A tribute to Hispanic Heritage Month

It’s almost that time of the year again!

Hispanic Heritage Month (September 15 – October 15) is a national holiday in the United States that began as a way to promote the history, contributions, and culture of Hispanic-Americans. Its observation started with a week-long celebration in 1968 and was enacted into law to cover 30 days on August 17, 1988. As a Latinx mathematician myself, this month embodies a time of reflection of all we have achieved and the challenges still ahead of us. Most of all, it allows us to know the stories of fellow Hispanic and Latinx mathematicians that contribute to mathematics through their research, teaching, mentoring, and/or service.

During this month, Lathisms.org  features the profile of a Latinx/Hispanic mathematician daily, providing a biography and information on their research, teaching and service contributions. It was founded by Alexander Díaz-López, Pamela E. Harris, Alicia Prieto-Langarica, and Gabriel Sosa on 2016 and continues to grow each year (read more about its origin here). Last year’s calendar featured early-career mathematicians including graduate students and post-docs. You can visualize the locations,  institutions, and research areas represented by the 2018 honorees’ in this map. (Note: The data displayed is based on the honorees profiles and might have changed since the calendar launch.)

This year’s theme is Mathematics Education  and you can already see a sneak-peak to this year’s calendar on the AMS September Notices communication, “2019 Lathisms: Latinxs and Hispanics in the Mathematical Sciences”, which features the profile of four of the honorees: Dr. Hortensia Soto (University of Northern Colorado), Dr. Enrique Treviño (Lake Forest College), Dr. Vilma Mesa (University of Michigan), and Dr. James A. Mendoza Álvarez (University of Texas at Arlington).

It will also continue its podcast series featuring interviews with previous honorees led by Evelyn Lamb. What excites me the most about getting to know this year’s honorees is summarized in Evelyn Lamb’s post “The Dangers of a Single Story in Mathematics”,

“There really is no one kind of person who becomes a mathematician.”

What a wonderful thing that is!  A theme of many of the past honorees’ profiles and interviews has been the importance of mentorship, early access to opportunities, and the big sense of responsibility to they feel towards making mathematics and inclusive environment for all.

“Hispanic Heritage Month means someone recognizes that we contribute to this country. It means that the sacrifice that my parents made for us was not in vain. It means that the work that my elementary teachers did for me is recognized. It is a mechanism to serve as a role model for others—regardless of gender, race, sexual orientation, religion, socio-economic status, level of education, etc. And, I get to do this in the same manner that it was bestowed upon me: through compassion. It means that as a Hispanic mathematics educator, I am valued.” —Dr. Hortensia Soto

In her blog post “For People Of Color, Succeeding In Academia Is A Political Statement” Melissa Gutierrez Gonzalez, a junior mathematics and philosophy student at Occidental College in Los Angeles, highlights some of impacts women and minority students face in academia.

“I couldn’t make a mistake, because if I did, what would others think of Mexicans? As someone who has always been a part of predominantly white institutional environments, ignoring the fact that I am acting as a representative for people of my ethnic background is incredibly difficult, because for many, I am the first Mexican they meet. For most, I am the first Mexican or Latino/a they meet in the mathematics field.”

These impacts are sometimes aggravated by the current political status of being an undocumented student. In “Requiem for a Dream”, Dr. Adriana Salerno shared the story of an undocumented mathematician and provides resources to support students affected by the changes in Deferred Action on Childhood Arrivals (DACA) program, which shields young undocumented immigrants from deportation. Representation and acknowledging the full identities of our students, teachers, professors, and colleagues matters. The importance of having faculty that can serve as role models for our students was highlighted in the following student quote from “Cluster Hiring Is Working for Us: Two Early Career Latinas in Math” by Dr. Selenne Bañuelos and Dr. Cynthia Flores,

“The fact that they were both Latina gave me the opportunity to communicate with them about my DACA status, and their support was invaluable to me.”

In the past years, there has been a growing recognition of how mathematics is political. For example, in her 2013 commentary, Dr. Rochelle Gutierrez proposes that,

“By virtue of mathematics being political, all mathematics teaching is political. All mathematics teachers are identity workers, regardless of whether they consider themselves as such or not. They contribute to the identities students construct as well as constantly reproduce what mathematics is and how people might relate to it (or not).”

When we are in the mathematics classroom, whether it is at the K-12 or college level, we are promoting more than mathematical knowledge, we are shaping the identity of  who is and can be successful in mathematics. This extends to other mathematical spaces such as workshops, conferences, and departments. As Dr. Pamela Harris shares in her recent blog post sometimes “It’s the little things” that make you question belonging in the mathematical community.

