The non-academic job search (Part 0)-Deciding to leave

26 Oct

Hi!  Pregnancy this time around has been kicking my butt, but I’m hoping as second trimester goes on that I’ll start feeling better and posting more/being more of an upright person.  Here’s the post, which is a mishmash of thoughts from the past year.

If you missed Part 1 of this, that doesn’t matter because it comes after!  But here’s the link just in case you wanted to see it.  I spend that post talking about the steps I took after deciding to leave, but realized that lots of people are in the position that I’m in and might want to know how I decided to leave mathademia, which has been my happy home for years (sometimes larger than I’d like to admit).

A mentor of mine from my undergraduate days wrote a fantastic piece about going from his tenure-track job to working for Google; I recommend the whole thing.  He talks about money, time, intellectual challenge, and committee work as his factors. Here’s an excerpt:

At the time, my assessment of the private sector  vs. academia was pretty bleak: Your salary is higher, but the price you pay for that is longer hours at a mind-numbing job with a micro-managing boss. But it turns out, things aren’t actually that extreme. In fact, there are a lot of nice things about the private sector, that make the comparison much more subtle, even if you take money completely out of the picture.

When I started seriously thinking about my future, I gave him a call and asked for advice on leaving academia and making the decision.  He strongly suggested picking up this book, which I also highly recommend:

This book made me turn from despairing and feeling like a failure to hopeful and inspired- it’s full of stories of people with Ph.D.s who went on to do other non-academic things, and concrete advice for turning a CV into a resume, etc.  I read this book before the other ones (parachute, in transition).  I also talked to as many non-academic math Ph.D.s as I could (or really, just the ones I ran into, which is a surprising number of people!  We’re everywhere!) about their transitions and how they chose their lives.

A lot of applied math or stat people are fine.  They do, in general, big data/data science and program and make lots of money (also, pure math people who know how to and enjoy programming also make lots of money and are fine).  I’ve heard of one particular data science fellowship specifically for master’s/Ph.D. students, and I’m sure there are others out there.  Also my friend Jeremy definitely does something with data now and is very nice and helpful and I’m just volunteering him now to talk to my blog readers (and point you toward his blog if this is something you are interested in).

That hopefulness really buoyed me forward, as did reading Jesse’s second blog post on this topic.  Here’s an excerpt again contrasting mathademia with non-academia:

In the end, the process of getting a non-academic job can be long and complex. At the beginning, it feels completely hopeless, but the more you learn and the more non-academics you talk to, the better it gets. And here’s the kicker: There are a lot of jobs out there where the supply and demand dynamics are completely the opposite of academia – where employers are desperately seeking qualified applicants. Once you find your way there, and see what it’s like applying for a job where you’re NOT one of 500 applicants for a single position, it’s completely worth it.

I ended up writing a big board of pros and cons of staying in academia- the biggest con for me is the moving/not having a choice of where to live and raise my family.  But plenty of academics successfully have families, so this con might not be as big to you.  The biggest pro is research/choosing what problems to work on, but that definitely did not outweigh the lack of control in where to live.  Of course my situation is a little different because I have a relatively immobile spouse (lots of professors seem to be married to other professors, doctors, or lawyers rather than high-power financial software developers), and if he wasn’t in the picture maybe my pro/con weights would be different.

Anyways, I agonized over this for a few months, reading that book, thinking about what people said.  One former post-doc, now software developer, told me he hates that he works “for someone else’s dream” vs. when he did his own research.  I guess that’s why they pay him the big bucks (or, y’know, at least some bucks).

When I did an ethnographic research project in Vietnam in 2009, one mathematician told me “what do I need money for?  I travel, I do what I love, I eat well, what would I spend more money on?”  My advisor told me about an exchange he had with a family member, where they asked him if he would do his job even without the money.  He said yes (though probably less of it).  It’s a theme I’ve run into a lot with mathematicians: mathematicians really, REALLY love math and/or teaching.

Back in 2012, I watched a video of an old friend of mine teaching a lesson about logarithms.  She LOVED teaching (and math).  Here’s a great minute-long clip.  You can tell just by watching how much she LOVED teaching.

Thinking about her, and the Vietnamese woman I’d spoken to those years ago, I just couldn’t compare my passion for these things to theirs.  Not to say that you have to be super passionate about your job (sometimes a job really is just a job), but if you have the luxury of making a choice, why not be a little picky?

