Public domain portrait of Émilie du Châtelet by Maurice Quentin de La Tour. Image posted on Wikimedia (under a Creative Commons license) by user RockMagnetist.
In the U.S., March is Women’s History Month. The vision of the National Girls Collaborative Project (NGCP) is to “bring together organizations throughout the United States that are committed to informing and encouraging girls to pursue careers in science, technology, engineering, and mathematics (STEM),” the organization states on its website. The organization currently consists of 33 collaboratives that serve 41 states by facilitating collaboration between 36,400 organizations that serve 20.15 million girls.
The NGCP blog includes posts about a myriad of topics. Here are a few of their recent posts that I think are interesting: Continue reading →
So, I’ve been eavesdropping on math history Twitter for the better part of a year now and there is one thread of conversation over there that I’ve been wanting to talk about, namely, the question of whether math – the numbers, variables, and equations themselves – can be inherently sexist, racist, or otherwise politically charged. Then this morning I was reading this incredibly stale and annoying op-ed in the New York Times that, in addition to other defects that I’ll let you uncover on your own, ends with this cringeworthy sentiment, “Math is one of the few institutions we have left free of doublespeak or embellishment or biased opinion. Its words are supposed to mean exactly what they say. Let’s keep them that way.” And I thought, ok, today’s the day.
My first entry to this conversation was captured in a blog post here on the Blog on Math Blogs in 2016, where I reviewed a Scientific American blog post by Michael J. Barany, math historian. In his post, Barany puts our current mathematical climate in context by describing historical mathematical gatekeeping, “elite mathematics today, while much more inclusive than it was one or five or fifty centuries ago, remains a discipline that vests special authority in those who, by virtue of gender, race, and class, are often already among our society’s most powerful.”
But from there it’s hard to say whether math is politicized, or whether mathematicians themselves are politicized, and whether or not those concepts are entirely distinct.
Then a thoughtful pivot to this discussion came across my Twitter feed from Alexander R. Galloway, who writes a blog that hits some nice points in technology and philosophy. Despite the fact that its title sounds like a pretty well-worn argument, the post “Are Algorithms Biased?” is full of thought-provoking and fairly new-to-me arguments and rebuttals about the politicization of math. Unlike Barany’s post above that is more rooted in the practice of math, Galloway’s post is firmly planted in the objects of math themselves.
Galloway’s Response #7 to the claim that “math is just a tool” — something along the lines of “there are no racist algorithms only racist coders” — especially resonated with me. I’m not quite sure I can fully get behind his position, but I can see how the tool and the user (as in the case of guns and shooters) can’t always be fully decoupled.
To see an example of racist and classist numbers in action, a 2011 paper by Barany discusses “savage numbers” — he defines these as “number-like or number-replacing concepts and practices attributed to peoples viewed as civilizationally inferior” — and their critical role in positioning the British on top of the heap of emerging science in the Victorian era.
The question of whose mathematical contributions count and why — most poignantly the de-colonization of math — is an interesting one. Academic mathematicians certainly know that the future directions of math are largely shaped by journal editors and funding bodies and all of their intrinsic biases, preferences, and motivations. Tangential to that topic, this blog post by C.K. Raju outlining his allegations of intellectual theft by Michael Atiyah and subsequent silencing by the AMS is a really wild ride.
If you’re in for a long read about philosophy and access to mathematical ideas and technology, I am happy to point you towards McKenzie Wark’s A Hacker Manifesto.
For shorter reads, you can also eavesdrop on the conversation about socio-historical mathematics on the #MTBoS. And as always if you have anything to contribute, endorse or disagree with, please hit me up on Twitter @extremefriday.
There are a myriad of ways that I could jump into this conversation, but I’ll start here: That people consider it heroic for a professor to hold a baby for one 50 minute math class so a college student can take better notes says quite a bit about the world we live in. Might I suggest a few different (and less dramatic) ways to describe that professor’s actions?
Invested in student success
Going above and beyond to help a student and their family
I don’t want to discount Alexander’s actions by any means, but if we choose to call them heroic, that puts them on a pedestal. “Why is that a problem?” some folks might ask. Here’s my answer:
Heroic actions are ones that we expect very few people to take. We call them heroic because they are so out of the ordinary that we’re surprised to hear they happened. But the fact of the matter is, there are many students with babies/toddlers/older children, childcare is expensive and its easy for that care to fall through at the last minute. Wouldn’t those students have a better chance at success if society started treating childcare issues as common ones that shouldn’t get in the way of learning or successful careers?
