela Harris was also one of the featured speakers at the SACNAS National Conference.  Her featured talk titled, “DREAMing,” shared her story as DREAMer and her mathematical journey into research and mentoring.

A snapshot of Pamela Harris’ featured talk.


I am blessed to have such a supportive mathematics/SACNISTA familia.  To end the blog post, I want to share something I mentioned at the conference. I overheard several people say that the math they do is not useful, but I want to challenge each of us to think more about the meaningfulness of our mathematics.  Sure, my math may not be applicable (at least right now) to anything “useful”, but it is meaningful to me.  It has given me a career path, it has allowed me to make wonderful friends and connections, and I get to share the beauty and meaning of it with people all over the world.  But, that’s a whole other topic for a blog post (too deep for this blog post), so I hope that you got a glimpse of the mathematical events that I experienced at this year’s SACNAS National Conference!  I look forward to seeing and meeting some of you at the 2020 SACNAS National Conference in Long Beach, CA!

Mathematicians after Pamela Harris’ talk! Building community.


Disclaimer: The opinions expressed on this blog are the views of the writer(s) and do not necessarily reflect the views and opinions of the American Mathematical Society.

Comments Guidelines: The AMS encourages your comments, and hopes you will join the discussions. We review comments before they are posted, and those that are offensive, abusive, off-topic or promoting a commercial product, person or website will not be posted. Expressing disagreement is fine, but mutual respect is required.

Posted in Conferences, Diversity, Mathematicians, Mathematics in Society | Leave a comment

Solvitur Ambulando

An algebraist, a finitist, and a determinist walk into a statistics classroom. They are all the same person and worse: the teacher, so the joke is on the students.

For reasons still partly obscure to me, my department has given me the opportunity to teach an introductory probability and statistics course for a second time. People often speak of impostor syndrome in mathematics, but this is something more like double agency. I feel like an embedded resistance fighter, my mind at intervals crafting subtle acts of sabotage, constantly wary that I might be found out.

I won’t deny the usefulness of adopting a probabilistic perspective, but its utility is also my chief complaint. Continue reading

Posted in Grad student life, Math, Math History, Math Teaching, Statistics, Teaching | Tagged , , , | Leave a comment