“It reminds me of little things that I have experienced and which have affected my self identity as a mathematician and made me question my place within the mathematical community. Itʼs the small actions or words or micro aggressions (regardless of intent) that take me out of doing mathematics and bring only selective parts of my identity front and center.”

What it means to be a Hispanic/Latinx mathematician is a multi-layered experience and we will not have a way to condense it all into a single narrative. Conferences such as SACNAS, Blackwell-Tapia Conference, Latinx in the Mathematical Sciences Conference (LatMath) play an important role in bringing together members of the Hispanic/Latinx community. Read some of the reflections on LatMath 2018 by previous participants Emily Alvarez, Dr. Adriana Salerno, and myself. These conferences hope to achieve true diversity in STEM, encourage and showcase the research being conducted by Hispanic and Latina/os at the forefronts of their fields, and to build a community around shared academic interests.

This Hispanic Heritage Month, let’s celebrate how far we’ve come, recognize the unique journey of the members of our community while continuing our work to make mathematics a place where all can belong.

Do you have suggestions of topics you would like us to consider covering in upcoming posts? Reach out to us in the comments below or let us know on Twitter! You can find me @MissVRiveraQ.

Posted in Current Events, Hispanic Heritage Month, Math Education | Leave a comment

Uncovering ‘What if?’ and ‘Why?’ in the A.I. era

Artificial intelligence, which has been extensively developed in the last few decades, cares about the power of a machine to copy intelligent human behavior.  As humans, we make decisions every day that rely on the cause and effects of our actions. For example, we know if we work out at the gym it will cause the number of calories we burn to go up. However, the implications this may have on our overall health is more difficult to address. This boils down to the difference between two statistical concepts: correlation and causation.

  • Correlation: measures the relationship between two things.
  • Causation: means that one thing will cause the other to happen.

The distinctions between the two can have important implications. In the website, “Spurious Correlations” by Tyler Vigen, you can explore a wide variety of correlations that are due to chance.  One of my favorites can be seen in Figure 1, which illustrates the correlation between math doctorates awarded and the Uranium stored at United States nuclear power plants. While these two variables have a correlation of 95.23%, it is highly unrealistic to think my degree caused an increase in the amount of Uranium stored in the United States.

Chart that illustrates how math doctorates awarded correlates with Uranium stored at US nuclear power plants over time.

Figure 1: Example of a spurious correlation by Tyler Vigen.

When we think of causality we want to prove that there is a direct relationship between two variables. This can be harder than expected since, as the famous phrase goes, “correlation doesn’t imply causation”. One of the first examples I encountered  as a student was based on the question: Do storks deliver babies? Many parents may wish the answer was yes to avoid explaining where babies come from to their kids. While the number of storks and human births exhibit a positive correlation (see “Stork Deliver Babies”  by Robert Matthews), again this is not true.

I like this simple example that Adam Kelleher uses in his article “If Correlation Doesn’t Imply Causation, Then What Does?”. Think of your daily commute, if your alarm doesn’t go off or there is traffic, you will be late for work. There are many events on your morning routine that could also make you late for work (i.e. traffic is fine but you spilled coffee on your way or your alarm goes off and you oversleep). We think of all this as noise and as the author mentions, “it takes care of the host of “what-if” questions that come up from all of the unlikely exceptions we haven’t taken into account”.

In the new era of big data, how do we discover the underlying relationships between big datasets and which relationships can we trust? “The Book of Why” by Judea Pearl and Dana Mackenzie, which was recently reviewed in the Notices of the AMS by Dr. Lisa R. Goldberg, tackles the question of how we can use the theory of causality to model and interpret data. In the review, the concept of “The Ladder of Causality” is summarized nicely:

“The bottom rung is for model-free statistical methods that rely strictly on association or correlation. The middle rung is for interventions that allow for the measurement of cause and effect. The top rung is for counterfactual analysis, the exploration of alternative realities.”

Figure 2: Illustration of the ladder of causality in “The Book of Why” by Judea Pearl and Dana Mackenzie.

To achieve intelligence, Pearl proposes a machine’s reasoning should move through the ladder illustrated in Figure 2.  Machines should move from seeing associations in data to doing and planning interventions to obtain a desired outcome, towards  becoming counterfactual learners  that can imagine what does not exist yet and infer from observed data. As mentioned by Pearl in an interview by Kevin Harnett from Quanta Magazine,

“If we want machines to reason about interventions (“What if we ban cigarettes?”) and introspection (“What if I had finished high school?”), we must invoke causal models. Associations are not enough — and this is a mathematical fact, not opinion.”

