Á​lvaro Lozano-Robledo’s Field Guide to Mathematics

Álvaro Lozano-Robledo standing on a rock at the Grand Canyon

Álvaro Lozano-Robledo at the Grand Canyon. His new blog is A Field Guide to Mathematics. Credit: Marisa Gioioso.

A Field Guide to Mathematics is a blog by Álvaro Lozano-Robledo, an associate professor of mathematics at the University of Connecticut. He launched the blog this February. It focuses on “stories about mathematics, students, professors, mathematicians, abstract nonsense, research, papers, publishing, and academia,” according to its description.

In an interview conducted over email, Lozano-Robledo answered questions about the blog. (The following interview has been lightly edited for length and clarity.)

Rachel Crowell: What inspired you to start a math blog?

Álvaro Lozano-Robledo: I’ve always loved writing stories, since I was a kid. Years ago (pre-tenure-track!) I wrote a bunch of stories – some in English, some in Spanish – that mixed fiction, reality and my own experiences. I submitted some of them to contests in Spain. You can find them here. Some of the stories were published in books about stories about mathematics (see https://www.rsme.es/2009/05/un-teorema-en-la-biblioteca-de-varios-autores-ed-anaya-y-rsme-2009/ and https://www.rsme.es/2008/10/sobre-numeros-y-letras-de-varios-autores-ed-anaya-y-rsme-2007/).

From time to time, people have liked my stories that they have found on my website (mostly “The Importance of Being Bounded,” since it is in English) and  have asked if I would write more. I always said “Yes, some day when I have more time.” Well, now in confinement and distancing mode, I have found more time to write.

Recently, I decided to share the stories I am writing in a blog that may be more accessible to people and enter the “blogsphere” to connect with other people writing blogs and writing about math.

RC: On your blog, you describe it as “stories about mathematics, students, professors, mathematicians, abstract nonsense, research, papers, publishing, and academia.” That is a pretty broad set of topics. Is there anything more you would like to share about the types of pieces readers can expect to find on your blog in coming months?

ALR: Sure! My goal is to write about mathematics from a mathematician’s point of view, but not about technical topics. Rather, I’m hoping to write about what it means to be a mathematician, in a way that both mathematicians and non-mathematicians can enjoy and relate to. I’m not sure if I’m achieving my goal, but that’s the focus! For now, I’m just writing the stories that I feel like writing at the moment and those that I am ready to share now.

However, I do have a more global view of the collection of stories that I’d like to put together. They span the entire life of a mathematician, from undergrad, grad school, postdocs, tenure-track to a tenured/permanent position, and include topics about learning math, doing research, discovery, failure, publishing, etc.

In addition to the main theme of the blog, I’d like to include “interludes” of fiction that are written for the sake of writing and entertainment.

RC: What do you envision as the target audience for your blog?

ALR: Continuing with the narrative of the previous answer, I have two audiences in mind.

I’d like to reach non-mathematicians that are curious about what a mathematician does, and how a mathematician works on proving theorems.

I’d also like to reach mathematicians, particularly “mathematicians in training,” who may want to read stories from the point of view of a more senior mathematician. I’m hoping they will relate to these stories or learn useful information about, say, what it’s like to be tenured or what it’s like to be a working mathematician and a parent in a household where both parents work and split childcare evenly. I hope the ‘realism’ in the writing helps people understand that we all struggle sometimes, that we have all gone through tough times and happy times during our careers and that almost all of us fight impostor syndrome.

RC: Other than your own blog, what are some of your favorite math blogs and why?

ALR: I am actually quite interested in the Blog on Math Blogs, because I keep finding out about blogs I didn’t know about or reminding myself of blogs I have not checked out lately. The blog by Matt Baker is excellent. Lately, I’ve been obsessed with Not Even Wrong, particularly the post on the abc conjecture with what I consider the most important comment section in the history of blogs and comment sections! The back and forth between Taylor Dupuy and Peter Scholze is especially gripping.

I also follow the AMS inclusion/exclusion blog, because I learn so much and I feel that I need to keep reading what they write in that blog to be a better member of the community. It is just very important stuff and they are doing a great job covering these very difficult topics. On a related topic, “Alice’s Adventures in Number Land” is an incredible set of stories that are so eye-opening that anyone who is in the business of math should be reading very carefully. After every entry, I am like, “wow.”

I love Jordan Ellenberg’s “Quomodocumque” blog, because I love his style of writing, his ideas and the way he thinks about things.

Now that I have a blog, I am discovering other blogs that I like. For example, I found Anthony Bonato’s recent entry on the pandemic so inspiring that I changed plans for my latest entry and spent a huge amount of time recreating my last 60 days of social isolation in one of my entries in my blog (the Logbook entry).

RC: Out of the posts you have written so far, which one is your favorite and why?

ALR: That’s like asking who is your favorite child! Ha ha. At the risk of hurting the feelings of my other entries, I have to go with the post about Quijote. “El Quijote” is my favorite book of all times, and the only non-math book that I have read more than once. In fact I’ve read it many times. And I had so much fun writing that entry, because I read a bunch of chapters from the Quijote once again, first in Spanish, and then in English, so that I could learn from a translation how the more archaic Spanish had been translated into English. Anyway, I do not expect most people to love that piece, but if anything, I hope it drives some mathematicians to read El Quijote, because it is so much fun, and so incredibly clever, that it is just amazing.

Quijote entry excluded, I think my other favorite piece was the “Love Letter to Birders,” which the reader may surmise is more of a love letter to my brother than anything else. The piece explores the connection of doing research in very specialized fields. I think it’s something that many scientists can relate to: when our passion is misunderstood by a large amount of the population, even our friends.

RC: Are there any suggestions or resources you would like to share with people who are considering starting their own blogs or who have just started one?

ALR: I would love to see more writing by mathematicians! Go ahead and write! It doesn’t need to be a technical piece. I’d love to read more about personal experiences. I’d love to see our field being more humanized.

Want to share feedback or ideas for future blog posts? Reach us in the comments or on Twitter (@writesRCrowell)!

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Bastian Rieck’s Blog: A Tour

Dr. Bastian Rieck is a senior assistant in the Machine Learning & Computational Biology Lab of Prof. Dr. Karsten Borgwardt at ETH Zürich. He is interested in understanding complex data sets and topology-based machine learning methods in biomedical contexts. Especially, those related to developing tools for personalized medicine.

In his blog, which has been active since 2006, he shares his musings on interesting topics related to programming, his research interests and projects, and many “how-to” posts. What I like about this blog is that it has a very nice balance between sharing the experience of being an academic, providing advice for other researches, and diving into topics related to machine learning and programming. In this tour, I’ll give you a glimpse of some of his most recent posts.