On a related note, these recent articles cover the intersection of STEM careers and parenting (especially motherhood):
“Motherhood and mathematics are not commonly discussed unless you identify as a ‘math mama.’ So why would the mathematics community need an entire issue of a journal discussing experiences by mathematical mothers? Moreover, why would we, as editors, not present an issue on parenthood and mathematics? The simple answer is that we are mothers who are mathematicians. We realized we were not anomalies but comprise a productive part of the mathematics community. So we sought to uncover hidden narratives like ours, full of hope and courage, involving women breaking the stereotype of what a mathematician and a mother should be,” they wrote.
In the first post for the blog, Emille wrote “Welcome to the first post of our new blog ‘Math Mamas’! We, the editors, were hoping to create a space where we can share our experiences, learn from each other, and discuss how our identity as women underrepresented in mathematics interacts with our role as a parent. Research shows that academic men benefit professionally from having children, yet women are penalized for having children. Therefore, the community we hope to create through this blog centers mothers and non-binary parents, particularly those who are raising or are considering raising children. We hope that our conversations will help all genders understand the joys and challenges of balancing life as a working mathematician and as a parent. Mathematics is the more formal part of our lives. Motherhood is the less structured and messier part of our lives. Each of these enriches and impacts the other. These roles are not separate and parallel. Instead, they are constantly intersecting which sometimes makes both jobs better and other times brings about unique difficulties.” Her second (thought-provoking) post is “The Road to Success.”
I’m excited to read future posts from the Math Mamas blog. Do you have stories to share about STEM careers and parenthood or suggestions for making STEM more inclusive of parents? Share your thoughts in the comments below or reach out to me on Twitter @writesRCrowell!
While I was recently cruising through the mathematical blogosphere, I landed on a post I enjoyed on Dan Meyer’s dy/dan blog. The post, titled “Stats Teachers: 2019 Is Your Year,” discusses proposed tax rates and using classroom examples to help students become “smarter about taxes in a day than fully half of Americans have been in their entire lives.”
In the first post, Meyer compares mistakes, which he defines as “the difference between what I did and what I meant to Do” and incorrect answers. He offers teachers this challenge:
“Our students offer us windows and we exchange them for mirrors. The next time you see an answer that is incorrect, don’t remind yourself about the right way to talk about a mistake. It probably isn’t a mistake. Ask yourself instead, ‘What question did this student answer correctly? What aspects of her thinking can I see through this window? Why would I want a mirror when this window is so much more interesting?’
In the second post, Meyer remarks on reader-submitted questions and comments about implementing this approach to responding to incorrect answers in the classroom. Here’s one of my favorite sections:
“I don’t have any problem saying a student’s answer is incorrect, that they didn’t correctly answer the question I was trying to ask. But my favorite mathematical questions defy categories like ‘correct’ and ‘incorrect’ entirely:
So how would you describe the pattern?
What do you think will happen next?
Would a table, equation, or graph be more useful to you here?
How are you thinking about the question right now?
What extra information do you think would be helpful?
How can you call any answer to those questions a mistake or incorrect? What would that even mean? Those descriptions feel inadequate next to the complexity of the mathematical ideas contained in those answers, which I interpret as a signal that I’m asking questions that matter.”
Come for the story of an interesting adventure; stay insights such as these:
From Meyer: “Children are teenagers are adults. I was struck hard by the similarities between all the different ages I’ve taught. People of all ages like puzzles. They respond well to the techniques of storytelling. Unless they’re wildly misplaced, they come to your class with some informal understanding of your lesson. They appreciate it when you try to surface that understanding, revoice it, challenge it, and help them formalize it.”
From Joshua, a commenter: “Everyone has their right to an aesthetic preference for particular areas/topics/levels of math. The cool thing about math is that (almost) every topic can be really fun to investigate because it is open to a deeper exploration of pattern, structure, and connections to other areas. A weakness of math education is that again, almost every topic can be presented in a way that is closed, shallow, isolated, and boring.”
We have a problem. I feel like we’re just not communicating properly. I hear you, but I don’t understand you. I appreciate that you have something to say, I just don’t like the way you’re saying it. I’m not angry, it’s just that I know you can do better. Don’t worry, I’m not going to leave you. But, dear speaker, I just wish you would do better.