I had to wrestle with feeling like a failure for not going into academia (this is a real thing) even though my advisor and others explicitly told me that I am not at all a failure for not following their path.  Eventually I had to listen to myself/the advice I’d been given a long time ago: “Swim in your own lane.”  I even say this at the beginning of this video.

Anyway, it’s a long and personal journey, and as a Ph.D. friend in industry once told me, “the hardest thing about leaving academia is deciding to leave academia.”  I can’t say I agree wholeheartedly with that yet (I still don’t have a job for next year), but I can definitely say that it was hard, and I’m around for you if you want to reach out and talk to me about it (contact info is all over this blog).


Peachberry pie, and news

11 Oct

Hello!  You may be wondering where I’ve been for three weeks.  Well, I’m still in Texas, and I have this old draft lying around that I never posted.  News at the end of the post!

I don’t know about where you are, but here in Texas it’s still summer and peach season.  I’ve made four peach pies in the last two weeks because they’re so cheap, so easy, and sooooo yummy.  I didn’t grow up eating a lot of peaches (I’m from Minnesota), but when I saw them for 88 cents a pound at the grocery store I remembered all the peach cobbler I’ve had in my travels since going to college.  Also I remembered that I still own the Moosewood cookbook, which definitely has an easy recipe for peach pie in it.

Of course, me being me I was unprepared with the number of peaches I had (I bought enough I promise but then we ate some oops), so I threw in some blackberries and strawberries I had lying around for one pie, and some blueberries in another, and the one in the oven right now is just peach.

For fruit pies, it’s nice to let the fruit macerate for a few minutes so that the sugar can suck the juices out.  So I make the filling first, then make the crust.  Peel and chop peaches, berries, etc. to make about six cups of filling.  Each medium-large peach gives a little less than a cup of peach slices, so with four peaches I had to add a dozen strawberries and a handful of blackberries.  Sprinkle the fruit with sugar and lemon juice and let sit while you make the crust.


It’s not the secret to world peach but my news is berry exciting.

Generally with pies I buy premade frozen pie crusts because I am lazy, but sometimes I’ll do the slightly less lazy mix-and-pat in the pie pan which gives you a nice oil-based slightly salty crust that’s very flaky and tender, or I’ll do the much less lazy butter-based pie crust that I used in this pie.  Honestly I prefer pie crusts made with a mix of shortening for texture and butter for flavor, but shortening freaks me out so I don’t have it in my house.


You’d butter scroll to the end of the post

This is the Moosewood pie crust recipe, where you cut together butter with flour and mix in cold liquid until it’s dough.  Pretty easy!  I used a knife to cut the butter into these small pieces, and a fork to break it into the dough until it looks like coarse crumbs and there’s no butter chunks bigger than a pea.


You won’t fork-ive yourself if you don’t read the end

Then add your liquid and mix it with your fork, then with your hands, and roll it out on a floured surface.  I LOVE my French rolling pin the way I love my mortar and pestle- I’m a very tactile person and these things feel good! Roll out the dough to just a bit bigger than the pie tin, and then carefully drape it over the whole thing.  Trim the edges and make a pretty design on the crust if you want (I am not a prettyfying person so I just leave it plain).

Now you’re ready to finish the filling!  Preheat the oven now, and add the flour and spices to the filling (cinnamon goes with every fruit!)  Gently and thoroughly toss, so all the fruit pieces have some sticky flour on them.  We add flour so you don’t have soup inside a pie crust- I think adding a little cornstarch mixed with berry juices would also work.


Glisten up, folks, cup your ears because I’ve got something to say

If I’m using a frozen pie crust/don’t have that much time, I just top the pie with the second pie crust, cut some slits in it to vent, and bake it.  But I waaaay prefer fruit pies with streusel topping.  Since I have a toddler, our house always has Ritz crackers in it.  Use a rolling pin to crush a sleeve of Ritz crackers- you can actually do this in the sleeve with little mess if you’re careful, or toss them in a plastic bag and whack away.

Then mix in melted butter, brown sugar, and that ever-present cinnamon.  Pour the fruit in the crust, pat on the streusel topping, and toss it in that preheated oven.  I like to put pie on a baking pan/cookie sheet in case of overflow (the bottom of my oven is a gross mess from previous drips).  Or put the baking sheet on the rack below.  Or forget it, like I did in this photo:


All alone and pie-tiful in the oven.  What a pie-ty if it drips (this one did not drip though!)

