The Pseudocontext 2016 Deserves

2016 has been the year of the lolsob. I have my reasons for feeling that way, and I’m guessing you might too. In that light, I’ve especially started looking forward to Dan Meyer’s “pseudocontext Saturday” postsIn each one, he finds a picture from a math book and challenges readers to figure out what math concept is being illustrated or tested with each one. Is a rock-climbing kid illustrating a question about types of quadrilaterals or counting by tens? Does a picture of a dartboard accompany a question about probability, circle sector areas, sequences of numbers, binomials, or the quadratic formula? With connections this tenuous, even if you get the question right, you lose.

Image: Sam Wolff, via Flickr.

Image: Sam Wolff, via Flickr.

What is pseudocontext? Meyer writes, “We create a pseudocontext when at least one of two conditions are met. First, given a context, the assigned question isn’t a question most human beings would ask about it. Second, given that question, the assigned method isn’t a method most human beings would use to find it.” (For my money, the all-time prize for pseudocontext will always be this question from the New York Regents Exam shared by Patrick Honner, though as he states, the story is so flimsy it’s not even pseudocontext.)

Pseudocontext Saturdays don’t just give us an opportunity to lolsob about the bizarre and irrelevant “real-world” questions math textbooks often ask. Commenters can also suggest better questions to ask that go with the picture or that explore the concept the picture was trying to ask about. Felicitously, as I was working on this post, I read Dana Ernst’s post about students generating examples on the MAA blog Teaching Tidbits. That post isn’t about students asking real-world questions necessarily, but it makes me wonder if it’s possible (or desirable) to get students in on the pseudocontext joke: 10 points to Gryffindor for the best math question that would actually relate to the picture in question!

If you’re not already reading Meyer’s blog, there’s a lot more there to enjoy beyond pseudocontext. Meyer is a former high school math teacher who now works for the online graphing calculator Desmos. Though I haven’t spent much time talking math with high schoolers, I appreciate the thought and energy he’s put into figuring out what will reach students the most effectively and how to spur them to ask the questions we want them to be asking about math. As a bonus, his blog is also one of the few places where you can really read the comments. He encourages people to participate and have real conversations in the comments section, often highlighting selected comments in his posts. How refreshing!

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New PBS Show All About Math

Last week PBS launched a new show on YouTube all about math called Infinite Series. The first three episodes are up and they’re a ton of fun. The show is hosted by Kelsey Houston-Edwards, who is a graduate student at Cornell studying probability theory and the 2016 AMS-AAAS Mass Media Fellow.

In the first installation of the series, Houston-Edwards contemplates the sphere-packing problem, something that we talked about over here a few months ago. Aided by really cool animation and sound effects, she helps us to visualize spheres in higher dimensions and get a sense of how they might be packed. I especially liked her explanation of what happens when you pack spheres in more than 9 dimensions in a box. My mind — much like the sides of that box — was blown!

The second episode takes a somewhat of a philosophical turn. In it Houston-Edwards, who got her bachelor’s degree is in the interdisciplinary study of mathematics and philosophy, asks “Are prime numbers made up?” She delves into some of those tricky questions about whether math was invented, discovered or just…is. A question that certainly vexes those among us who dabble in math and patent law. Houston-Edwards says we can expect a few more episodes of this flavor.

Today I got a chance to catch up with Houston-Edwards to ask her about what’s headed our way in the next few episodes. “There are a couple of episodes like that which just came from personal knowledge, stuff that I just happen to know quite a bit about,” she says, “but the cool part about it, now that it’s aired, people are coming up to me like ‘Oh! You should make an episode about this!’ And that part’s really cool.” And given that she’s the one dreaming up all the ideas of the show I asked her if she was excited for all this feedback. She said, “Totally! I am more than happy to hear any ideas!” So feel free to pitch her all of your most strange and pressing math questions.

Kelsey Houston-Edwards, host of the new PBS online show about math.

Kelsey Houston-Edwards, host of the new PBS web series Infinite Series.

The most recent episode gives a very approachable treatment of the pigeon hole principle by answering that question that I know we all are wondering, “How many humans have the same number of body hairs?” Spoiler: tons and tons.

We can expect a new episode of Infinite Series every Thursday. If you’re interested in becoming a blogger or hosting a YouTube show of your own, a great place to start is with the AAAS Mass Media Fellowship. Evelyn and I are also both proud alumni of the program, and to learn more you can read about my experience at NPR or Evelyn’s experience at Scientific America. The fellowship program is accepting applications now until January 15th.

You can find Kelsey on Twitter @KelseyAHE. And while you’re there, you can find me too, @extremefriday, and let me know what else you’d like to see on this blog.

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What Should Mathematicians Do Now?