In 1992 the physicist N. David Mermin wrote an article for Physics Today, in which he describes Physics talks saying, “the only pleasure it affords is the relief that washes over you as you realize, finally, that perhaps the end is in sight.” In math, we tend to suffer from a similar disaffectedness. Talks that just go on and on interminably and it’s not clear that a single person in the room knows what’s going on. Sometimes it even feels like that’s just the acceptable norm.
A few years ago one of those really validating bits of research came out confirming that boring speakers really do go on longer than exciting ones. Being exciting is hard. We can’t reasonably expect exciting speakers all the time. But keeping an eye on the time is not only easy, it’s a minimum display of respect that you can demonstrate for your audience.
The matter of giving a talk that your audience can actually understand, is a different thing altogether.
It’s been my experience that in the culture of mathematics, there is a certain fear of giving a talk that can be perceived as too elementary, causing speakers to whiplash too far in the other direction. Myriad are the talks I’ve seen aimed at the “experts” in the room, and typically the “experts” in the room consist of a cohort of 0 to 1 individuals who would likely be very happy to speak with you privately for 20 minutes after your talk.
And I guess it’s ok for only one person in the room to understand you by the very end, but everyone in the room should understand the first 5 minutes, half of people should understand the first 30 minutes (I know, ambitious) and, ok, from there I guess you can go nuts. And I use the word “understand” quite loosely here, give us definitions, give us notation, give us a chance. I’m talking to you, colloquium speaker who opened with “Let G be the k-dimensional Grassmanian on V.”
And I say this all with an understanding that a Colloquium, an Algebra, Combinatorics, and Geometry Seminar, and a Number Theory Seminar will likely have a different expectation of prerequisite knowledge.
As the imaginary Professer Mozart in Mermin’s article suggests, “strive to place as far as possible from the beginning the grim moment when more than 90% of your audience is able to make sense of less than 10% of anything you say.”
Having said all of this, the burden doesn’t rest entirely on the shoulders of the speaker. It’s also important to be a good audience member. When I was a graduate student someone pointed me towards the “3 Things” exercise that Ravi Vakil wrote about many years ago. The idea is, from any good talk you should be able to write down three things. Whether definitions, questions, ideas, theorems, or the like, these should be things that are interesting to you. In a way, these things represent hand-holds. These are places where, regardless of how divergent your research area is from the speaker, you are able to catch a little relatable tidbit that you can put in the context of your own knowledge.
This worked well for me as a graduate student. It certainly made me more attentive during talks, and had an added (perhaps unintended) bonus, that when I wasn’t able to find three things in a talk, I would walk around feeling righteously indignant for having sat blamelessly, martyrlike, through a terrible talk.
I always write down one clear goal and circle it. In likelihood I won’t remember a talk I saw 2 years ago, but I can easily flip back in my notebook and recall what someone was up to back in 2016. Bonus points if you can articulate at least one obstruction to achieving the goal.
Since then, in my wisdom and maturity, I’ve added two more components to the exercise. I try to write down a single one-sentence “goal” at the end of the talk. If a talk is good (and I pay close attention) it should always be possible to write down at least one goal or large overarching purpose of the research described. I also try to write down one purposeful question. If you haven’t done it before, this is good training for being a session chair, a position in which (in my opinion) it is your duty to be armed with a question after every talk, just in case.
And finally, as I always tell a young friend of mine when she complains about going to church, they can make you go, but they can’t make you listen. If it’s boring, congratulations, you’ve just earned yourself 45 minutes to daydream and think about other problems that are more interesting to you, or failing that, daydream about your fantasy tiny home or whatever.
A seminar is like a special gift exchange between the speaker and the listener. So please join me in this pledge to always take only the allotted time, throw your audience a lifeline early and often, strive to be exciting — and failing that, aim for just being excited — and commit to hunting for interesting things for as long as you possibly can. If you have some more thoughts about this, ideas about giving better talks, tips and tricks for being an active listener, or if you totally disagree with me, feel free to let me know @extremefriday.