Reaching the top of the ladder of causality may still be out of our grasp. As our understanding progresses, I would love to see how we integrate the qualitative and quantitative aspects of building a world around data. As Andrew Gelman points out in his review of the book,

“If you think you’re working with a purely qualitative model, it turns out that, no, you’re actually making lots of data-based quantitative decisions about which effects and interactions you decide are real and which ones you decide are not there. And if you think you’re working with a purely quantitative model, no, you’re really making lots of assumptions (causal or otherwise) about how your data connect to reality.”

In my perspective, as humans, we are only able to imagine when we consider both. For machines to answer “what-if?” and “why?” they must do so as well.

Posted in Artificial Intelligence, Data Science, Statistics | Leave a comment

Mathematical oncology blog posts

In July, The Mathematical Oncology Blog was launched. This community blog, which focuses on mathematical and computational oncology, is looking for contributors. Presently, the blog has several posts and seems to be off to an great start.

I find it convenient that links to manuscripts are included at the tops of some of the posts — such as “Quantifying Tumor Heterogeneity” by Elana Fertig and “Space Accelerates Evolution” by Jeffrey West. I am also excited to see that so far, the contributors on the blog have chosen to cover varied topics.

For instance, in “The Colors of Cancer,” Thomas Hillen uses a paint analogy to argue against the “popular myth that the pharma companies have a Golden-Bullet-drug against cancer in their drawers and refuse to use it as to maximize profits” (emphasis is Hillen’s). He then takes his argument further by explaining why “even more so, it is not even theoretically possible to have such a Golden Bullet drug against cancer.”

Taking a totally different approach and critiquing the modeling in a Nature Communications paper published in 2017, Fred Adler’s “All pithy maxims about modeling are wrong, but some are useful” on the blog begins with this:

“In science, criticism is perhaps the highest compliment, showing that we take work so seriously that we are inspired to spend time thinking about and formulating how work can be improved. It is in this spirit that I lay out some of the many issues that I have with the model of Zhang et al (2017) developed by my friends and colleagues at the Moffitt Cancer Center. This model has been widely cited as providing support for the appealing idea of adaptive therapy in prostate and other cancers, the approach of adjusting therapy continuously in response to tumor status in order to maintain long-term control by delaying or avoiding resistance. However, I have been arguing for some time this model is severely flawed in its assumptions, the way it implements those assumptions, and in the presentation and interpretation of results. I take this opportunity to present a brief outline of these flaws. How much they weaken the justification for adaptive therapy is a broader question, as is the question of whether I have wasted my career trying to write models that avoid flaws of this sort.”

Artem Kaznatcheev, who is part of the group that launched the blog, has also written posts about cancer on the Theory, Evolution and Games Group Blog at the University of Oxford. That blog is in its ninth year. Just a few of the posts Kaznatcheev has written about cancer for TheEGG include “Hamiltonian systems and closed orbits in replicator dynamics of cancer,” “Symmetry breaking and non-cell-autonomous growth rates in cancer” and “Abstracting evolutionary games in cancer.”

On the SpringerOpen blog, Jorge Gómez Tejeda Zañudo wrote “Using physics, math and models to fight cancer drug resistance.”

Know about particular blogs or topics you would like us to consider covering in upcoming posts? Reach out to us in the comments below or let us know on Twitter! You can find me @writesRCrowell.

Posted in Applied Math, Game Theory | Tagged , , , | 1 Comment

Let’s Talk About Viral Equations

Recently, there was a viral post about solving the equation below:

Many mathematicians and social media powerhouses have weighed in on what the answer should be. But, why has this equation led to a lot of debate? This is not the first time that an equation or math problem has become an internet sensation and I suspect it won’t be the last (see “10 viral math equations that stumped the internet”). Depending on the order of operations you apply to this equation you will end up with an answer of 16 or 1.

Every time a new viral equation storms the internet, I casually scroll through all the responses.  What draws my attention the most is the way people interact with these types of posts. Many seem to jump at the opportunity to flex their math muscles while others reach for their calculators. The perception seems to be that this basic math question should have solely one answer and however disagrees is wrong. The answer to this viral equation, as Steven Strogatz explains in his recent article, depends on what conventions you are using.