Mathematicians sometimes pretend we are above the everyday vicissitudes of life, preferring to inhabit a realm of abstraction and perfection, but that’s a lie. We live here too. We are voters, citizens, residents, and teachers. What happens in our country matters. I’m sure Anna and I will eventually get back to writing about other parts of the math blogosphere, but the election is still big news, and we as mathematicians need to ask ourselves what to do next.

I know our readers are not a monolith, but a large number of you are mathematicians at universities in the US. I’ve written this post with that in mind, though much of it will be relevant to people in other careers as well. I am also aware that though I did not support Trump, some of my readers probably did. I am not arguing with you about that. I trust that in spite of that difference, we have similar standards for how to treat others, and we are in favor of a strong, healthy culture of math and science research.

So what are mathematicians to do? Many of the actions we take are the same actions any citizens should take right now: talk to our representatives about issues that are important to us, donate to groups that need our help, reach out to friends and family who are feeling scared, and take care of ourselves so we can continue those other actions long-term. But I think there are a few ways to take action that relate specifically to mathematicians and the jobs they do.

1. Keep students safe

In the wake of Trump’s election, many people feel scared. Trump’s rhetoric energized some people who are racist, sexist, Islamaphobic, homophobic, and transphobic. Since the election, there have been numerous reports of hate crimes targeting people of color, religious minorities, and LGBTQIA+ people. Professors should be doing everything they can to make sure their classrooms and campuses are safe.

It’s tempting to think that math classrooms should be politics-free, but the right response to the election is probably not business as usual. Many educators have written about how they’ve talked with their classes since the election. I especially appreciate Jose Vilson’s post: Politics are always at play in our classrooms. We also need to continue promoting diversity in mathematics. One way of doing that is to cut back on the hero-worship of dead white men. Astrophysicist Chanda Hsu Prescod-Weinstein has a list of resources for decolonizing science that can help us do just that. I’ve also written posts with resources about black mathematicians, Hispanic/Latinx mathematicians, and women in math.

One group likely to be at risk in the next administration is undocumented immigrants. If you are concerned about undocumented students, you might consider joining the hundreds of other professors who have signed this petition to extend the Deferred Action for Childhood Arrivals (DACA) program. DACA allows undocumented people who came to the US as children to obtain work permits and remain in the country.

2. Fight misinformation

As Anna mentioned in her last post, there is evidence that misinformation (“fake news”) may have affected the outcome of the election, thanks to the Facebook algorithm bubble. Since then, a lot has been written about how important the phenomenon was to this election and what we need to do to stop it. Cathy O’Neil’s book Weapons of Math Destruction feels especially prescient right now. (Read my review of it here.) Her blog mathbabe.org is one of my go-to resources, and she is part of a New York Times debate about how to best stop the fake news problem. Here are some other things I’ve read recently about fake news and the election:

This Analysis Shows How Fake Election News Stories Outperformed Read News On Facebook by Craig Silverman
Fake News Is Not the Only Problem by Gilad Lotan
The “They Had Their Minds Made Up Anyway” Excuse by Mike Caulfield
Factiness by Nathan Jurgenson
Post-Truth Antidote: Our Roles in Virtuous Spirals of Trust in Science by Hilda Bastian

Fighting misinformation is an area in which I think mathematicians are especially, though certainly not uniquely, equipped to take action. When we write proofs, we are trying to construct watertight arguments using pure logic. Ideally, we attempt to poke holes in our own work until we can ensure that it is impenetrable.

We need to use those skills when we read the news or the outrageous videos our friends share on Facebook, whether we agree or disagree with the conclusions of those stories or videos. Apply the same skepticism to the stories you want to believe are true as the ones you reject. Check Snopes, try to find the numbers instead of taking someone else’s word for it, listen to the full context of the quote, see how other sites are spinning it. Settle for an answer of “it’s complicated” if it is.

An example: in the past few days, a growing number of people have been calling for an audit of the vote in Wisconsin, Michigan, and Pennsylvania (update: as I’m posting this, the audit is looking more and more likely). Those of us who wanted a different outcome could latch on to the story that statistical anomalies make the election look “rigged.” There are a lot of numbers floating around in that article, and it sounds truthy. But J. Alex Halderman, one of the computer scientists urging Clinton to call for a recount, is more measured. “Were this year’s deviations from pre-election polls the results of a cyberattack? Probably not. I believe the most likely explanation is that the polls were systematically wrong, rather than that the election was hacked.” Zeynep Tufekci, a sociologist who studies our relationship to technology, wrote about voting machine vulnerability before the election. Her message is that it’s not likely that it affected this election, but we should be auditing the vote regularly and making sure we leave a paper trail. Halderman’s and Tufekci’s messages aren’t as sexy as “rigged election!” but we need to fight the urge to jump to the sexiest conclusions without sufficient evidence.

How else can we fight misinformation? By supporting real journalism. I recently subscribed to the Washington Post because I’ve found a lot of value in their coverage of Trump’s appointments and financial dealings, but there are many other media outlets that you might find equally or more valuable. The media certainly made mistakes in its coverage of the election, but we still need to support journalism. As subscribers, we should also hold media outlets accountable when they screw up.