The Power of Admitting Ignorance 

In this post, Rieck shares the story of his experience as an undergrad taking an advanced mathematics course. He describes what I feel many of us have experienced at some point in our careers in which you wonder how your knowledge stacks up with that of your peers. In this class, he found himself in awe of his peers which seemed to understand all the concepts quickly even when they were introduced. This led to feeling increasingly out of place. He then recalls how his professor, by being honest about his limited knowledge on a subject, really changed his perspective. In a footnote, he even highlights how this particular interaction became a changing point in his career!

“There is a power in being as honest and outspoken as Prof. Kreck was. Here is this proficient and prolific member of THEM, and he could have just made up something on the spot to make me feel dumb. Instead, he chose the intellectually honest option, and made it clear that this is the normal state of affairs in mathematics (or any sufficiently complicated topic). I relish the fact that such a small action could have such a profound impact on one person, and I am grateful that I dared pose my question.

In the years since, in my own dealings with researchers, I never once feigned knowledge when I was not feeling sufficiently confident about it. I think it is important to be honest about what you know and what you do not know. Ignorance is not a moral blemish—pretending to be smarter than you are is (just as choosing to remain in a state of ignorance is).

So the moral of this story is: do not be afraid of not knowing or not understanding something.”

Similarly, I appreciated his honesty in describing this experience. It made me reflect on similar instances in my career and how, by being vulnerable when we don’t understand something, we can humanize ourselves to our students and peers.

Machine Learning Needs a Langlands Programme

This post caught my attention with the beautiful illustration of ‘The Land of Middle Math” (see Figure 1) by Prof. Dr. Franka Miriam Brückler. In this post, he argues that machine learning as an ever growing-field would benefit from having a structure of  communicating among its different branches. Especially, since this can be a difficult task even though the branches share commonalities.  He discusses some solutions including creating something similar to the Langlands Programme, which aims to study the connections between number theory and geometry. I love his analogy where he describes the program as the ‘Rosetta Stone’ for mathematics.

“The individual branches of mathematics are represented as different columns on the stone. Each statement and each theorem have their counterpart in another domain. The beauty of this is that, if I have a certain problem that I cannot solve in one domain, I just translate it to another one! André Weil discussed this analogy in a letter to his sister, and his work is a fascinating example of using parts of the mathematical Rosetta Stone to prove theorems.”

Figure 1: The land of Middle Math drawn by Prof. Dr. Franka Miriam Brückler. Obtained from blog post.

He argues, that the main benefit of a program like this would be to make as many connections among results in different fields to avoid in a sense over specializing in the tools that as researchers are created.

“The classical way of writing a machine learning paper is to present a novel solution to a specific problem. We want to say ‘Look, we are able to do things now that we could not do before!’, such as the aforementioned learning on sets. This is highly relevant, but we must not forget that we should also look at how our novel approach is connected to the field. Does it maybe permit generalising statements? Does it shed some light on a problem that was poorly understood before? If we never explore the links, we risk making ourselves into toolmakers with too many bits and pieces. Looking for the general instead of the specific is the key to avoid this—and this is why machine learning needs its own version of the Langlands programme. It does not have to be so ambitious or far-reaching, but it should be a motivation for us to investigate outside our respective niche.”

The Power of Defaults 

In this post, Rieck highlights how similar the choices designers make in creating an installation script for a program, researchers who develop packages also make are. In particular, the dangers of providing misleading parameters or defaults to users.

“It dawned on me at some point that we, i.e. researchers that develop a software package in addition to their research, are doing precisely the same thing. We create a software tool for solving a certain problem. It might be an itch that we want to scratch, or it might be software that is related to our research—in the end, we all write some code in some language to produce some kind of value. How often do we think about the dangers of the API that we are exposing, though?”

I found this post super helpful in talking to my students in my machine learning class about important considerations when training a model. Many machine learning models are implemented in the Python library scikit-learn and come with a set of defaults that when misunderstood or misused could lead you to draw incorrect conclusions. For example, he discusses that by default when training a Logistic Regression model, one may choose to alter how the algorithm changes the model to improve its performance on a new data point by using a technique called regularization. However, applying this technique to the data should be the user’s choice and could affect the reproducibility of results.

“In the worst case, it might trick users into believing that they did not employ regularisation when in fact they did: when comparing to other methods in a publication, it is common practice to report the parameters that one selected for a classifier. A somewhat hidden assumption on the model can be very problematic for the reproducibility of a paper.”

He ends by discussing the benefits of having parameter defaults (and that by no means they should be removed!) and provides tips on how to address setting default parameters for complex algorithms.

Do you have suggestions of topics or blogs you would like us to consider covering in upcoming posts? Resources to share? Reach out to us in the comments below or let us know on Twitter (@MissVRiveraQ)

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Math on the Dynamic Ecology Blog

Dynamic Ecology is a group blog by Jeremy Fox, an ecologist and evolutionary biologist at the University of Calgary, Brian McGill, a macroecologist at the University of Maine. and Meghan Duffy, an aquatic and disease ecologist at the University of Michigan. Invited guest posts are also occasionally published on the blog.

“We post ideas, opinions, commentary, advice, and humor that we think might be of interest to our fellow academic ecologists and ecology students,” the bloggers note. While the blog itself isn’t math-themed, there are many posts on the blog discussing math topics or ones that are relevant to folks working in a variety of STEM fields. Here are just a few interesting posts from the blog.

“Poll results: How mathy are ecology, evolution, and genetics?”

Duffy wrote this post in 2017, but it’s still informative. Three groups of people — 271 introductory biology students (at the beginning of the semester), 349 readers of the blog, and, more specifically, 225 readers of the blog who identified as ecologists — were polled about how much math they thought geneticists, ecologists and evolutionary biologists use in their work. Duffy shared the following results:

  • 75% of incoming Intro Bio students think geneticists use a “moderate” or “substantial” amount of math. But only 33% think ecologists do.”
  • 64.7% of Dynamic Ecology poll respondents think geneticists use a “moderate” or “substantial” amount of math. 78.5% think ecologists do.”
  • 80% of DE poll respondents who identified as ecologists said they use a “moderate” or “substantial” amount of math.”

“In other words: there is a really big difference between the amount of math that students just starting Intro Bio think ecology will involve vs. how much ecologists say it involves,” Duffy wrote.

“I’ve been thinking about how I will talk about this with students. I think that, at the start of the population ecology lecture, I will tell them that there’s something that often surprises students: ecology involves math. I will note that most people haven’t been exposed to ecology before taking the course – it was certainly true for me that I never thought about ecology before getting to college. I think that, as a first year college student, I didn’t really know what ecology was, but probably had a vague sense that it was what you see in the nature videos on PBS. It definitely did not occur to me that it involved math…My hope with this is not to scare [the students], but to better prepare them for what is coming,” Duffy added.