What jumps at me is that, when presented with solving an equation, it’s is rare to discuss how we write mathematics and why we interpret it in a particular way. Mathematical grammar matters and conveying the “right” statement of a problem relies on using the symbols that have become our language. As told in this 2013 article “What Is the Answer to That Stupid Math Problem on Facebook?”  by Tara Haelle, ‘Consider how often people debate grammar. Math has syntax just as language does—with the same potential for ambiguities. And just as word-based riddles exploit the ambiguities of language, so do these math problems’. As Hanna Fry mentions, ‘This is like a maths version of the sentence “He fed her cat food”. Does it mean the man gave some food to a cat? Or – slightly darker- fed some cat food to a woman. It’s impossible to tell from the information we’ve been given’. We have allowed the perception that math is unambiguous to reign. But different from a language, being right or wrong in math, tends to be associated with how smart a person is. This mindset ultimately is what leads to these heated debates and causes a divide. As expressed in this essay  by Kenneth Chang, “It implies that the point of mathematics is to trip up other people with stupid rules.”

Don’t get me wrong, mathematicians spend a lot of time trying to be as unambiguous and precise as possible. However, math can be written in ways that make the reader interpret its meaning in unintended ways. Last year, I taught a course that was aimed at future elementary school teachers. This class was a great way to see how we can build our interpretation of math when most of the tools we use are suddenly are unavailable. Students struggled with playing with assumptions, definitions, and ultimately engaging with mathematics in a playful way. We explored the number systems that were used in different cultures, build proofs using physical objects, and played with what makes and breaks definitions. Yet, the idea that there is only one way to interpret a problem stayed throughout the course. The more time I’ve spent teaching (and learning) mathematics the more dangerous this perception feels. It hides away the fact mathematics was built, written, and interpreted by humans, and sometimes this leads to fun internet debates.

Mathematics has a rich history of how we’ve built the conventions that we use every day. In his blog “What is 00, and who decides, and why does it matter? Definitions in mathematics”, Art Duval shares why definitions (I would also extend this notion to conventions) are useful and highlights how we can still have choices to make even for precise definitions.  For example, Terry Moore’s short TED video, “Why is ‘x’ the symbol for an unknown?”, illustrates that even some conventions have origin stories outside of mathematics. But often, students learn acronyms like PEMDAS (parenthesis, exponents, multiplication, division, addition, and subtraction) without knowing the history of these conventions. We may not have the time to unpack the history of all the conventions that we use but we can highlight how they help us communicate math. Next time a viral equation floods the internet, don’t fret! This can be the perfect opportunity to share a bit of the history of our conventions and the importance of how we write (and interpret) mathematics.

Posted in History of Mathematics, Math Communication, Recreational Mathematics, Uncategorized | Leave a comment

Introducing Vanessa!

Woman holding a flower bouquet

Vanessa Rivera Quiñones at her defense in April 2019. Welcome to the blog! Photo courtesy of Vanessa Rivera Quiñones

Starting this month, Vanessa Rivera Quiñones (@MissVRiveraQ) will be co-editing the blog with me! She received her Ph.D. in mathematics this year from the University of Illinois at Urbana–Champaign and she’s currently looking for a job in Belgium.

Last year, Vanessa wrote three guest posts on the AMS Graduate Student Blog: “Communicating Mathematics to a Broader Audience,” “Towards Embracing Diverse Mathematical Communities” and “Staying Organized to Improve Productivity.” She is currently in the process of launching her own math blog.

Vanessa brings to this blog her broad interests in such areas as mathematical biology, data science, interdisciplinary research, science communication and teaching. She’s also passionate about exploring the intersection of those fields with equity, inclusion and social justice.

Vanessa says she views math blogging as “a nifty way to get ideas out there” and discuss “topics that don’t come up as naturally” within the mathematical community. She’s eager to jump into writing about a wide range of topics, including those outside of her areas of expertise and finds writing about different topics to be a great way to learn more about them.

Her doctoral research, which involved collaborating with a biology laboratory, focused on using differential equations and other mathematical tools to study the disease dynamics of the Daphnia-Metschnikowia system. She also participated in several other research programs. During a Research Experiences for Graduate Students (also at the University of Illinois at Urbana–Champaign) opportunity, she studied “Variable Annuities with Guaranteed Minimum Benefits.” She also participated in the Research in Industrial Projects for Students program at the Institute for Pure and Applied Mathematics (IPAM) where her group (sponsored by Standard and Poor’s) researched ‘Pricing and Risk in the Credit Markets: Investigation of Credit Default Swaps.” Her project at the Iowa Summer Institute in Biostatistics was the ‘Study of Glaucoma Change Probability for Open-angle Glaucoma.”

Vanessa was born in Puerto Rico and she went to college at the University of Puerto Rico at Río Piedras, where she earned a bachelor’s degree in pure mathematics with a minor in finance. She says that she didn’t have a lot of mathematical role models at the beginning of her undergraduate studies, but when she got involved with SACNAS and other organizations aimed at underrepresented students, that really helped.