We should probably also read more media we disagree with. Yen Duong of Baking and Math recommends the National Review. I recently read “You are still crying wolf” by Scott Alexander of Slate Star Codex. I don’t agree completely with his thesis in that post, but thinking about why instead of dismissing it outright has helped me think about where my preconceived notions come from and how to engage in this conversation.

3. Support climate change research

This is more specific than the above suggestions, but a Trump advisor recently suggested that we should defund NASA’s climate change research. Climate change is likely the most pressing issue of our time. We have to keep studying it and try to find ways to mitigate the damage it is causing.

4. Read history

I hope the people who are warning us that the US is falling into authoritarianism/fascism/kleptocracy are wrong. Or that their warnings help us avoid those dire predictions. But it has happened before, and it can happen again. I think mathematicians would do well to read up on the history of math in Göttingen in the 1930s, perhaps in this Notices article from 1995 by Saunders Mac Lane.

Finally, I’ll leave you with this post by Matilde of the blog Listening to Golem about the moral responsibilities of mathematics and science: “Pack all the tools you need in your bag: network theory, bayesian analysis, probability, differential equations, cryptography, computing, game theory, neural networks. We need them all and we need them now. Get down to work for the sake of our future.”

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As The Dust Settles, Let’s Check The Numbers

I really didn’t want to write about the election. But probably, much like you, it’s all I can think about right now. News media is completely saturated with it and the blogs are churning out a steady stream of predictions and post mortem.

Even among those with college degrees and 2016 election was a divisive one.

Even among those with college degrees and 2016 election was a divisive one.

When we consider voters with post-graduate degrees, then we really start to see the ivory tower effect.

When we consider voters with post-graduate degrees, then we really start to see the ivory tower effect.

As an academic, I’m really troubled, but also fascinated by what this election and the reactions to it on college campuses tells us about the state of higher ed. Many of us wrestled with what to do last Wednesday when we stood in front of a room full of wide-eyed millennials. As Beth wrote over on the blog PhD Plus Epsilon, it was tough. The responses on college campuses have been extreme, and they tell a story perhaps different from the one we imagined.

On the one hand, the popular notion is of the ivory tower as a liberal bastion, and yet news anecdotes are giving the impression of college campuses which are massively divided, even in the least purple of states. But after the dust begins to settle, we can begin to try and understand more by looking at the numbers.

Several data sets published by the researches at The Chronicle analyze the voting outcomes over the past several elections across different swaths of the academic ecosystem. And it appears that our students (being people, I guess technically, without college degrees) have a much greater polarity that we do on the faculty. From these numbers, the whole liberal bastion ivory tower business doesn’t even seem to apply to students in the universities. For reasons I won’t delve into right here and now, I consider this a bit strange.

This data, gathered by the Chronicle of Higher Ed, shows a tendency towards the left in counties housing flagship universities.

This data, gathered by the Chronicle of Higher Ed, shows a tendency towards the left in counties housing flagship universities.

As the Chronicle of Higher Ed reported this week, college towns tend to be more liberal than the states they inhabit. In their research, counties that housed flagship universities tended to view the republican candidate less favorably that the state as a whole. Wisconsin-Madison was a particularly good example. The republican candidate won the state by about 1% but lost Dane County (home of University of Wisconsin – Madison) by about 48%. So the take-home here is that college towns lean left, which isn’t really a surprise. But then we also need to keep in mind that those left leanings are coming largely from the university affiliates and residents of the counties, not students themselves, since they typically aren’t registered to vote in the same place they go to college.

But in any case, I don’t exactly take heart at the sight of this data, because those numbers aren’t telling us college campuses are unified, as much as they are telling us that we as universities are alienated from our surroundings, and we as faculty are alienated from our students, which doesn’t feel so great. The Chronicle team generated several other data sets to explore the demographics of the vote across academic cross sections, also considering race and gender.

There are still plenty of lingering questions about what all of this means for us, as educators and academics. The Chronicle of Higher Ed is keeping us up to date with a lot of this in their series A Stunning Upset (my apologies, many of their articles are behind a paywall). Specific questions that I am concerned about, include what this all means for federal funding for research and, more broadly, for universities? Will the changing priorities of the government be reflected in changing priorities of institutions? And what’s in store for students who are still in the process of financing their educations?

I guess we wait and see.

I should also mention, as a mathematician, there is also a lot of interesting conversation going on about the efficacy of polling, and how biased algorithms might have shaped the outcome of the election. Blogger extraordinaire, Cathy O’Neil, has done some particularly great work in the past week discussing some of the data driven pitfalls of utter chaos 2016. Among other things, this election and the journalism surrounding it has reminded me how important it is to understand where numbers come from. An infographic with a needle swinging side-to-side is all well and good when it’s swinging in the proper direction, but when it starts to lean the other way, suddenly I’m forced to ask myself, “Wait, what am I even looking at right now?”