I also enjoyed reading the comments on this blog post. For instance, commenter Art Weis wrote:

When I teach Ecology, the first words out of my mouth are always the ecology in at it core a quantitative science. Each and every aspect of ecology can be boiled down to the question “under what conditions does the net reproductive rate of a population exceed 1.0, and what are the conditions where it doesn’t. Similarly, in the evolution course, the most basic question is when does the net replication rate of a locus exceed 1.0.? In any particular case the answer can be due to deterministic or stochastic processes, but, the key question is greater than or less than 1.0.

This post also left me wondering what can be done from the math instruction side of things to inform more students about connections between ecology and math.

“What math should ecologists teach”

This 2014 post by McGill builds on Fox’s “What should ecologists learn LESS of?” post (in which asked readers to “name the one thing you think it’s most important for ecologists to learn more of, and the one thing you think ecologists should learn less of, in order to free up time for them to learn more of whatever it is you think they should learn more of”).

“More math skills was a common answer of what should be prioritized,” wrote McGill, who notes in his post that his bachelor’s degree is in math. McGill then shares his thoughts on bridging the gap between the math he thinks ecologists should know and the offerings that are available to them through many university math departments:

I often get asked by earnest graduate students what math courses they should take if they want to add to their math skills. My usual answer is nothing – the way math departments teach math is very inefficient for ecologists, you should teach yourself. But its not a great answer.

He explains that a student would usually have to take “7 courses over and above 1st year calculus to get to all the material” he thinks “a well-trained mathematical ecologist needs!” His phrasing comes across as a bit strong to me in certain sections (such as this sentence: “This is an extraordinary waste of time since over half of what is taught in those classes is pretty much useless in ecology even if you’re pursuing deep into theory”). However, I think his overall message —  that the current math offerings aren’t meeting the needs of ecology students — merits consideration and brainstorming about how to enact changes that will benefit these students.

McGill closes out the piece by listing the topics he thinks well-trained mathematical ecologists need to know and discussing different options for delivering instruction on those topics. One alternative that I don’t see listed but that I wish universities would consider? Interdisciplinary courses co-taught by ecologists and mathematicians. I understand that could come with significant logistical challenges, but I think that if departments could make it work, it would be a great option for students. The post also drew (as of this writing) 44 comments from readers, which also enhance the discussion.

“Guest post: What if my hobby — what I do for ‘fun’ — is being a workaholic?”

Now, as much as ever, many of us are seeing the lines between our work and home lives blur. In this post, guest writer Greg Crowther, a biology instructor at Everett Community College in Washington, wrote about his decision to pursue therapy:

“Again and again, I devote unusually large amounts of time to certain work-related tasks, leaving less time for sleep, exercise, family, friends, and so on. You name it, I’m neglecting it (at least intermittently). If this lament sounds like a humblebrag, well, I don’t mean it as such.  I don’t like the health-neglecting, people-neglecting version of myself, and I’m about to get professional help.”

In the comments section, readers share many helpful experiences and insights about workaholism and pursuing their passions while also tending to their mental and physical health.

A four part “Mathematical constraints in ecology” series was also posted on the blog. It seems worth a read (although I’ll admit that I’m still working my way through it).

Want to reach out to us? Please leave a comment below or connect with us on Twitter (@writesRCrowell).

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Matt Baker’s Math Blog: A Tour

This week I dived into the math blogosphere and found this cool blog Matt Baker’s Math Blog by Dr. Matt Baker,  a professor, and Associate Dean at Georgia Tech School of Mathematics.  This blog was featured back in 2013 in Evelyn’s post “How Quadratic Reciprocity Is Like Dealing Cards“. There she talks about a blog post in which Baker uses a deck of cards to describe quadratic reciprocity, a theorem in modular arithmetic that gives condition for when it’s possible to solve a quadratic equation modulo prime numbers. What caught my attention about this blog is that it has been active since 2013 and covers a wide breadth of topics including but not limited to “number theory, graphs, dynamical systems, tropical geometry, pedagogy, puzzles, and the p-adics”. As described in the about me page by Baker himself,

“Many of my recent papers are kind of long, and I’m hoping to post overviews of what’s in them and why a person might hypothetically care.  I also want to post some new perspectives on older papers of mine, for example streamlined proofs or links to related work.  The blog won’t be just about my own work, though: I also want to highlight recent preprints that I find exciting and share my thoughts on them.  In addition, I hope to revive some old chestnuts from the past which I think deserve to be better known.  I also want to share some thoughts about teaching in the 21st century with the hope of starting interesting and/or valuable dialogues.  Finally, I hope to share some of the simple joys I find in math problems with beautiful solutions or things that are just plain fun.  So hopefully there will be something for everyone in this blog — well, not everyone but you know what I mean.”

In this post, I will give a glimpse of some of his most recent posts.

Mental Math and Calendar Calculations

In this post, Baker talks about the many different systems to mentally calculate the day of the week on any given date. He reflects on a discussion he had with John Conway, about the pros and cons of these systems. Here he covers two systems, the Gauss-Zeller algorithm (i.e. Day of the Week = Month code + Day + Year Code + Century Adjustment (modulo 7)). and Conway’s Doomsday Method (i.e. Day of the week for Doomsday = Year Code + Century Adjustment (modulo 7)).  Both these methods rely on encoding the year and century adjustment of the date. As he mentions, calculating the year code is one of the most intensive aspects of these methods and provides alternatives to speed up the calculations such as the Lewis Carroll’s method, Mike Walters’s “Easy Doomsday” method, The “Odd + 11” method which he describes in detail. What I enjoyed the most about this post were the many examples to practice mental calculations and the detailed explanations of each method.

Colorings and embeddings of Graphs

As a tribute to colleague and friend Robin Thomas who passed away last March from Amyotrophic lateral sclerosis (ALS). In this post, Baker shares some personal remarks about his friendship with Thomas and two of his most famous theorems. This post gives a glimpse of Robin Thomas beyond his math which I deeply appreciated and it’s a great way to remember him by. The first theorem he tackles is Thomas, Robertson and Seymour’s 1993  proof of the Hadwiger’s conjecture, which is a generalization of the four-color theorem, for graphs without a $K_6$-minor. The second theorem which he highlights is their classification of the forbidden minors for linklessly embeddable graphs. He states, “a graph is called intrinsically linked if every embedding in $\Bbb R^3$ contains a pair of linked cycles, and linklessly embeddable otherwise.”  In this description of the theorem, he explains that the Petersen family of graphs that are intrinsically linked provides a link (pun intended) between a connection the minors of a graph and a graph being linklessly embeddable. Mainly, he states that “the theorem of Robertson-Seymour-Thomas asserts, conversely, that a graph with no minor belonging to the Petersen family is linklessly embeddable.”

Figure. The 7 intrinsically linked graphs in the Petersen family. Illustration by David Eppstein. Obtained from: Colorings and embeddings of Graphs.