It’s critical to “look for stories that portray a lot of people that do math,” Vanessa says. She finds that while today’s students have access to certain websites (such as “Mathematically Gifted & Black”) and other resources that weren’t available when she started her undergrad, it’s still challenging for many of them to find role models. She says that meeting mentors with different backgrounds not often seen in mathematics can help students find the representation they crave. Some ways she thinks instructors can do this are by opening up with students about different aspects of their identities outside of mathematics and by encouraging students to connect with mathematicians of varied backgrounds at conferences.

Just a few of Vanessa’s writing plans include creating blog tours similar to this one and highlighting blogs covering interdisciplinary, collaborative research. She also says she “would love to see more blogs about books aimed at the general audience and explaining mathematical concepts in an accessible way.”

“I admire a lot the work of Tai-Danae Bradley, Nicky Case Explorables, and MathMunch. I think as mathematics becomes more interdisciplinary, the efforts made by QUBES Hub with their blog of bringing together quantitative biology, mathematics, and education is another important contribution,” Vanessa says.

Outside of math, Vanessa enjoys dancing, drawing and Zumba.

Know about new blogs we haven’t covered yet or want us to take another look at one of your favorite blogs that hasn’t been discussed here in awhile? Please reach out in the comments or on Twitter!

Posted in Applied Math, Biomath, Data Science, Math Communication, Math Education, people in math, women in math | Tagged , , , , , , | Leave a comment

Math Instruction for Students Learning English

As of 2016, 4.9 million students — or 9.6% of students in U.S. public schools — were identified as English Language Learners (ELL), according to the National Center for Education Statistics. While different folks advocate using different terms to describe those students (for instance, some advocate using the term “multilingual students” instead, this Education Week blog post notes), at least one thing is certain: We need to think about how to set those students up for success in school, including in math classes.

“The Challenges of Teaching Math to English Learners”

“Many educators share the misconception that because it uses symbols, mathematics is not associated with any language or culture and is ideal for facilitating the transition of recent immigrant students into English instruction. To the contrary, language plays an important role in learning mathematics. Teachers use language to explain mathematical concepts and carry out math procedures,” Rusty Bresser wrote for the Math Solutions blog.

“The challenge of teaching math to English learners lies not only in making math lessons comprehensible to students but also in ensuring that students have the language needed to understand instruction and express their grasp of math concepts both orally and with written language. ELLs have the dual task of learning a second language and content simultaneously,” Bresser added.

In that post, he explains that ELL students often struggle in math class when they don’t understand the vocabulary, syntax and grammar used in instruction. He also provides specific examples of this.

“How Do We Support English Learners Success in Mathematics?

This post on the National Council of Teachers of Mathematics (NCTM) blog invites us picture what many ELL students go through.

“Imagine that throughout your whole life, the only language you’ve heard or spoken is Spanish. You’re from a rural town in Honduras, the only home you know, and then at age six your family moved to the USA. Once there, you were signed up for 1st grade at the local elementary school, and you were thrown right into an English-speaking classroom. While at school, you received some English language support, but what you heard all day long at school is English,” wrote Evgeny Milyutin.

‘Take another look, you used to love math class in Honduras; yet, in your American classroom you feel bored, exhausted and frustrated. In fact, instead of feeling smart and capable, you’re actually starting to believe you’ll never be a good student in your American math classroom,” Milyutin added.

Milyutin reminds us that ensuring that ELL students attending public schools receive a proper education isn’t merely a goal to aim for, but, instead, a mandate. “Federal law requires that school districts ensure that ELLs can ‘participate meaningfully in schools’ educational program[s],’ and that schools strive to bridge language barriers…More recently, legislation has gone as far to require that districts use strategies and programs to help ELLs that are backed by scientific evidence,” Milyutin wrote, citing the Education Week article “Teaching English-Language Learners: What Does the Research Tell Us?”

In the second half of the article, Milyutin shares a list of what to do — and what not to do — when teaching ELL students mathematics. The list is based on an interview Milyutin had with Lisa Meyer, director of programming for Dual Language Education of New Mexico.

“ELLs Count on Language Support in Math”

This post was included in a publication of the ASCD (formerly the Association for Supervision and Curriculum Development).

Megan Rowe, a math teacher at Borah High School “in a linguistically diverse district outside Boise, Idaho” told article author Laura Varlas “Language is the entirety of the mathematics classroom. From the language I use when I’m teaching to the language students use when they’re reasoning among their peers—I don’t know how you could ever teach mathematics now without focusing on language.”