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Which One Doesn’t Belong?

1, 2, 4,…. What’s the next number in the sequence? I was a rule-follower as a kid, so I always got the “right” answer on questions like that, but they still bugged me. Sure, 8 would be predictable, but why couldn’t it be 7, 9, or 34 million, for that matter? It seemed like we were making an awful lot of assumptions about how sequences were going to behave without much evidence. Pattern recognition is an important part of doing math, but so is the skepticism that made me feel uneasy when I predicted what a sequence would do based on just a few beginning terms. Owen Elton describes why any answer would be “correct” using one of those awful Facebook “only 1 in a thousand will get it” math riddles that pops up every now and then.

Christopher Danielson’s book Which One Doesn’t Belong and Mary Bourassa’s blog of the same name would have been great for me as a kid. Each page in the book is a set of four shapes, and you have to say which one doesn’t belong. But any answer can be “right.” Each prompt can start a discussion of what traits the shapes/numbers/graphs have in common and do not. Instead of learning the one right answer and moving on, kids can discuss which answers jumped out at them and why. They can have open-ended conversations about math rather than just trying to find the one right answer.

I’ve seen posts about #wodb all over the #MTBoS, so I won’t even try to link to everyone who’s talked about using these prompts in the classroom, but I do want to mention Tracy Zager, who has a thoughtful post about using “which one doesn’t belong” in a second-grade classroom and the way open-ended math discussions can get both students and teachers thinking about what math words mean.

Danielson also writes the blog Talking Math with Your Kids, which aims to foster mathematical reasoning skills in early childhood by helping parents have low-stress conversations about math with their kids. Yes, please!

Helping parents have low-stress conversations about math with their kids is the aim of Bedtime Math, an app and blog. Each day it gives parents a fun prompt and some questions to start the discussion. I also love reading Malke Rosenfeld (currently blogging at Math in Unexpected Spaces) and Mike Lawler of Mike’s Math Page, who talk to their kids about math a lot. (I got nerdsniped yesterday by a fun area question from Lawler’s blog.)

I don’t have kids, so I’m mostly a bystander in talking math with kids, but I do have two young goddaughters. When we get together, we often count things together, and I hope as they grow up, I can keep talking with them about math in ways that are age-appropriate and fun. Reading blogs like Danielson’s, Zager’s, Rosenfeld’s, and Lawler’s and following the #tmwyk hashtag on Twitter are helpful for me when I’m thinking about how to talk with my goddaughters about math. I’m also partial to the #wodb hashtag. It’s just fun to see the cool mathematical “which one doesn’t belong” pictures created by both students and teachers. I’m hoping that in a few years, my goddaughters and I will be making some of them for ourselves.

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

Math Games Might Be Sort Of Good For Your Brain

Good news, all that time you spent playing World of Warcraft might have made you smarter. A study out of Stanford just showed that playing video games just 10 minutes each day can make you better at math. The study involved two cohorts of third grades, one group was taught math in the standard manner, and the other was given 10 minutes each day to play the game Wuzzit Trouble on school issued iPads. The video game playing group demonstrated significant improvement in what the researchers call “number sense,” including an improved ability to “apply their number sense to an unconventional problem.”

RoTopo may not give you number sense, but make you understand how cubes work.

RoTopo may not give you number sense, but make you understand how cubes work.

But wait, whoa, not so fast. Before you pick up that controller, I should note that the study was based on a very particular game. Certainly other similar games might see a similar effect, but I suspect Pokemon does very little to improve one’s number sense. And according to people who know a lot about this sort of thing, most math video games marketed as educational tools aren’t even all that impressive.

Incidentally, this study was well-timed to coincide with the American Academy of Pediatric (AAP) revised guidelines for kids and screentime, namely, that screens aren’t as bad for little brains as they initially thought.

I don't mean to brag, but...

I don’t mean to brag, but…

But for the full-grown brains of grown-up mathematicians, the internet is a cornucopia of highly educational addictive math games. In a recent post on Math Munch I learned about several online games exploring geometry and dimension. Rotopo is really fun, and has really soothing background music. The game doesn’t necessarily address math explicitly, but there is a strategy and spatial sense that you gain from the geometry of the game. If you need to procrastinate, then I highly recommend it.

Another game that recently came to my attention (tip of the hat to TJ Hitchman) is Euclidia. Using points, lines and circles (i.e. pencil, straightedge, and compass) you move through a series of exercises to construct equilateral triangles, perpendicular bisectors and increasingly difficult geometric constructions. I didn’t think it would be as fun as it is, and yet I started playing and couldn’t stop. The premise is simple, and yet it’s kind of a rush to actually do the constructions. And I would imagine even cooler if you were doing them for the first time. If I were teaching Euclidean geometry I would love to find a way to integrate this game into the course.