As a parting thought, he remarks,

“Of course, I’ve barely scratched the surface here, both in terms of Robin Thomas’s contributions to mathematics (he published over 115 papers from 1984 to 2019) and on the subjects of graph colorings and graph embeddings. But I hope this little panoply helps highlight some of the marvelous contributions of Robin Thomas (and John Conway) to the subject.”

The Balanced Centrifuge Problem

I enjoyed reading this 2018 blog post with a neat biological application. Baker recounts chatting with a cancer researcher, Iswar Hariharan, and learning about an interesting problem he had been thinking about for a while. Centrifuges, a laboratory device that separates liquids by density by spinning test tubes, must be balanced to avoid being damaged. In this context, balanced means that “the center of mass of the collection of test tubes coincides with the center of mass of the centrifuge itself”. He poses the following question,

“If you spend a lot of time balancing centrifuges and have a mathematically curious mind, the following question might naturally arise: For which pairs (n,k) with 1 ≤ k ≤ n can you find a way to balance k identical test tubes in an n-hole centrifuge?”

Throughout the post, he provides the details on some special cases of configurations of test tubes, discusses Iswar’s conjecture which states that “you can balance k identical test tubes, 1 ≤ k ≤ n, in an n-hole centrifuge if and only if both k and n-k can be expressed as a sum of prime divisors of n”. Curiously, by translating the question into a problem about linear relations between roots of unity he found it was proven in 2010 by Gary Sivek.

He is also a mathemagician and author of ‘The Buena Vista Shuffle Club’, a book dedicated to magic tricks.  I took a look at the introduction and found a great description of his magic.

“My magic tends to appeal more to the mind than to the eyes. It’s primarily card magic, frequently with some kind of mathematical principle happening in the background. But I try not to limit myself by viewing these general characteristics as constraints; on the contrary, I’m constantly testing boundaries4 to see if I can challenge myself with something unfamiliar. If you’re willing to come along for the journey, I hope you’ll enjoy the diversity of effects and methods which you’ll find in these pages.”

As he mentions in the article ‘The Magic of Math’: “There’s a lot of math in card magic,” he said. “Just like with a recipe, you might be able to follow the recipe and execute it, but you may not know enough about how it works to vary it. With card magic, I know enough to be able to combine principles in new ways and jazz around with existing effects.” Many times mathematics has seemed truly magical to me. Through his blog or his magic, Baker takes us through a pretty neat journey of mathematical discovery.

Do you have suggestions of topics or blogs you would like us to consider covering in upcoming posts? Resources to share? Reach out to us in the comments below or let us know on Twitter (@MissVRiveraQ)


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Marilyn Burns’s Math Blog: A Tour

Marilyn Burns’s math blog has been around since 2015. Her posts cover a wide range of topics, including math games (some of which appeal to kids and adults alike), teacher resources, math and children’s literature, and more. Please join me on a tour of just a few interesting posts on her blog that might be fun or useful to engage with, especially while staying at home during these unprecedented times.

“What’s the Longest Number String Possible?”

Burns explains how to play the “Factors and Multiples” game. It’s supposedly for kids ages 7 to 16, but I found it fun enough to play several rounds myself. It’s designed for two players, but I found the online, interactive version enjoyable even when I was playing against myself. Players are given bubbles with positive integers between 1 and 100 written on them. The first player chooses an even number less than 50 from the group to start the string. The next player must then choose a number that is either a factor or a multiple of the first number to continue the string. Play continues in this manner until one of the players is unable to find a number that can be used to continue the string. That player loses.

The game is hosted on the University of Cambridge’s NRICH website. The NRICH project “aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice,” according to its website, which contains other games, projects and resources (for teachers and students) sorted by age/academic level.

“What Are Good Math Questions to Ask Students?”

I often think about how the quality of math questions impacts students — for better or worse. In this post, Burns reviews three components of good math questions presented in the book “Good Questions for Math Teaching: Why Ask Them and What to Ask, K–6″ by Peter Sullivan and Pat Lilburn.

“These features sing to me. Good questions require more than remembering a fact or reproducing a skill. It’s possible for students to learn by answering the question. There may be several acceptable answers,” Burns wrote.

She then shares some of the sample questions from the book, along with the rationale behind them and tips for tweaking them to meet different students’ needs. She also points out that there is a companion book focused on questions for middle school students.

“Race for 20―A Counting Game for All Ages”

In this post, Burns presents a simple game (along with variations) that can engage people of all ages. “Race for 20” seems like a great game to play with family, especially since many of us are now spending extended time periods at home. There are only three rules in the basic version.

  1. Choose who will start and then take turns.
  2. Starting at 0, when it’s someone’s turn, they can add 1 or 2 positive numbers to the string of numbers. For instance, if the first players says “1,” the second player would say either “1, 2” or “1, 2, 3.”
  3. Whichever player gets to the number 20 wins.

Burns presents options for making the game more accessible to kids who are still learning how to count to 20, ways to make the game more concrete and more. At the end of her post, she shares connections between the game and game theory.

Race for 20 fits into the category of the game of Nim. For more information, there’s lots online. Here’s a definition of Game Theory that I’ve cobbled together from a slew of online choices: Game theory is the study of how and why people make decisions. It is the branch of mathematics concerned with the analysis of strategies for dealing with competitive situations where the outcome of a participant’s choice of action depends critically on the actions of other participants. Game theory has been applied to contexts in economics, business, and biology,” she wrote.

“Using Math Menus: Some Nuts & Bolts”

In an Educational Leadership piece on the “Math Solutions” website, Burns explains what math menus are and how they can be used in classrooms. “A math menu is a list of math options posted for all to see. The options can include problems, investigations, games, and other activities that promote students’ understanding, support their reasoning, or provide practice with the content and skills they’ve been learning,” Burns wrote in the Educational Leadership piece. The approach also seems like it would be helpful to parents who are currently educating their kids at home due to the pandemic and are looking for additional ways to supplement their instruction.

She explains that these menus can be used to respond to three big questions from teachers: “What can I do with students who finish their math assignments more quickly?” “How can I free up time to work with students who need extra help?” and “How can I differentiate experiences to support struggling learners while also meeting the needs of students who need additional challenges?”

In her blog post, Burns describes how she responded to some questions about the approach posed by Jill Downing, a Title 1 Educator with the Helena Public Schools in Montana. Burns also shares some of the written responses students have shared about their experiences with math menus.

Want to share an idea with us? Reach out in the comments below or on Twitter (@writesRCrowell)!

Posted in Blogs, Book/App, Current Events, Game Theory, Interactive, K-12 Mathematics, Math Education, Recreational Mathematics | Tagged , , , , | Comments Off on Marilyn Burns’s Math Blog: A Tour

Junk Charts: A Tour

Kaiser Fung’s “Junk Charts” blog is full of treasures, including ones related to the COVID-19 pandemic. Evelyn wrote a post about the blog back in 2017. Please join me on a tour of a few of the posts Fung has written since then.