“Once you start looking at math through the lens of language, you see linguistic demand everywhere,” Bill Zahner, a San Diego State University professor and former high school math teacher told Varlas.

The rest of the article describes how educators can help ELL students, such as “building a baseline” and “weeding wordy problems.”

Posted in Issues in Higher Education, K-12 Mathematics, Math Communication, Math Education | Tagged , , , , | 1 Comment

A Blog On Blog On Math Blogs

Your blogger blogging, one last time.

Folks, I’m packing it in. After 97 posts and nearly 5 years of covering the math blog beat, the time has come for me to pack up my blogging tools and hit the high road to adventure.

I’ve really enjoyed blogging so much, but there is a funny thing I’ve observed over the years. The posts I like the most or am the most proud of are often not the ones that get the most traffic. Since this is my final and farewell post, I wanted to share the three favorite posts that I’ve written here. What makes them my favorite? Usually it’s that I feel like I’ve told a good story, or learned a lot in researching the post, or that I just find myself talking to friends often about the topic. I hope you enjoy these posts (perhaps, again).

  • Black Hat, White Hat, a tale of cybersecurity and a hero blogger who saved the internet.
  • The Blockchain Party, an explanation of some of the math behind bitcoin and the blockchain, published in 2017 at the pinnacle of bitcoin mania.
  • Do Evaluations Really Add Up?, an inspection of some (mostly bad) attitudes on the internet about about student evaluations of teaching.

When I joined Evelyn Lamb as a co-editor of this blog in 2015, the internet felt like a different place. We were still in the golden age of math blogging, the art of podcasting was on the rise, and Twitter was a platform for the people. Since then, the landscape has shifted, but the #MTBoS remains a rich and wonderful place.

Accordingly, as one might notice from my blog posts, my interests have shifted away from basic problems in math and become more directed towards the ways that bloggers are using the tools of math to make a societal difference in issues like gun control, vaccination, climate change, gerrymandering and elections.

To be clear, when I say basic problems in math, I’m talking about things like the Erdős Discrepancy Problem and the Graph Isomorphism Theorem. So maybe basic isn’t quite the right word. But you know what I mean. There are still some incredible bloggers writing about various explorations in mathematical pedagogy, visual artists working with core ideas in mathematics, and all manner of opining on the intrigue of academia.

As for this blog, stick around, there’s more to come from the Blog on Math Blogs! Later this summer, the talented Rachel Crowell with be joined by a brand new to the blog Vanessa Rivera Quiñones. I’m looking forward to their posts, and I might just pop back in for the occasional guest post. In the meantime, you can find me on Twitter @extremefriday.

Posted in Uncategorized | 6 Comments

Updates on Gerrymandering

A court gavel rests on a sound block

Photo by Blogtrepreneur via Wikimedia CC

The U.S. Supreme Court ruled last month on gerrymandering. “In a 5-4 decision along traditional conservative-liberal ideological lines, the Supreme Court ruled that partisan redistricting is a political question — not reviewable by federal courts — and that those courts can’t judge if extreme gerrymandering violates the Constitution,” NPR reported, adding, “The ruling puts the onus on the legislative branch, and on individual states, to police redistricting efforts.”

With that decision handed down, folks are still discussing the issue of gerrymandering and attempting to answer the question “What now?”

Some background

Anna discussed gerrymandering in her 2018 “Not Those Midterms” post and her 2017 “Hacking Cracking & Packing” post. I recommend checking those out if you haven’t already. The Capital Currents blog also has numerous posts about gerrymandering. Cathy O’Neil also has a post on her blog about the history of gerrymandering, “how to gerrymander,” “how not to gerrymander,” detecting gerrymandering and problems with detecting gerrymandering.

Commentary on the Supreme Court ruling

“The Mathematics of Gerrymandering and the Supreme Court,” a post on the MAA’s Math Values blog by Rachel Levy, deputy executive director of the MAA, with an excerpt from Jeanne Clelland, a professor of mathematics at the University of Colorado, Boulder, covers the recent ruling.

The excerpt from Jeanne Clelland explains a strategy developed by several groups for “quantifying gerrymandering based on statistical sampling and outlier analysis and gives her take based on her reading of the text of the entire ruling.

“In this week’s decision, Justice Roberts basically threw up his hands and declared that the search for a manageable judicial standard for measuring gerrymandering is hopeless, and therefore such claims will no longer be considered justiciable in federal courts. He seemed not to clearly understand the mathematical argument; he repeatedly referred to the proposed outlier analysis as attempting to measure deviation from proportional representation, which it absolutely does NOT do. More significantly, he opined that it was not the Court’s business to decide how much deviation was permissible, and that therefore the entire question should be left up to the states and to Congress,” Clelland wrote.