“Which MATHEMATICAL superpower would you prefer?” Ben Orlin asked on his Math with Bad Drawings blog. He offered readers three superpower options: super approximation, or “the ability to immediately answer any numerical question to within 20% accuracy,” super visualization, or “the ability to picture extra spatial dimensions in your mind” and super counterexamples, which is “the ability to immediately furnish the counterexample to any statement where one exists.” His post also includes an option to cast a vote for one of those powers. (I chose super visualization.)
I love Orlin’s lighthearted question, but thinking about superpowers inspired me to ponder how society distributes or withholds power and privilege.
So, for this post, let’s discuss something different related to the theme of Black History Month and power.
Let’s suppose the existence of a higher mathematical being capable of endowing people with mathematical superpowers. Here are some power problems that need to be addressed to make the mathematics community a more welcoming and opportunity-filled one for Black mathematicians and students. In the context of the superpower conversation, I argue that they need to be fixed as soon as possible, but definitely before the universe bestows people with any mathematical superpowers (no matter how cool-sounding the superpowers might be). After all, how can we justify — even in an imaginary scenario — gifting superpowers to some people when so much inequality already exists with the power structure we already have?
Many Black students still aren’t receiving an equitable mathematics education.
“Equity for black learners in math education is a delusion — a compromise consistent with other historical compromises; undergirded by antiblackness; rooted in the fictions and fantasies of white imaginaries and white benevolence; held hostage by white sensibilities and sensitivities; and characterized, at best, by incremental changes that do little to threaten the maintenance of white supremacy and racial hierarchies inside or outside of mathematics education,” according to a partial transcript of Danny Martin’s talk “Taking a Knee in Math Education,” which he gave at the 2018 National Council of Teachers of Mathematics Annual Meeting and Exposition. (There are also posts about this talk on the arbitrarilyclose and HerMathness blogs.)
In a study of 25 mathematics classrooms in middle schools that were either predominantly Black or white, researchers found that “White teachers in predominantly black schools were more likely than white teachers in predominantly white schools, or black teachers in predominantly black schools, to respond in negative ways to student behavior, emotions and ability. For example, their response to behavioral issues was more likely to include multiple, intense back-and-forth exchanges more apt to escalate problems than solve them,” according to a news release about the study.
“The need for targeted recruitment of black teachers is as critical as ever – as is the need to train teachers of all backgrounds to handle conflicts in ways that encourage student success without showing racial bias. This can include learning to avoid drawing the class’ attention to an individual student’s behavioral issues, and learning not to unnecessarily escalate conflicts with threats to call home or send a student to the principal. Instead, they can try to understand the cause of the behavioral issue, handle it privately with the student, and approach the student with warmth,” Dan Battey, lead author on the study, noted in the news release.
Space: We need to make more of it for Black mathematicians.
“When a black woman centers herself and demands equal access, it is nothing short of revolutionary. What you can do to change math? Make. Space. For. Me,” Piper Harron wrote in a 2016 post for The Liberated Mathematician blog.
White supremacy is pretty adaptable; taking easy and practical steps to increase diversity is not in itself dismantling privilege, and often privilege will find a way to prevail…What I want to talk about is ending oppression. What I want to do is upset the status quo.
So one day I sat down and thought, what is my real, completely impractical, unfeasible, non-starter answer to what white men can do? It’s they can get out the way; they can quit. Not just increase the number of seats I have at the table, but actually leave the table all together.
Why bother advising the impossible? To get people to think. I expected people to understand I offered no practical solutions, but to challenge themselves to reevaluate their current practices.
Ditto with highlighting the accomplishments of Black mathematicians.
One of my goals for this year is to write about more mathematicians who are Black, as well as members of other underrepresented groups. So, if you know of a math blogger from an underrepresented group (or are such a blogger yourself), please reach out to me in the comments or on Twitter @writesRCrowell.
If you could have any mathematical superpower, what would you choose?
Does Pi Day have anything on the newly announced Thirdsday? Photo credit: Amit Patel via Wikimedia CC
I might be stating the obvious here, but the longest partial government shutdown to date gave the U.S. a rocky start to 2019. Though the government has re-opened (read the AMS announcement about it here), a long-term solution still needs to be reached or America will face another partial shutdown. I’ll admit all of this has put me in a funk. I’ve been alternating between feeling strong concern about at least three things (which are probably just the tip of the iceberg when it comes to the shutdown’s impacts):
1. The families of federal workers and contractors whose jobs were affected by the shutdown
3. Joshua Tree and other national parks that were so damaged during the shutdown that they likely won’t fully recover in our lifetimes
Surely I’m not the only one in search of some math-based cheer to distract me from what’s happening in the government or, say, the polar vortex that’s hit the Midwest . Here’s roundup of a few cool math-related things I’ve compiled: Continue reading →
Multiple news sites recently reported about a wedding planned between two mathematicians in which the happy couple decided to reveal their guests’ dinner seating arrangements as the answers to math problems.