Let sit for at least 15 minutes after baking so the inside cools a bit and glops up, then serve warm with vanilla ice cream (yummmm!)  We ate it too fast for me to take photos of the finished pie.



Okay, time for NEWS/partial explanation for why I haven’t been posting.  I’m having another baby!!!  She’s due in March!  She’s also making my life a little complicated; I’d forgotten that I spent most of first trimester last time throwing up and lying down.  This time I laid down a lot, didn’t throw up a ton, but did have a lot of pain!  Now I’m into second trimester and ready to be a person again.  And by this time next year, my daughter will be becoming a person too!  Also, my son turned two last week, which is cool because those of you who have been reading this blog for a long time were there when I got engaged, married, and had my first baby.  Yay!!!

Peachberry pie (adapted from the Moosewood cookbook and allrecipes).

Crust: 1 c flour

4 TB (half a stick) very cold butter

2 TB cold water or milk

Filling: 6 c sliced fruit (6 peaches, or peaches and enough berries to fill in the rest)

1/4 c sugar

2 TB lemon juice (or squeeze half a lemon)

3 TB flour

1 tsp cinnamon

Topping: 1 c crushed Ritz crackers (about one sleeve)

1/2 c brown sugar

1/2 tsp cinnamon

4 TB (other half of the stick) butter, melted

  1. Mix the fruit with the sugar and lemon juice, let sit.
  2. Cut the butter into tiny pieces and mix with the flour for crust, until very small pieces (smaller than a pea) remain.  Mix in liquid teaspoon by teaspoon until a dough forms.  Roll out to bigger than the pie pan, and carefully place into pie pan.  Trim crust.
  3. Mix the flour and cinnamon for filling, gently mix into the macerated fruit mixture.  Pour into prepared crust.
  4. Preheat oven to 375.
  5. Crush the Ritz crackers, mix with brown sugar and cinnamon.  Melt the butter, and mix with the topping mix.  Pat filling evenly onto pie.
  6. Bake for 40 minutes, until bubbly on the edges and golden brown on top and crust.  Serve warm with ice cream

Carnival of Mathematics 138

19 Sep

I am super pumped to be hosting the 138th Carnival of Mathematics, a monthly round-up of great stuff on the internet that has to do with math.  Last month it was hosted over on the AMS Blog on Math Blogs by Anna Haensch (who also has a lovely podcast called The Other Half ) and Evelyn Lamb (my fairy blogmother who also writes for Scientific American, Slate, etc.).  Curiously, the first thing that came up when I looked up “138” was a 1978 song by the horror punk band The Misfits:

A little bit catchy, but not quite my cup of tea.  What is my cup of tea?  An integer sequence that does not appear in the amazing OEIS!  138 is the smallest product of three primes such that the third is the concatenation of the first two: so 138 is 2\cdot 3\cdot 23, 777 is 3\cdot 7 \cdot 37, and 4642 and 10263 are the next in this sequence (I applied for an account to OEIS to submit this, so if you find a smaller one or the next several in the sequence let me know).  So off we go, to venture into the great unknown (aka the internet)!  This month we have a fun mix of grammar, history/sociology, math, and games!

  • First, grammar: Manun Shah over at Math Misery [which hosted CoM#136] posted Does 11=8 + 3? to chat about linguistics and mathematics.  If you love those memes about the Oxford comma, this post might be right up your alley.  My favorite sentence: “I bought orange juice and dishwasher detergent and drank it for breakfast.”  He argues we should think more about linguistics when teaching math, and the implicit biases that language might have on students as they learn mathematical reasoning.
  • Also in grammar, Thomas Oléron Evans of Mathistophiles posted Understanding an Abused Unit: The Kilometre-Hour, which delves deeper into a specific example of how common language can hurt mathematical understanding, and he uses a DELIGHTFUL example of turtles.  Favorite sentence here: “Unless they sidestep across the beach, of course, like some sort of synchronised reptilian dressage.”  Here’s an amazing graph from his example:

A delightful graph from Mathistophiles

  • Keeping up with his fun theme, Thomas submitted a SUPER FUN game by David Peter called cube composer which is all about functions.  Do please do go play it!  It’s so fun!  It’s an intuitive individual puzzle game, and you can fly through the levels.  It also remembers your progress, but you can skip levels if you want too.  Here’s a screenshot of me picking random functions and not solving the puzzle:

A screenshot of me poorly playing cube composer

  • A high school math teacher friend texted me about another game called Square It on a website for math educators supported by the University of Cambridge.  We proceeded to lose, lose, lose, and continue to lose against the computer.  I played against my spouse a few times, and he won his first time.  Those darn programmers and their algorithm-minds!  For the record I did eventually win.  This one is faster and lighter than cube composer, and it offers different mathematical questions to think about in different size grids.

Here I am losing in Square It to a computer

Square It! is also great to play with kids.  Two more submissions are also kid-friendly.  

  • Brent Yorgey of Math Less Traveled submitted his post about Making Tesselations, which delves into the math behind the delightful new children’s book Tessalation! that I will definitely be reading to my toddler.  In his post he also talks about ants on a doughnut, and y’all know how we mathematicians love our analogies to lean toward the absurd.  Here’s a wonderful joke Brent nonchalantly sneaks into his post:  “The ant is so small that it can’t tell that the surface it lives on is curved. To the ant, it just looks flat. (You may know some tiny creatures in a similar situation who live on a sphere.)”  So fun.
  • Matthew Scroggs submitted a post dear to my heart, written by Belgin Seymenoglu over at Chalkdust Magazine: an ode to the delightful half hour film Donald in Mathemagic Land.  The post includes a link to the 1959 cartoon, which I’ve watched many times since I first saw it when I was 15.  I guess this is a fun month, because I really really recommend watching this cute and funny cartoon that includes actual math in it.

Now for a sort of random assortment of history/sociology/whatever posts that have to do with math:

  • Paul Plowman wrote a 2 minute 20 second guitar song using the number e, and posted about it over on his blog as Transcendental Music.  Sort of a silly but fun little exercise like memorizing digits of \pi, and the riff sounds nice.
  •  Poppy Brady submitted a story she wrote for The Voice about Nira Chamberlain, titled Teachers said I could be a boxer, but Never a Mathematician, one of those feel-good stories about mathematicians.  One fun quote by Chamberlain: “I also like what British mathematician Sir John Kingman once said that ‘mathematicians are better if they stay a bit childish and play the game as a game.’”  I think that keeps in line with our theme this month!
  • Over in Nature, Davide Castelvecchi wrote a news story about how the Majority of mathematicians hail from just 24 scientific ‘families’, a result by Floriana Gargiulo who analyzed the Mathematics Genealogy Project.  Every grad student has used the MGP to stalk their advisor/potential advisor to see their lineage, and you can print out a tree and give it to your advisor as a defense present!  So it was fun to read about someone actually analyzing this trove of data.
  • Finally, saving the best for last, the brilliant Evelyn Lamb, explainer extraordinaire, wrote a post on Roots of Unity at Scientific American about How Converting Between Addition and Multiplication makes Math Easier.  If you don’t follow/read everything that Evelyn writes, you really should.  So approachable and so lucid.  She also wrote a fun piece about using different bases for your birthday candles, so you should read these two articles, follow her on Twitter, and tell her happy birthday!

If you run into anything interesting on the math-internet from now until October 15th, submit them to the Carnival of Mathematics site; the Carnival will be hosted next month at the online magazine Gonit Sora.  Hope you had as much fun as I did with the submissions this month!

My mom’s Banh Xeo (Vietnamese turmeric crepes)

7 Sep

Over the past twenty years or so, bánh xèo has been a mainstay of family and friend gatherings if my mom is around.  Yen’s visiting home from college?  Better make bánh xèo!  You want to have some friends over for dinner?  Time for bánh xèo!  It’s a Saturday in October and the cousins are coming around?  Let’s do some bánh xèo, baby!

These are a super fun party food (where the party is the food): everyone gets a plate and a little saucer for dipping sauce, and the giant fresh pancakes go on platters in the middle.  You take a small amount with your chopsticks, trying to get the perfect mix of batter, onions, bean sprouts, and meat/seafood, and wrap it in a little taco of lettuce, mint, apple/cucumber, and whatever other herbs you have on hand.  Dip the whole taco in your sauce and eat it in two or three bites.  Then do it again.  And everyone does it at once!