Pandemic-related posts

This exercise plan for your lock-down work-out is inspired by Venn”

This post includes a Venn diagram with so many compartments that it’s a bit dizzying. The chart came from a Nature article and it’s supposed to show symptoms that users of a UK app reported after testing positive for COVID-19.

It “fails the self-sufficiency test because if you remove the data from it, you end up with a data container – like a world map showing country boundaries and no data,” Fung wrote, adding “If you’re new here: if a graphic requires the entire dataset to be printed on it for comprehension, then the visual elements of the graphic are not doing any work. The graphic cannot stand on its own.”

“The numbers on this graphic add to 1,764 whereas the study population in the preprint was 1,702,” Fung noted. He then comments on the struggle of trying to interpret the information the chart is supposed to convey:

“The chart also strains the reader. Take the number 18, right in the middle. What combination of symptoms did these 18 people experience? You have to figure out the layers sitting beneath the number. You see dark blue, light blue, orange. If you blink, you might miss the gray at the bottom. Then you have to flip your eyes up to the legend to map these colors to diarrhoea, shortness of breath, anosmia, and fatigue. Oops, I missed the yellow, which is the cough. To be sure, you look at the remaining categories to see where they stand – I’ve named all of them except fever. The number 18 lies outside fever so this compartment represents everything except fever.”

 “When the visual runs away from the data” and “Make your color legend better with one simple rule” 

Both of these posts are related to the same pie chart, which is supposed to show survey respondents’ biggest worries about COVID-19. The options were “getting it,” “family getting it” and “the economy.”

In the first post, Fung removed the data from the chart in order to look at how much information the chart actually gives by itself. He calls this exercise a “self-sufficiency test.”

“The idea of self-sufficiency is to test how much work the visual elements of the graphic are doing to convey its message,” he noted. He explains that each of the slices of the pie chart don’t accurately represent the amounts they are supposed to (for instance, “the economy” slice takes up 38% of the pie, but 68% of people responded that the economy was their biggest worry). Furthermore, the data for the three categories add up to 178%, making a pie chart a confusing way of conveying this information. Fung recommends using a bar chart instead.

In the second post, Fung uses the chart to show “why we should follow a basic rule of constructing color legends: order the categories in the way you expect readers to encounter them.” He then recommends re-ordering the legend to better fit the order in which people will likely view the categories.

Other posts

“Too many colors on a chart is bad, but why?”

I usually enjoy colorful charts and graphics, but I agree with Fung here:

“The reason why the coloring scheme backfires is that readers may look for meaning in the colors. What’s common between Iceland, United States and Germany for them to be assigned green? What about Japan, New Zealand, Spain and France, all of which shown yellow? The readers’ instinct is driven by a set of unspoken rules that govern the production of data visualization.

Specifically, the rule here is: color differences reflect data differences. When such a rule is violated, the reader is misled and confused.”

“This Excel chart looks standard but gets everything wrong”

Fung dissects a chart that seems to show global car sales by region. However, he points out that there are at least four major problems with it.

Have an idea we should cover in a future post? Reach out in the comments below or on Twitter (@writesRCrowell).

Posted in Current Events, Data Science, Math Communication, Visualizations | Tagged , , , , , , | 2 Comments

Math in the time of COVID-19

In the past few posts, I’ve been avoiding writing about the current Coronavirus outbreak. Honestly, I’ve been having a hard time coping with the uncertainty and worry about how we are going to survive and move forward from this. Around the blogosphere, there has been an overwhelming amount of post talking about exponential growth, pedagogical tools as we transition to distance learning, ways to keep connected, to keep the research going, to keep moving forward.

I stopped to reflect on what math means at a time like this and came up with many different answers. But the biggest themes of all were empathy, kindness, and a lot of flexibility. For many, this period will be one of collective grieving. During this time some seek to ground themselves with math, others seek to distance themselves from it, both responses should be expected and welcomed as we face this unprecedented challenge. In this post, I want to share a compilation of some of the math-related resources that I’ve found to help me navigate this pandemic. 

As we transition to distance learning, many posts have addressed the challenges not only in supporting our students and faculty but in how grading is promoting/highlighting inequities. In Grading as an issue of justice in this time of transition by Brian Katz and Kate Owens, there is a great discussion on what our concerns and priorities should be. Many of the concerns such as “students’ access to computers, internet, and quiet time/space and equity of this access, the need to adjust goals, changes in our ability to support students, and allowing students to make the hard choices based on their contexts and priorities”, are discussed and some ideas are provided on how to address them.

For example, making the grades this semester “Unsatisfactory/Satisfactory” would ease the pressure on students, if carefully implemented to take into account for “students who need a certain GPA, who can’t have P/NC courses count toward their major, and who might lose NCAA eligibility.” But as mentioned in the post, I think it is crucial (and I cannot emphasize this more) that we put the humanity of our students first, as Owens states,

“If we can’t do something in the best interest of the mental and emotional health of thousands of people because of (obscure regulation), then I maintain the regulation should be expected to adapt, not the people. We are all being forced to adapt to stressors and situations none of us ever imagined a month ago. We need to lighten the burden felt by all of us. Cut the red tape — trust me, it’ll be easier to repair that than emotional baggage when things go back to normal (which I hope is soon).” -Kate Owens

Another great post that provides resources for transitioning to distance learning is “Mathematics Education in time of COVID-19” by David Bressoud, a compiled list of resources by the MAA, “MAA recommendations for COVID-19 response”“Accessible Teaching in the time of COVID-19” by Aimi Hamraie, whose suggestions come from the disability culture and community. This is a great time for conversations about how we perceive accommodations and rethink how to better support students with disabilities.

Inequality will be increased not only in our student population but throughout the academic ladder. In this recent post, The pandemic and the female academic, Alessandra Minello talks about how in the world of academic clocks we will see gender inequality exacerbated by during this pandemic, she proposed that the lockdown period is taken as a care leave as a way to support families during this time, particularly single parents who most often tend to be women.  

With the footnote “*Everything is definitely not fine.” , I am very grateful to Piper H for sharing in Everything * is fine” the challenges and thoughts on the human side of this pandemic. I felt very seen especially as we rethink our responsibility as teachers and to each other.

“If we lose a member of our community to illness due to lack of funds, lack of resources, or lack of connection, who cares if we successfully zoomed our lectures?? I’ve heard it said that we have an obligation to our students to provide them what they paid for, but what about our moral obligations to each other? If I’m having breakdowns because I have to navigate caregivers whose exposure I can’t control, whose availability I can’t rely on, and I get a mass mailing with a thousand links about administering exams, all I can think is my workplace doesn’t care if I survive this.