A second important result in quantum computing came from Ewin Tang, an 18-year old recent graduate of the University of Texas, Austin. From prior results in quantum computing it was thought that a certain Netflix-type recommendation algorithms was a strong candidate for exponential speedup with quantum algorithms as opposed to classical algorithms. But in this paper, Tang showed that this is not actually the case, by giving a “quantum-inspired” classical algorithm.
In gender equality news, Harvard hired its second ever female tenured professor.
The last senior female professor hire was Sophie Morel in 2009. She left the department after three years. Hopefully this will be a solid first step toward gender parity or at least non-zero representation.
Worst of 2018
A major bummer of 2018 was the dissolution of the partnership between the AMS and the MAA to follow the 2021 Joint Meetings. Motivated by a desire to steer resources in a direction most beneficial to its members, the MAA will focus on the annual MathFest as its national meeting. This is sad news since the JMM is such a cherished institution, and also troubling since it seems to magnify the split between the teaching of math and the doing of math. You can read a more in depth statement on this decision in MAA Focus.
And as I’ve done for the lastseveral years I have an update on the status of the ABC Conjecture, and I’m afraid it doesn’t look so good. Very broadly, a dealbreaking hole has finally been found in Mochizuki’s work, which has been under discussion for the past 6 years. The full saga is nicely told by Erica Klarreich for Quanta. With this the ABC Conjecture can once again be regarded as open (that is, if you ever stopped regarding it as such).
To everyone traveling to the 2019 JMM next month, have a safe and pleasant journey. I’ll be there tweeting and blogging the whole thing @extremefriday. Hope to see you in the new year!
[01/06/19 Editors Note: In the original post the author referred to Ewin Tang as Edwin Tang. The post has been corrected and updated]
Today, I’m reflecting on vision and mathematics. That’s largely because as I write this, I’m also simultaneously evaluating whether a new computer I received as an early Christmas present is going to be a good fit for me or if I’ll need to return it in favor of one that I find more accessible given a specific set of eye muscle problems I have. Those eye muscle problems cause images to double, switch back and forth, or even twist in a way that can best be described as appearing to be melted.
Even as a kid, I thought “wandering eyes” and “lazy eye” were pretty mild descriptors for what I was experiencing: wonky eyes that mostly seemed to operate out of their own accord and without consulting one another. For instance, sometimes I just couldn’t keep one eye from turning in towards my nose. So, for a good chunk of the day, I would be trying to learn or play while also getting constant and disruptive views of my nose. Without being able to do anything to change the images I was receiving. Talk about distracting and frustrating. Often, glasses on or glasses off, I couldn’t see very well.
Somehow – I’m still not 100% certain how – I thrived academically, though I was never given the option of receiving academic accommodations for my vision issues until I reached college. Even then, my vision issues greatly impacted my education and the quality of life I experienced while I was in school. I had to work incredibly hard to master concepts that I knew wouldn’t be so challenging if I wasn’t visually impaired. I graduated, triumphant but burned out from having to push myself so hard to excel despite my visual disability, and uncertain that I wanted to attend graduate school, despite my deep love of math.
Things are better now. After I was told at age 24 that my only option for ameliorating my double-vision was for me to wear an eye patch at all times for the rest of my life, I got fed up and pursued a direction that is still controversial in the medical community: vision therapy. Specifically, mine is a combination of exercises and a virtual reality program in which I play games designed to help my eyes work together more effectively. Two years into therapy, things are better now, but I still have a long way to go on my journey to better vision.
Reflecting on all of this, I don’t think we talk enough about mathematics and vision, or about how vision problems can affect mathematical education. As a student, when I was struggling because of vision issues, sometimes I felt lost about how to begin discussions with professors about the medical challenges I was facing and I often wasn’t aware of the options that might have been available to help me in different ways.
Below is a short list of pieces related to the topic of mathematics and vision problems. Continue reading →
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