I don’t know about your storage capacity, but for me this is a mega-bite.

Note: these can definitely be made vegetarian or vegan.  The batter is vegan, and for filling we’ve had great luck with mushrooms, sprouts, and mung beans.  For the dipping sauce, substitute soy sauce for the fish sauce and add a little bit more lime and a little less sugar to balance out the saltiness.

I’m not usually a huge mise en place fan; I like chopping while things are cooking, but bánh xèo happen so fast that it’s worth it to put in extra prep.  For eating, you need to wash all your vegetables and put them out on a platter.  You’ll probably have time to make the dipping sauce while a pancake is cooking, but it takes a lot of time to pluck Vietnamese perilla (shiso would work in a pinch) and mint leaves off their stems, leaf lettuce, thinly slice cucumbers and apples, etc.  So lay those out.  Now the batter has to rest for ten minutes or so after mixing it, so do that before you start chopping your raw ingredients.


I want to put a pun here but I can’t because the perspectives on this photo are too confusing.  The ingredients are on a counter; my feet are several feet below; the bowl on the right is inside a sink that the cutting board is hovering over.  

Growing up we always had squid in our bánh xèo, but we stopped doing that when we moved away from easily accessible Asian markets.  So now it’s mostly pork (a lean, unfatty cut like tenderloin is good here) and shrimp, mainstays of Vietnamese cooking.  My mom prefers buying the unpeeled shrimp because she says they’re sweeter and more flavorful (I agree), and we slice them in half down the spine so they cook super fast.  You want very thinly sliced pork; it helps if it’s chilled.  Also thinly sliced onions are key, as well as a ton of green onion (the more the better).  My mom puts in two bunches of sliced up green onion per packet of batter, which makes around 6-8 very large servings (depending on the size of your pan, that’s 10-20 pancakes).  Hence the party food-nature of this dish.

The batter is important- if you’re super hardcore I guess you could make your own, but we always buy from a bag.  Our favorite is the one with elephants on it, below–certain other brands are a little too gluey or not crispy enough, or include coconut flour and pretend that coconut flour+water=coconut milk.  If you can’t find Bon Con Voi Banh Xeo batter, just try to buy one that requires adding coconut milk.  Then follow the instructions on the bag: mix in the turmeric, a can of coconut milk, and a can or two of water (read the label).  Let sit while you chop the other stuff.


Photo from this mysteriously empty website, Nguyen Eternal.  You don’t need to get on a boat to buy this bot, which is made here in the USA!  (Bot means flour in Vietnamese).


In the shadow universe, the copy of me is so jealous of this batter.  She’s a green un-Yen. (Yes I have made this pun before no it does not get old.)

Now it’s time to cook!  Mix those prechopped green onions into the batter.  Heat up your nonstick skillet (or two if you’re ambitious).  Add in a bit of oil and a handful of thinly sliced onions, then after 30 seconds or so put in your thinly sliced pork and shrimp and cook them for a minute or two, until they’re done.


Stop hogging all the space!  There’s MUCH ROOM in the pan; even the shrimps deserve some breathing room.

Now ladle on just enough of the batter to cover the pan if you swirl it.  Think the thinness of crepes.  I’d lean toward ladling on not enough, swirl, and then add in a bit more to fill the pan rather than having a thick gluey pancake.


If the band Rudimental were making banh xeo, I bet they’d invite Ed Sheeran over for this step, so they could lay-it-all (LADLE) on him.

Now you’ll have a pale daffodil soft thing with some cooked meat inside it, and a clearly slightly liquid middle.  Fill it with a generous handful of bean sprouts (mung beans if you’re into that sort of thing too), and cover it with a lid to lightly steam the sprouts while cooking the pancake.  Give it about a minute (so this whole process is taking you about 5 minutes per pancake), until the pancake is no longer pale but a golden turmeric color, and its visibly cooked.


I should invite my cousin Scott over and ask him to help me cook this, and then try to gently prod him into calling the middle uncooked portion liquid gold.  Take that, furniture polish!  

Gently fold it in half like an omelet, and slide it out of the pan onto a waiting plate.  Serve immediately with dipping sauce and that premade plate of veggies!