And the worst thing is I know I’m super privileged in this.

Everyone makes connections; reach out to others and let’s remember those who didn’t. I will no longer be intimidated by mathematicians who failed this massive test in decency.” – Piper H

There has been a boom in the number of posts tackling the main features of transmission and spread using mathematics. As a math biologist, I am no stranger to modeling infectious diseases. We see talk about flattening the curve, exponential growth, transmission rates, basic reproduction number, among many other terms used at the intersection of math and epidemiology.

I’ve been so impressed with the efforts to demystify the math behind some of the key features of this outbreak. It might be in your family and friend circles, or also to your students, but I think part of our contribution can be helping the public better understand what these numbers/concepts mean. I really enjoyed Kamuela E. Yong’s, “The mathematics of a pandemic”,  3Blue1bBrown’s on exponential/logistic growth and epidemics , “Coronavirus, by the Numbers” by and “Why outbreaks like coronavirus spread exponentially, and how to “flatten the curve”.

Professional societies have also made available compiled lists of resources such as the American Mathematical Society’s list “AMS Resources & Updates related to COVID-19, the Society for Industrial and Applied Mathematics “Mathematical Resources to Help Understand COVID-19”, Mathematical Association of America’s “COVID-19 Update”, and the Association for Women in Mathematics’ “COVID-19 and the AWM Community. These include lists of online seminars, updates on the status of big community events, resources for teaching, articles of the current research, among others. 

For me, being part of a community is everything and in these isolated times we must find ways to support each other. As Carrie Diaz Eaton discusses in “Community in a time of COVID-19”,

“One of the most beautiful things I’ve seen is the crowdsourcing of help documents and Zoom chat meetups on Facebook and Twitter, the formation of open education communities like the one on MAA Connect and QUBES, and beautiful stories on my email about how my own campus community is helping students and each other through this with as much support as possible. Even without our formal gatherings, our community is still there for us. Don’t do this alone. You don’t have to. Remember that we already are a community, even in a time of COVID-19.” – Carrie Diaz Eaton

At times like this, I am reminded of Francis Su’s words from his 2017 speech at the Joint Math Meetings. 

“Because we are not mathematical machines. We live, we breathe, we feel, we bleed. If your students are struggling, and you don’t acknowledge it, their education becomes disconnected and irrelevant. Why should anyone care about mathematics if it doesn’t connect deeply to some human desire: to play, seek the truth, pursue beauty, fight for justice? You can be that connection.”  – Francis Su

During challenging times, having a connection to others is needed more than ever. Reach out to each other and extend as much kindness as you can, build structures of support for yourself, your students, and others, and stay safe. 

Do you have suggestions of topics or blogs you would like us to consider covering in upcoming posts? Resources to share? Reach out to us in the comments below or let us know on Twitter (@MissVRiveraQ)

Posted in Applied Math, Biomath, Blogs, Current Events, Issues in Higher Education, Math Communication, Math Education, Mental Health, women in math | 1 Comment

Logic ForAll: A Tour

From the blog post ‘Vanity Trip’. Translation: Valerria de Paiva: Brazilian Logician and Computer Scientist

While touring the math blogosphere I was very excited to find Logic ForAll’, a blog dedicated to making math accessible by mathematician and computer scientist Dr. Valeria de Paiva. She also writes in another great blog Women in Logic, which is used to organize and keep links to studies and graphs that show the extent of the problem and the tools other people have found to fight it. Women in Logic is also a Facebook group for women in Logic, philosophical, mathematical or computational or any other kind of formal logic that you care about. They have almost 500 members now and as described in the blog “so far, we have been finding it useful to discuss issues that affect us in our daily lives. There is also a Women in Logic spreadsheet with names of female logicians, organized by continent. This is an attempt at showing that there are plenty of female logicians around.”

Back in 2015, Dr. de Paiva was featured in the MAA article where she provides a brief description of her background and research interests.

“I am a Brazilian, from Rio de Janeiro, but I got my doctorate in Mathematics in Cambridge, UK, for work on “Dialectica Categories” written under Martin Hyland’s supervision. Working in Cambridge was a life-changing experience: I am now proud to say that my “academic great-grandfather” is none less than the founder of theoretical computer science, Alan Turing. I have, since my Cambridge days, worked on logical approaches to computation. My research interests include categorical proof theory, type theory, programming languages, logics for knowledge representation, logics of context, linear logic, intuitionistic modal logics and linguistic applications of logic. My work spans several different fields and I like all of my ‘hats’: mathematician, logician, computer scientist, and more recently computational linguist.”

One of the aspects I like most about the blog is the fact that it captures the life of a researcher quite well. Her writing combines a mix of styles that remind me of a mix between a classroom, research seminar, and talking with colleagues. I was curious to know more about the inspiration behind the ‘Logic ForAll’ blog so, in this tour, I hope to give you a glimpse of the blog’s style, content, and insights from Dr. Valeria de Paiva herself!

1. VRQ: Can you tell our readers a bit about yourself and your blog?

Valeria de Paiva: “Sure. I am a mathematician, an AI scientist and a computational linguist. I did my PhD in Cambridge, UK on Category Theory and I was a professor of Theoretical Computer Science at the University of Birmingham, UK, until I moved to the Bay Area, some twenty years ago. Here I have worked for some nine years at Xerox PARC and then in a series of other enterprises, like Nuance Communications and Samsung Research America. Along this way I have accumulated several different lines of research, so now I do work on several things, with different people. My blog started when I was teaching “baby logic” at Stanford and Santa Clara Universities and wanted to give students things to read. But nowadays its main function is to help me keep balancing these different projects. A sketchy description of the projects in the blog simply gives names to the buckets of things I do: Categorical Structures for (Linear) Logic, Constructive Modal Logics and IMLA, Lexical Portuguese Resources and OpenWordNet-PT, Lean Logic and Entailment and Contradiction Detection (ECD). This is in vaguely chronological order, but I actually work most when I have collaborators to play mental ping-pong with: I have an idea, you don’t like a bit of it, we try again, and the game goes on until we decide that we have a nice story of making a dent on our common ignorance.”

2.VRQ: What is the inspiration behind your blog?

Valeria de Paiva: “I’ve got inspiration from many mathematicians that I see trying to make mathematics more accessible to everyone. The name of the blog is “Logic ForAll”, now this is what I want, all people using logic formalized or not in the daily activities. But the name is also a pun, because in Brazilian Portuguese we have a dance and a style of music called “forro’ “. I only realized very late that the music (which is great and very danceable) comes from a mispronunciation of the English expression “for all”. So I wanted my blog to be like the music, fun and enjoyable and for all. Also, if possible full of little puzzles and games that it didn’t matter if you didn’t get them. It’s not about competition, it’s about fun!”