Apps are also a great place to get your math video fix. For the commuting and smart-phone wielding mathematician, The Aperiodical gave a good roundup of worthwhile games. Evelyn Lamb also wrote about games for understanding hyperbolic space for Scientific American.

And I just finally beat 2048, the most annoyingly addictive game to come out since snood (remember that?). So I’m feeling pretty good.

Posted in Math Education, Recreational Mathematics | Tagged , , , , | 1 Comment

Topology in the Limelight

Topology is having a moment. Maybe not as much as this never-ending election season or this Pringles “ringle” with 40,000 retweets and counting (seriously, you should go look—it’s a self-supporting ring of potato chips, need I say more?), but it’s been getting more recognition than usual for a field of theoretical math. Somewhat ironically, it’s all because of the Nobel prize, and there’s not even a Nobel for math. (And no, it’s not because a mathematician had an affair with Nobel’s wife; he was a bachelor.) Earlier this month, the Nobel prize in physics went to three physicists for their work on topological phase transitions and topological phases of matter.

Delicious topology. Image: Dave Crosby, via Flickr. CC BY-SA 2.0

Delicious topology. Image: Dave Crosby, via Flickr. CC BY-SA 2.0

As science news editors across the globe sighed and shelved their pre-written explainers about LIGO and gravitational waves, they got to work figuring out how to talk about the work that actually won the prize this year. The easiest part of the prize to explain ends up being the most off-putting word, topology, so the bagels and coffee cups were at the ready.

Nobel Committee member Thor Hans Hansson had an adorable illustration of the basic idea of a topological property, in this case genus. But his explanation and some of the other ones I saw sometimes gave people the impression that the physicists were studying literal, if miniature, bagel- and pretzel-shaped objects floating around in superconducting materials. That’s not quite right. I tried to make it a bit clearer in an article I wrote for Scientific American. I can also recommend Kevin Knudson’s article about it for The Conversation and Brian Handwerk’s piece for Smithsonian. Vasudevan Mukunth also has a nice article on The Wire reminding us that the value of these physics discoveries is not necessarily in their utility or applications.

For me, one of the most fun things to come out of the Nobel’s mathematical connection is a series of interviews Rachael Boyd did on the blog Picture This Maths. (I wrote about Picture This Maths this past July.) One of the interviewees, Ruben Verresen, complains about the usual description of topology so many of us give of topology, which tends to be of the donut-coffee mug variety. “The issue is that they seem very arbitrary: what’s so special about holes?” Even if a reader or listener understands what you’re describing, he thinks it’s not all that interesting. He writes, “if I explain topology by comparing a donut to a coffee mug, I can just see my listener slowly turning off.” Instead, he thinks we should emphasize the difference between properties that are local and those that aren’t. Local properties even include things like height, anything that can be assessed by looking at the property in a small region and then combining those observations over the entire object. He says that emphasizing this distinction can make it more clear why someone should care about topology in the first place.

Boyd’s interviews also made me aware that someone’s been writing a comic strip about topology and nobody told me! The strip, by Tom Hockenhull, is in Chalkdust Magazine.

I’ve seen topology around a few other places recently, so this post comes with a dessert course. Mathematician Jean-Luc Thiffeault used ideas from topology to analyze taffy-pullers, both modern and old-timey, and I was ON IT for Smithsonian. Candy and math? Yes, please. Then there’s this Nature News Q&A with Microsoft researcher Alex Bocharov about why Microsoft is investing to heavily in building a topological quantum computer. One of the most interesting things I learned when I was writing about the physics Nobel prize was that physicists are trying to figure out how to use topology to build a quantum computer. Once you’ve heard it, it makes sense: topological properties are more robust to small perturbations than other properties, so in theory, information would be less prone to degradation from outside noise.

Finally, behold the ultradonut topology of the nuclear envelope, a real paper title from the Proceedings of the National Academy of Sciences. Mmm, ultradonut.

Posted in Applied Math, Theoretical Mathematics | Tagged , , | 4 Comments

How Polling Works…Or Doesn’t Work

From the perpetual pit in my stomach, to the sleepless nights, to the eyes bloodshot from peering at endless forecast models and polling predictions, only one thing can be true: the election is nigh upon us. In a time of uncertainty, where opinions and gut feelings seem to dominate, the mathematician in me craves the concreteness of numbers. And polling does just that. It gives me a quantified sense of what the future will look like. And sure, it’s something cozy to wrap myself up in. But what do those numbers mean? What am I really looking at when I see election forecasting?

First, there’s the question of the act of polling itself. Like anytime you gather data for statistical analyses, there’s always a chance for sampling bias. Since it’s impossible to contact every single person in the country, pollsters need to find some representative subset. That is, polls need to use a small number of opinions to extrapolate the national opinion. National polls are typically conducted by phone, and Pew Research reports that — largely due to the disappearance of land lines over the past 20 years — response rates have gone from 36% in 1997 to 9% in 2012. Since landlines can be autodialed while cell phones must be dialed by hand, calling land lines is still the best way to reach the largest swath of people as fast as possible.