“In Justice Kagan’s scathing dissent, on the other hand, she made it clear that she understands the math and believes that it could and should form the basis for a judicial standard. She did not attempt to set a clear threshold for how much deviation from the mean should be permissible, but she thinks that in the North Carolina and Maryland cases at hand – both of which are way out on the tails of their respective bell curves – the Court should say, ‘This much is DEFINITELY too much.’ Then it would be up to future litigation, legislation, etc. to work out the question of where to set limits on how much deviation from the mean is permissible, similar to the process that has played out for racial gerrymandering,” Clelland added.

What now?

Sam Wang, a professor of neuroscience and molecular biology at Princeton University and founder of the Princeton Gerrymandering Project, wrote the New York Times opinion piece If the Supreme Court Won’t Prevent Gerrymandering, Who Will?”

“Progressives have long looked to federal courts to guard the rights of racial minorities and dissenters. But that protection is weakening. Faced with the enormous injustice of partisan gerrymandering, the Supreme Court last month permitted politicians drawing election district maps to discriminate by party and even potentially mask their racial “packing” and “cracking” as mere partisanship. To fill this growing gap, reformers should take an unexpected route: states’ rights,” Wang states at the beginning of his piece.

Throughout the remainder of his piece, Wang outlines the details of that approach. Towards the end of it, he states, “Putting all federalist routes together — courts, voter initiatives, laws and elections — I estimate that reform is actually possible in the vast majority of states, even without the Supreme Court’s help.”

Wang closes with some analogies: “In biological systems, my other area of expertise, self-correction prevents living systems from going off-kilter. If we don’t sweat, we overheat. When cells disregard the boundaries of the organ where they belong, the result is cancer. So too in democracy: Without a mechanism to ensure fair districts, a political party can ensconce itself in power indefinitely. By introducing self-correction mechanisms, we can reverse the erosion of faith in democracy that comes from gerrymandering.”

The blog for the Princeton Gerrymandering Project has numerous resources, including a U.S. map with a state-by-state assessment of “the best route to reform.”

Posted in Current Events, Math Communication | Tagged , , , , , , , , , | Leave a comment

Mathematical Resilience

The MAA and AMS recently co-published “Living Proof: Stories of Resilience Along the Mathematical Journey” and the e-book is free to download here. The book was edited by Allison K. Henrich, a mathematician at Seattle University, Emille D. Lawrence, a mathematician at the University of San Francisco and editor-in-chief of the Math Mamas blog, Matthew A. Pons, a mathematician at North Central College in Naperville, Illinois and David G. Taylor, a mathematician at Roanoke College in Salem, Virginia.

Each chapter is written by a different contributor. The chapters are organized into four sections “organized around common themes in the experiences. Part I is about math getting hard and people hitting a wall. Part II is about struggling to belong in math (and is particularly well aligned with the goals of this blog). Part III is about persevering through and overcoming difficulties. And Part IV is about the sometimes challenge of integrating our mathematical identities with the rest of our lives,” Brian Katz wrote for the inclusion/exclusion blog.

“As you read this, we hope that you will find some inspiration and common ground in these pages. We trust that there is at least one story here that you can connect with. For those stories that you cannot relate to, we hope that you will come to better appreciate the diversity of our mathematical community and the challenges that others have faced. We also hope that you will laugh with some of our authors as they recount some of the more absurd struggles they have faced. In the end, we hope that you are motivated to share your own stories as you learn more about the experiences of the people in your own mathematical lives,” the book’s editors wrote in the preface.

Some of the chapter authors are also math bloggers. Here are some highlights about a few of the chapters:

8: “Hitting the Wall” by Laura Taalman

“Math was easy for me, until suddenly it wasn’t. I suspect this is a transition that many people go through,” wrote Laura Taalman, who is a mathematician at James Madison University in Harrisonburg, Virginia. In this chapter, she describes an honors calculus sequence that was a “real shock” to her, in which she “easily had to work ten times as hard as everyone else in the class.” Yet, Taalman wrote:

“Having to work so hard that semester and develop a thick skin for feeling stupid all the time in a math course really helped me in my career. I don’t think mathematics was ever ‘easy’’ for me again after I got to college; it was always a struggle…But at each step, it was a struggle that I loved working through. I didn’t mind being stuck and feeling dumb. I knew I could get through it if I kept plugging away. In today’s language, I would say that I was lucky to have formed a ‘growth mindset’’’about learning math—I was willing to work on hard problems to find success—rather than a ‘fixed mindset,’ where I judged myself harshly when I didn’t know something. To this day, I still benefit from this mindset, and I’ve basically made a career out of trying new things that I don’t know anything about. It’s in the process of making mistakes and figuring out how to make progress where the real fun begins.”