My mom’s banh xeo.  Makes so much (serves 8 hungry people)

1 package of banh xeo flour

1 can coconut milk

2-3 bunches of green onion

2 lb pork tenderloin or butt or any non-fatty cut

2 lb shrimp

1 big onion (yellow or white is fine)

2 packages of bean sprouts

2 heads of lettuce (I prefer red leaf, my mom likes Romaine but she is wrong here)

2 cucumbers, 2 Fuji apples

2 bunches of Vietnamese perilla or shiso, 1-2 bunches of cilantro, 1-2 bunches of mint (the regular grocery store mint is fine)

2 limes

2 TB Fish sauce

2 TB Sugar

1 carrot and a carrot-sized piece of daikon if you’re feeling ambitious (we did not)

  1. Batter: Finely chop up all your green onion, then follow package instructions.
  2. Veggies: Wash everything.  Leaf the lettuce and herbs, cut the apples and cucumbers into thin slices (cut the cucumber in thirds lengthwise, then cut into slices).
  3. Dipping sauce: Mix two tablespoons of sugar with the juice of the limes and 2 TB of water until dissolved.  Add in two tablespoons of fish sauce.  Taste.  Adjust levels of everything until it’s not too sweet, not too salty, and not too sour.  If it’s overpowering, add more water.  If you’re ambitious, finely grate the carrot and daikon into the sauce; they’ll slightly pickle while it’s sitting and offer some textural contrast when you eat.
  4. Pancakes: Thinly slice pork (about 1/8 of an inch thick if you can, 1 inch by 2 inch rectangles), peel shrimp and slice in half, thinly slice onion. Heat large skillet over medium high.  Add about 1 TB of neutral oil and half a handful of onion, stir.  Then add 4-8 pieces each of pork and shrimp and gently saute until just cooked.  Ladle only a little bit of batter over the cooked ingredients, and swirl to cover pan.  Edges should cook very quickly.
  5. Cover pancake with a handful of bean sprouts, then cover with a lid.  Leave for 1-2 minutes, until bean sprouts are slightly steamed and center of pancake is cooked and edges are lightly browned.  Fold in half with a spatula, slide onto a plate, and serve immediately with veggies and dipping sauce.

Note: you’ll be in the kitchen for a while with this; we usually have two or three pans going at once to feed a big crowd.

What is a “trigger warning”? What is a “safe space”?

26 Aug

This week a professor friend of mine posted and lauded the letter that University of Chicago president sent out to all incoming freshmen which said a bunch of reasonable and universal/noncontroversial stuff, and also this paragraph:

Our commitment to academic freedom means that we do not support so called ‘trigger warnings,’ we do not cancel invited speakers because their topics might prove controversial, and we do not condone the creation of intellectual ‘safe spaces’ where individuals can retreat from ideas and perspectives at odds with their own.

They, being a professor, then did some research into what exactly trigger warnings and safe spaces are, and then posted that this letter was “an embarrassment.”  So why did my friend have such a change of heart?  For that, let’s learn what these phrases mean.

trigger warning is a statement given before someone interacts with new material (e.g. a book, an article, a video, etc.) which alerts them of potentially disturbing content (e.g. graphic description of sexual violence, war scenes, etc.).  There’s a great op-ed piece in the NYT from last year that delves deeply into this:

Triggered reactions can be intense and unpleasant, and may even overtake our consciousness, as with a flashback experienced by a war veteran. But even more common conditions can have this effect. Think, for example, about the experience of intense nausea. It comes upon a person unbidden, without rational reflection. And you can no more reason your way out of it than you reasoned your way into it. It’s also hard, if not impossible, to engage productively with other matters while you are in the grip of it. You might say that such states temporarily eclipse our rational capacities.

The idea behind trigger warnings is that they give time for the reader/viewer/listener to prepare themselves or brace themselves for what’s coming, in hopes that they can rationally deal with the material.  In practice, they’re basically the same as the little box that says “this movie rated PG-13 for containing partial nudity” and most people can ignore them (idea from that op-ed).  There are many arguments out there against trigger warnings; one of the most cited is the “Coddling of the American Mind” article, where they analogize avoiding difficult subjects with phobias:

A person who is trapped in an elevator during a power outage may panic and think she is going to die. That frightening experience can change neural connections in her amygdala, leading to an elevator phobia. If you want this woman to retain her fear for life, you should help her avoid elevators.