This of course brings with it some problem of bias, since the set of all land line owners in the United States is a very particular demographic, not necessarily representative of the country as a whole. But the Pew Research Center says that through careful weighting of poll responses they are able to overcome these biases. So a single poll, which already contains thousands of responses is weighted to correct biases and massaged to give the most accurate picture of national opinion.

But typically the poll results that you see on popular news sites don’t just reflect a single poll, they are often aggregates of the top 5 state and national polls in some cases, to several thousands of polls in other cases. And then the thousands of polls — some of which are more reliable than others — are weighted to reflect their reliability, sample size, and representative regional demographics.

And finally an aggregation of polls becomes and mathematical model when a few more factors are added into the mix. Depending on the agency doing the modeling they will factor in effects like the convention bounce, the shape of the economy, and accuracy in prediction in certain states in past elections. All of these factors come together to build a robust mathematical model to forecast the election.

As one example, The New York Times maintains an active “Who Will Be President?” Scoreboard, comparing their aggregate model will several of the other top forecasts like fivethirtyeight, Daily Kos, HuffPost, and Princeton Election Consortium. And to game things out even further they also have an interactive chart weighing out the probabilities of each candidates path to the presidency based on electoral votes and states that have determined election outcomes in the past.

And then there’s this dimly lit corner of election forecasting that doesn’t rely on polls at all. These are places like the Cook Political Report which produces forecasts based more on reporting trends and expert opinions, or PredictWise which bases its forecasting on a combination of polls and betting markets.

There are a host of quantitative ways to deal with the election right now — and some slightly more qualitative ways as well — but I find the best thing to do is light some aromatherapy candles, immerse yourself in a warm bath of polls and forecasting, breathe deep cleansing breaths, and wait for November 8th.

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Celebrating Latin@s and Hispanics in Mathematics

September 15-October 15 is Hispanic Heritage Month in the U.S. (In case you were wondering, it starts on September 15 to coincide with the Independence Days of several Latin American countries.) The new website Lathisms.org helps us in the math community celebrate by sharing a photo and brief biography of a Latina, Latino, or Hispanic mathematician every day during this month. I’ve seen a few familiar names and faces and a lot of new people to learn about.

Ten of the Latina, Latino, and Hispanic mathematicians featured for Hispanic Heritage Month on the Lathisms.org website. For full image credits, click here.

Ten of the Latina, Latino, and Hispanic mathematicians featured this month on the Lathisms.org website. Image from the AMS Notices article about LathismsFor full image credit information, click here.

Alexander Diaz-Lopez, Pamela Harris, Alicia Prieto Langarica, and Gabriel Sosa are the mathematicians behind Lathisms. Harris and Sosa were gracious enough to chat with me last week about what inspired them to create Lathisms and why they think it’s an important project. Below is an abridged transcript of our conversation. (Note: This is an AMS blog, and the AMS has been supportive of Lathisms, but the AMS was not involved in my decision to write about the site.)

Evelyn Lamb: What inspired the creation of Lathisms?

Gabriel Sosa: It was during February, it was Black History month. I was asking people whether we knew of a poster featuring prominent African American mathematicians. The AMS has this really nice poster about women in math. When I started in grad school, I was like, how many famous women mathematicians have there been? If you look back in time there were not that many. Of course it’s because women were not allowed to do math back then. But there are so many examples, so many amazing people on this poster. I thought, what a wonderful thing. Maybe there should be one for African Americans too. And Pam said there isn’t one for Latinos. So she said, “Let’s do one!” [Editor’s note: I published a roundup of resources for learning about African American mathematicians on this blog in February.]

Pamela Harris: It’s one of those things that sort of happened over Facebook. Alicia, Gabriel, Alexander, and I have met each other at multiple different conferences, and we work together amongst ourselves doing research. It became this natural thing, another project we could do. I think what was really beautiful about it was that without even intending it to be this way, we found two Hispanic women and two Hispanic men to do this project. It was this idea that sprung up from having Gabriel ask this question, does such a poster exist?

EL: So will there be a poster at the end, or will it all be online?

PH: The original idea was for us to get information out as soon as possible. Alexander has a connection at the AMS. He has written for the Graduate Student Blog, and he is an editor for Notices of the AMS. Immediately we knew that Alexander was somebody who had a nice connection and good rapport with the AMS. We knew that maybe we could write a short article featuring some mathematicians.

The AMS was extremely supportive of this endeavor from the start. It was pretty incredible. We found out that the cover October issue of Notices has always been reserved to feature the city of JMM. This year, they put part of our collage of photos there. The fact that they went above and beyond to feature the Latinos and Hispanics in our community this year has been an extremely positive experience. They really stepped up and made this be something that adds value to the community. We are extremely thankful for them for their support.