Taalman writes about “design, math, and failure” on her “Hacktastic” blog.

30: “A Close Call How a Near Failure Propelled Me to Succeed” by Terence Tao

Terence Tao wrote about how his lack of systematic study habits and habit of “improvising” his way through homework and exams, almost made him fail his “‘generals’ — the oral qualifying exams, often lasting over two hours, that one would take in front of three faculty members” in his graduate studies at Princeton University until he “was saved by a stroke of pure luck.” His original write-up about his generals is still available online here.

Tao is a mathematician at UCLA and on his blog, he shares “updates on my research and expository papers, discussion of open problems, and other maths-related topics.

27: “Just Don’t Bomb the GRE” by Amanda Ruiz

Amanda Ruiz wrote about her experience with studying for and taking the GRE. “Every time I opened that GRE study book, I felt like an impostor. It made me feel stupid. It didn’t value my kind of smart. So, I devalued it the same way it devalued me,” she wrote. She subsequently “bombed the GRE,” which put her dream school out of reach.

“If I had been at my ‘dream school,’ it is unlikely that I would have been able to continue to work towards my PhD or, at the very least, finish in a timely manner while caring for my daughter. If I had gone to my dream school, my career trajectory would look different, and I would not have allowed myself to start a family until after tenure, which would have been biologically too late for me. So maybe, in a weird way, bombing that GRE was exactly what needed to happen,” Ruiz wrote.

Ruiz, who is a mathematician at the University of San Diego, is also an editor of the Math Mamas blog.

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Planet Math

This is what Boston looks like with a 6 ft rise in sea level, which some experts have declared “physically plausible” in the next century. Image via coast.noaa.gov.

I was recently talking to a friend of mine about real estate. In particular, he was interested in buying a beautiful house on a beautiful street with bright new siding and a shiny array of solar panels. We had the usual conversation that one has with a friend buying a house: trends in the market, accessibility by public transit, distance to the riverfront jogging path and whether or not the backyard was big enough to play croquet. And then the conversation took a turn that felt very particular to the times. He pulled up a map of the 100-year flood forecast of the area and began weighing the likelihood of his croquet pitch being underwater before the term of his 30 year mortgage.

Our planet is very vulnerable. This is a well known fact. But besides eating a plant-based diet, ditching your car, and having fewer kids, there are the big pushes in math and science that need to be made to really make a change.

For a wealth of information about the math of our teetering ecological crisis, an excellent resource in the #MTBoS is the work of mathematical physicist John Carlos Baez, who you should definitely follow on Twitter. Baez is a big time contributor to The Azimuth Project which is a forum for STEM-type folks to share information about topics pertinent to the threats to our global ecology, and Baez also writes the Azimuth blog.

How to reduce your contribution to climate change, via Phys.org.

Like with most things in the world, it’s relatively easy to nod in vigorous agreement when someone suggests that mathematicians have a lot they can contribute to our fight to save the planet, but for many people it can be hard to imagine just why or how (other than gathering lots of data and making graphs that are totally scary). But The Azimuth Project very handily connects the dots between mathematics/engineering and important topics in ecological science like sustainable energy and geoengineering.

The Azimuth Project shows that there’s a lot to be done, and they say “we need to do it now, because people don’t always get better at optimizing their collective behavior when things get worse.” Ugh. True. “When people are struggling to survive, they often do things like start wars. And then we’ll wish we’d taken action sooner.”

Perhaps you don’t feel in a position to develop the next big breakthrough in carbon sequestration — although I’d urge you to try! — but at the very least we are all capable of informing ourselves and our friends and students.

If you are interested in learning about more applications, you might consider joining SIAM’s activity group on Mathematics of Planet Earth, which exists “to provide a forum for mathematicians and computational scientists to study Planet Earth, its life-supporting capacity, and the impact of human activities.”

When I tweeted out a request for information on mathematicians studying sustainable energy last week I also got so many more recommendations of people doing cool things. Like Julie Lundquist studying the impacts of wind energy, or Ellen Webborn studying energy usage through smart meter data, or the Porous Media Group who study the math of geothermal energy and subsurface energy storage.

If you have more resources you’d like to share, and if you have any photos of cool looking leaves, you can tweet them at me @extremefriday. Enjoy the outdoors this summer!

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