3.VRQ: What is the most interesting thing you’ve learned through blogging?

Valeria de Paiva: “I think I learned a while back that I only understand things when I am able to explain it to others — wherein others, I include myself. Once it’s written, it looks like another person did it, so I can debate it and discuss it all over again. I think one of the first posts in my blog, (I’m afraid I don’t remember where I copied it from) shows what I mean well 

From the webcomic Abstruse Goose.

You don’t just read mathematics, you fight it. An attitude that we should carry over to all kinds of things we read, right?”

4. VRQ:  Do you have advice for other mathematicians interested in creating their own blog?

Valeria de Paiva: “I do not think that I am good enough at this job, to be giving advice. My blog is a mess, I cannot keep the number of posts reasonable. I cannot find things I need that I know are there. I cannot write latex in it, I end up in a latex pidgin, where some things are their latex symbols, some others whatever name I prefer to give them, etc. But I’d suggest that any amount of demystification that we can do of mathematics is a good thing. It’s not rocket science, actually not even rocket science is rocket science, you just have to put the effort to understand it. And, as Barbara Fantechi was saying in Twitter the other day “most mathematicians aren’t like the gentlemen in this picture (Erdos and Tao). We’re not geniuses, just honest workers, motivated by a love of beauty, and patterns, and discovery. Most of us cover a variety of social roles, and not all of our time is for maths. We all count.” But we count more when we’re not impenetrable, when we have pictures and drawings, when we make our ideas more accessible, even if they do get a tiny bit less precise. It’s worth the trade-off, I say. Also, if English is not your first language (like it’s the case for me) using some grammar and spelling software does wonders for you (and your prepositions!).”

Some of her recent blog posts include:

“SICK (the data set) in these trying times” 

Here Dr. de Paiva describes her work with colleagues involving the Sentences Involving Compositional Knowledge (SICK) data set, provides a list of references, and shares her future research directions. In particular, she shares her article “Textual Inference: getting logic from humans, and her belief that their systems should learn from datasets that agree with human experience and how the single implication cases in SICK, they expected to find many problems. She mentions a few directions of the work towards addressing these problems.

“Artifacts in NLP”

In this post, Dr. de Paiva shares the work that is being done to track the progress (i.e. frameworks, tasks, and datasets) in the area of Natural Language Processing (NLP). She explains that in the area of Natural Language Inference (NIL) which  “is the task of determining whether a “hypothesis” is true (entailment), false (contradiction), or undetermined (neutral) given a “premise””. As she remarks, many of the results reported on the NLI task seem to be the outcome of biases on the datasets constructed to detect inference, and these are called artifacts.  I really enjoyed reading this post and learning about the growing literature regarding NLP and modeling inference and its challenges.

Do you have suggestions of topics or blogs you would like us to consider covering in upcoming posts? Reach out to us in the comments below or let us know on Twitter (@MissVRiveraQ)

Posted in Applied Math, Artificial Intelligence, Blogs, Category Theory, Math Communication, Mathematics and Computing, Theoretical Mathematics, women in math | Tagged , , , , , , | 2 Comments

Joyful Learning in the Early Years: A Tour

With schools shutting down for weeks or the rest of the semester in response to COVID-19, many guardians are concerned about how to support or even direct their children’s education from home. This seems particularly true when the children are young enough that online classes might not be feasible (or the school district has opted not to offer them).

Deanna Pecaski McLennan’s Joyful Learning in the Early Years blog offers educational resources for folks with young children.  McLennan “is an educator in Southern Ontario who is greatly influenced by the Reggio Emilia approach to Early Childhood Education. She believes in a play-based, exploratory, democratic learning environment,” according to her profile on the blog. (If you’re like me and don’t know much about the Reggio Emilia approach, the Compass School in Illinois has a blog post explaining a bit about that child-centered approach.) Here are a few interesting posts that could help parents and other caregivers keep their kids engaged with learning math during this stressful time.

“Spring Math”

“In times of uncertainty, helping one another is one of the best ways to get through the stress and worry of what awaits. I know that many educators and families right now are wondering how to help support children even when we can’t be together physically,” Pecaski McLennan wrote. She created the post “to continually provide ideas for how children can explore math in their natural world.”

“The CDC is asking us to engage in social distancing and being aware of what is recommended is important. Right now being outdoors in our yards, on trails, and in gardens is still safe and encouraged. I realize that some of us are limited by our personal circumstances and not everyone has access to a yard or natural trail. I will try my best to vary activities in order to meet as many circumstances as possible. I will also tweet ideas for math learning on a regular basis @McLennan1977,” she added.

Many of the activities discussed in the post could also be adapted to be done indoors if safe outdoor options aren’t available. At the end of the post, Pecaski McLennan shares a link to a free Kindle version of her Spring Math Walk book.

“Virtual Math Question”

“In our school hallway we have a dry erase board that asks rich, low floor high ceiling questions. Students and staff that walk by are encouraged to consider the question for a few days and then contribute their ideas using dry erase markers,” Pecaski McLennan wrote. For instance, she shares the question “If 24 is the answer, then what might the question have been?” By asking questions such as this, caregivers could give kids of multiple ages and levels of math background something to think about. After pondering the question for a few hours or days, the family could come together to discuss their varied answers to the question.

“Printable Pentominoes”

Pecaski McLennan shares a set of printable pentominoes. (She recommends printing them on cardstock and laminating them, but for easy, temporary, at-home use, they could also just be printed on ordinary printer paper and used without lamination.)

She describes these manipulatives as “an essential tool for any early childhood classroom,” because they encourage a positive attitude toward math, inspire children to cooperate and collaborate and “promote math thinking in a variety of areas including spatial reasoning (logic when solving puzzles, symmetry, reflection, rotation, design), measurement (considering the area and perimeter of designs), and number sense (counting the number of tiles or squares in a design, calculating the total number of squares using the anchor of 5).”

However, these tools can also be used in activities with older children. For instance, there are pentomino activities for middle schoolers on the

“Cereal Stringing”

While this activity isn’t inherently math-related, there are definitely ways to make it so. For instance, a caregiver and kids could each make a secret pattern using cereal on a pipe cleaner. Then the children could guess what pattern the adult created and if they can’t guess it, the adult could give them clues until they guess the pattern correctly. Each kid could then explain the pattern they created on their own bracelet. Alternatively, parents could play a game with kids in which everyone makes a bracelet without counting the number of cereal pieces they use. After the bracelets are made, everyone could make their own guess about how many pieces are strung on each bracelet, explain how they reached their guesses and then count the actual number of pieces together.

I also like this activity because it only requires a few materials and those can be easily swapped out. (Don’t have pipe cleaners at home? Use string or strips of fabric instead. Don’t have cereal? Use beads or help your kiddo thread stale popcorn onto string.)