GS: I was pleasantly surprised. I never expected that the moment we asked to do an article, they would say, oh, go ahead. They replied back that same day two hours later.

EL: I haven’t gone through carefully. Are the people you feature all working in the US?

PH: That was the idea. The reason for that is not that we are trying to not feature other mathematicians, but the idea for Hispanic Heritage Month is really to celebrate the culture and accomplishments and contributions of US-based Latinos and Hispanics. Solely for that purpose, and because we organized it for that particular month, we focused on featuring US-based mathematicians.

EL: I saw some discussion on Facebook about this, so I have a burning question: how do you pronounce the website name?

GS: Lat-isms. The “h” is silent in Spanish.

EL: What are your goals for the project this year? Are you going to do something similar next year? How will that evolve?

PH: The goal for this project to begin with was for us to inspire a new generation of students and junior faculty while being able to honor those who have come before and have done a phenomenal amount of research and a phenomenal amount of mentoring and service in the math community and specifically for underrepresented mathematicians and students. That was really the goal for us, to have this platform on which we could feature these mathematicians and their contributions to this community.

For next year the goal is to continue working on this. It is a pretty extensive time requirement to put this together. The plan is moving forward to maybe not every year feature this many mathematicians but for sure to have some subset of the month covered by mathematicians, and possibly bring in some more junior up-and-coming leaders in the field. There are a lot of phenomenal junior mathematicians that are maybe not getting the amount of press that they deserve for whatever reason. We thought that moving forward that’s something we want to provide.

EL: Have you gotten much feedback from people on it?

PH: Absolutely. Through the website there is a contact us link. We’ve gotten numerous emails. One of the most recent ones was a math professor who mentioned that they love our website, they wish that this had existed before, that he actually has been looking for a poster that features more diverse mathematicians.

Most of the comments have been complete support for the project, very thankful that we spent time doing this. That’s great. We never did this in order to be thanked. In my opinion it was a project that I needed. At this point in my career, I need to be reminded that I can achieve the goals I have set for myself, that there are people that look like me that have had similar life experiences as mine that are serving as great role models. Not only was it for us to share these mathematicians, it was very fulfilling for us to learn about the phenomenal work that our mentors are doing.

GS: To add to that, the person who sent this email mentioned that Juan Meza visited his institution at one point. He said it was life changing because they have a 25% Latino student body. For them to see him and hear his personal story, besides his research, was something that changed the way they thought about it.

EL: When you were in undergrad and grad school, did you have Hispanic and Latino mathematicians to look up to?

PH: Gabriel and I had very, very different experiences. I did my undergraduate in Milwaukee, Wisconsin. The first time I actually met a Latina or Latino who had a Ph.D., it was a dear friend of mine, Alejandra Alvarado. I met her five years ago. I was at a women’s conference. I was presenting a poster on my research, and she came up to me and said, “Are you Latina?” I said, “I’m Mexican.” She said, “So am I.” I was like, “You have a math Ph.D.? There’s more of us? There’s more of us!” From there it really became like this small avalanche. I met Alejandra, then I met Maria Vega, who has also become a dear friend of mine. Then I met Erika Camacho, then Alicia and Gabriel and Alexander. it’s amazing how many phenomenal people we have. But it really did take a long time for me, being US-based, to have met some of my peers and some of my mentors. It was very late in my career.

GS: I think it’s a very big difference because Pam did her Ph.D. here and immigrated to the US very young. In the case of Alicia and me, we came here after undergrad, so obviously all our professors had been Latinos, so we knew it was achievable. For instance, I ended up here because one of my professors got his Ph.D. from Purdue. He said, “You should consider that place because I was Latino and I succeeded there. We know that you have everything that you need there to have a support system.” I’m always like, “Pam, how did you do it?” To me it’s hard to even imagine what would have happened if I had not had these people before telling me I should go there and do this.

PH: I did have mentors, they just did not happen to be Hispanic or Latino. My mentors were phenomenal, and clearly they pushed me in the right direction. Otherwise I would not have continued in mathematics. But in addition to having a good mentor, being able to see yourself in someone is extremely important. It’s something that I missed for a very long time. Having a community of peers and collaborators and colleagues that are members of underrepresented groups has really helped me grow not only as a mathematician, but also as a person.

It does give me a lot of pride, that even though I missed having Hispanic mentors I was able to succeed. But I think that’s the reason why we needed to do this kind of program. I don’t think it’s fair for someone to be as old as I was and not have known about Carlos Castillo-Chavez, or Erika Camacho. Featuring these mathematicians on this platform, what we’re doing is we’re reaching people at a much earlier age.

EL: Do you have recommendations of other resources for people to learn about Hispanic and Latino and Latina mathematicians, or resources for students in those groups?

PH: Alicia, myself, and Marco Martinez put together a list through the MAA. We have a page on their website solely dedicated to resources for students coming from underrepresented groups and faculty who work with those students. [Editor’s note: Find their list here.]

For me SACNAS [Society for Advancements of Chicanos/Hispanics and Native Americans in Science] has been a phenomenal organization that has always provided a great balance between diversity and pushing the boundaries of science. They really blend beautifully the idea that we can be proud of our culture and continue our traditions and love our heritage, but we can also be amazing leaders in science. Anytime I meet students I make sure they know about SACNAS.

GS: I was a member of SACNAS, and when I went to the annual conference for the first time my mind was blown. All of these amazing things are happening. You can still be you and still be amazing.

PH: For me that’s the best thing. You do not understand the amount of community building you make at a conference like that, how close you feel to people that are geographically thousands of miles away.  That amount of community building is something that SACNAS provides that I’ve never experienced anywhere else.

EL: Sometimes as a woman in math, you feel like have to act like a man, or try to hide your femininity to blend in with a more dominant culture. I’d imagine that happens for other groups as well. And not having to do that must be a really important thing.

PH: It’s very true. Sadly, I’ve had very negative experiences given that my name is Pamela Harris. Really, my name is not Pamela, it’s Pamela. Having immigrated to the United States at a very early age and the fact that maybe I don’t have much of an accent when I speak English, it’s very easy for people, when they talk to me on the phone or when they haven’t yet met me, not to realize that I’m not who they might imagine I am. I’ve had very negative experiences in job interviews. I show up and people’s jaws drop because I don’t embody in their mind what somebody with my name should look like. It is something that’s difficult. Also as a woman, we know there’s discrimination based on our name and our assumed gender. Having SACNAS to be able to go the annual conference and to not ever think about that is really refreshing, it’s freeing. And it allows us to build community, but also to focus on why we’re there, which is the science.

EL: I’d imagine this project helped you all meet new people and make more connections too.

PH: When we started thinking about this project and who we wanted to feature, of course prominent people come to mind: Erika Camacho, Carlos Castillo-Chavez, Ricardo Cortez, Richard Tapia, among many others. At the same time, what we wanted to do, and what we ended up doing, was reaching out to a large group of Hispanic mathematicians for them to give us input on who we should feature this year. We basically crowd-sourced.

Having a diverse group of people really provides us so many more learning opportunities. We should take advantage of that. We’re educators, we’re mathematicians, we’re scientists. It’s something I’m quite proud of our group for doing.

I think the greatest joy is to finally see the end product and get such positive feedback and such interest from the community at large about what we have done. It’s just been a very happy experience overall.

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The Mathematical Tweet Beat

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I was a twitter skeptic for a very long time. And now my love affair with twitter is so deep, it’s hard to even remember what my reservations were in the first place. I first joined in 2013, compelled by my hard-tweeting cohort of the AAAS Mass Media Fellowship. And what I discovered was the most pleasant online community of mathematicians and educators chatting all day about…well, math and education!

I get some of my best lesson plan ideas from Twitter, I learn about new math research papers, I get links to every possible math blog in the universe, and perhaps most relevant to you, I get all of my ideas for this blog. So I wanted to take this week to tell you about some of my favorite math tweeters and hashtags.

So first things first, a few hashtags to get you on your way.

This week the MAA hosted the #loveyourmath challenge. Tweeters posted on a different topic each day of the week, including, favorite math puzzles, proudest math moments, and mathematical arts and crafts. I didn’t find the challenge itself particularly inspiring, but if you’re new to the medium, it’s a good introduction to the mathematical twittersphere.

When I’m looking for fun problems and puzzles, I love to peruse the tweets on #mathchat. It tends to skew more towards K-12 teachers, but there are fantastic videos and links to technology and lesson ideas that I would never otherwise find.

Now on to people. At the very least, you can follow the big mathematical societies. I frequently check in with the AMS, the MAA and the AWM to see what they’ve found on the internet in a given week.

If you’ll forgive the blatant log rolling, my co-blogger Evelyn Lamb maintains a highly entertaining twitter account. She also wrote about her favorite mathy ladies on twitter for her blog at Scientific American several years about.

Mathematicians and tweeters John Allen Paulos and Marcus du Sautoy were listed among Science Magazine’s top 50 science stars of twitter. Other top mathematicians who tweet are Steven Strogatz, Laura Albert McLay, Matt Parker and Hannah Fry, to name just a few.

Some of my favorite math tweets over the years have also come from the collective hive mind behind The Aperiodical: Christian Perfect, Peter Rowlett, and Katie Steckles.

Finally, there are accounts that are dedicated to spitting out intermitted math facts just when you need them most. Like Algebra Fact, Prime Numbers and the not exactly mathematical but still fun in a mathy sort of way, Wolfram|Alpha Can’t.

So here are just a few ideas to get your started. Happy tweeting!

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