The Joyful Learning in the Early Years blog abounds with other ideas that could be adapted to meet the needs of guardians educating their own children during the pandemic, even if outdoor access isn’t available or if the children they’re educating are older than the kindergarteners that Pecaski McLennan teaches.

Looking for additional ideas? The Bedtime Math website and app offer free activities. The new “Cabin Fever Math” section focuses on non-screen math activities that families can do together.

Thank you for reading! If you have ideas or feedback to share, please reach out in the comments or on Twitter (@writesRCrowell).

Posted in Book/App, Current Events, Interactive, K-12 Mathematics, Math Communication, Math Education, Mathematics and the Arts | Tagged , , , , , , , , , | Comments Off on Joyful Learning in the Early Years: A Tour

Old and New Math Celebrations

With all the news about the coronavirus, the uncertainty, and stress many are currently facing, I wanted to write a post with some levity ¹. What better day than this! Today is both the first International Day of Mathematics (IDM) and Pi Day. These two celebrations cause great joy in math enthusiasts and give space to learn new (and old) exciting facts.

International Day of Mathematics Logo.

Proclaimed by UNESCO back in November,  the goal of the IDM is to  “explain and celebrate the essential role that mathematics and mathematics education play in breakthroughs in science and technology, improving the quality of life, empowering women and girls, and contributing to the achievement of the Sustainable Development Goals of the 2030 Agenda (SDG1-17) of the United Nations.”

This lofty goal is hoped to be achieved by worldwide events for all in schools, museums, libraries, and other spaces. This year’s International Day of Mathematics theme is “Mathematics is Everywhere” and there is a great website dedicated to exploring many examples of this theme available in seven different languages. Among my favorite examples on the page is “Search for Alien Life”, “Predicting Weather”, and “Epidemic Analysis”. Fun fact, in “Search of Alien Life”, they talk about the famous Arecibo Message sent from Earth to space back in 1974 from Puerto Rico. As explained in Arecibo Message” by the SETI Institute,

“The message consists of 1679 bits, arranged into 73 lines of 23 characters per line (these are both prime numbers, and may help the aliens decode the message). The “ones” and “zeroes” were transmitted by frequency shifting at the rate of 10 bits per second. The total broadcast was less than three minutes. A graphic showing the message is reproduced here. It consists, among other things, of the Arecibo telescope, our solar system, DNA, a stick figure of a human, and some of the biochemicals of earthly life. Although it’s unlikely that this short inquiry will ever prompt a reply, the experiment was useful in getting us to think a bit about the difficulties of communicating across space, time, and a presumably wide culture gap.” – SETI Institute

Through their Twitter account, IDM also shared this really neat collective video featuring submissions from all over the world in many languages showcasing all the places you can find math around you.

The fact that this was the first celebration of the International Day of Math made me curious about the history of Pi Day. I was surprised to find that it started in 1988 and it was founded by physicist Larry Shaw. The first celebration was at the Exploratorium interactive science museum and consisted of a circular parade and eating fruit pies. You can still celebrate Pi Day at the Exploratorium by joining online and checking out some of their fun $\pi$ inspired activities.

The symbol for pi wasn’t used until the 1700s. As described in PiDay.org, before the symbol was used it was described as  “the quantity which, when the diameter is multiplied by it, yields the circumference” and other long, roundabout descriptions. In the 1700s, the Swiss mathematician and physicist named Euler formalized the use of the Greek lowercase letter, π, as the notation for pi. This is the first letter of the Greek word, perimetros, which loosely translates to “circumference.”

In “Getting Ready for Pi Day, and also the Playful Math Blog Carnival”, Joseph Nebus shares a few some of his Pi day content in his archive including “Six or Arguably Four Things for Pi Day” on different ways to compute $\pi$ and a great list of comic strips from previous years. In the Crooked Pencil blog, Priya Narayanan writes about Ramanujan: He who had the Pi & ate it too!

“While Ramanujan’s formulae were progressively more and more accurate, what is more important to us today is his approach to the calculations, which provided the foundation for the fastest- known algorithm that, in 1987, allowed mathematician and programmer Bill Gosper to use the computer to churn out the value of π to around 17 million decimal places. Later, mathematicians David and Gregory Chudnovsky used his formulae as the basis of their own variants that allowed them to calculate the value of π to an astounding 4 billion decimal places using their homemade parallel computer.”

The number $\pi$ has a really interesting history. In his book, Tales of Impossibility, David Richeson discusses how “compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—have served as ever-present muses for mathematicians for more than two millennia.” A review of the book in The Math Less Travel blog, describes the chapters as follows,

“Alternating with the “regular” chapters, Richeson includes a number of “tangents”, each one a short, fascinating glimpse into some topic which is related to the previous chapter but isn’t strictly necessary for driving the story forward (e.g. toothpick constructions, Crockett Johnson, origami, the Indiana pi bill, computing digits of pi, the tau vs pi debate, etc.). Even though none of them are strictly necessary, taken as a whole these “tangent” chapters do a lot to round out the story and give a fuller sense of the many explorations inspired by the problems of antiquity.”

You also find many cool facts in this short article, “Here’s how pi matters every day not just March 14“, in particular, what is the current Guinness World Record for computing $\pi$.

“The Guinness World Record for a calculation of pi was set in 2019 by Emma Haruka Iwao using Google cloud software. She calculated pi to 31,415,926,535,897 digits.”

Pretty amazing! You can hear from Haruka herself on how she achieved this here. Another really interesting find was that IBM has released a new tutorial as part of its open-source online textbook to estimate $\pi$ on a quantum computer.

“The thing we’re trying to do here is to stay away from computing a million digits of Pi and more to use the theme of Pi Day to educate people on what quantum algorithms look like.” – Abraham “Abe” Asfaw, Global lead of quantum education at IBM.

But what makes Pi so interesting? As explained by Tom Crawford in “Make your Own Pi” it turns up in many important theories like Heisenberg’s Uncertainty Principle, Einstein Field Equations, and Newton’s Gravitational Constant to name a few.

“You may know it in terms of circles, but it has the rather fantastic knack of cropping up in the most unexpected places… Quantum Theory? Check. Einstein’s Theory of Relativity? Check. Newton’s Law of Gravity? Check. Three of the most important theories we use to explain the universe, and each of them has a formula containing the number Pi.”

Whether you celebrate International Mathematics Day and/or Pi Day, stay safe! Have ideas or feedback to share with us? You can reach us in the comments below or on Twitter (@MissVRiveraQ)!

¹ Note: Though I will recommend watching this great video from 3Blue1bBrown’s on exponential/logistic growth and epidemics and this recent article “Coronavirus, by the Numbers”.

Posted in Applied Math, Current Events, History of Mathematics, Math Communication, Mathematics and Computing, Recreational Mathematics | 1 Comment