There are great points in that article; namely, that turning disclaimers of difficult readings into optional readings does a disservice to students (they offer the example of professors not wanting to teach rape law).  I think the authors of this article and the professor of the first op-ed can agree that the point is for students to engage with difficult material.  However, the Atlantic piece authors believe that not including trigger warnings is the way to do so, while the NYT piece author believes the exact opposite.  So which is it?  Why the different views?

This is why mathematicians love definitions.  The Atlantic piece authors start with the same definition as I did, but then add another consequence:

Trigger warnings are alerts that professors are expected to issue if something in a course might cause a strong emotional response. For example, some students have called for warnings that Chinua Achebe’s Things Fall Apart describes racial violence and that F. Scott Fitzgerald’s The Great Gatsby portrays misogyny and physical abuse, so that students who have been previously victimized by racism or domestic violence can choose to avoid these works, which they believe might “trigger” a recurrence of past trauma.

And therein lies the problem!  Trigger warnings exist so that students can engage with a work, but the authors say they exist so students can choose to not do so.  This jumbled definition is why there seems to be a fundamental disconnect between some news sources which laud “not supporting trigger warnings” (The Federalist (conservative/libetartarian), Reason magazine (libertarian), Intellectual Takeout (conservative/liberal)) and those that do not (Slate (liberal), Vox (this is a great piece), New Republic (this is not as good as the Vox piece)).

Of course, nothing happens in a vacuum (besides math?).  This whole controversy is part of a larger trend as demographics change, political landscapes change, and universities change.  There are many examples in practice of students actively refusing to engage with material that might question their assumptions (first example that comes to my mind was the Duke freshmen not wanting to read the non-required recommendation “Fun Home”), and this is something that all these public intellectuals of various political backgrounds want to avoid.

There’s a lot to say about this, but I want to move on to the next definition, so I’ll leave you with this article by NYMagazine, which happily acknowledges that the U of C letter totally messes up on ‘trigger warnings’ and ‘safe spaces’ but also says that it has some important things to say.  Here’s a quote:

First, in addition to the absence of evidence that trigger warnings have any impact on the average college campuses, there’s also solid evidence that many of the tropes that have taken hold about “coddled” or“microaggressed” or “oversensitive” or anti-free-speech college students are seriously overblown. In many cases, these ideas have been bandied about so gleefully and frequently and uncritically by conservatives that the terms themselves have lost all meaning….But: There have absolutely been recent instances in which campus outrage has snowballed out of hand, in which protesters have actually impinged on the ability for real debate to take place, and these episodes matter.

Funnily enough the article refers to the controversy at Yale as also being disproportional, which I also wrote about in a similar vein as this post.

Next, a safe space is a physical location for marginalized people (historically LGBT folks) to exist with allies without fear of marginalization/hate speech.  Examples are church basements for Christian youth groups, gay bars, and the U Chicago LGBTQ Safe Space program.  The U of C letter refers to “intellectual safe spaces” as what it’s against, and includes a semi-definition as spaces where “individuals can retreat from ideas and perspectives at odds with their own.”  This is not a normal use of the term, and there again seems to be some confusion about what the phrase “safe space” means.  There’s a fantastic article on Vox that goes into what a safe space is and why it matters in depth:

You don’t have to explain to other black women why your hair is the way it is, she said, or what a certain word means, or countless other little cultural signifiers. “Everybody has a need to just be able to be themselves somewhere, without having to do that translation and without having to always be on guard to justify yourself.”

I liked this Vox Explainer article so much because it really delves into the reasons that people are against the idea of safe spaces.  To close this SUPER LONG blog post, here are the last three paragraphs from it:

Some people get upset because they don’t understand why they can’t be included in a certain group, or why their input on certain issues might not be welcome. A man might ask in good faith whether catcalls are really just “compliments” when women are trying to discuss their own experiences with street harassment, and he might be taken aback when those women get immediately upset or exasperated with him. To him, perhaps he was just asking an innocent question and trying to have an intellectual debate. But to the women, it’s pretty insulting to suggest that their life experiences are up for “debate” — plus they’ve heard remarks like these a hundred times, and nine times out of 10 it just derails the conversation, so they’re just sick of dealing with it.

The question of who belongs and who doesn’t, who is excluded and who isn’t, is a constant worry for most of us. But on top of the personal rejections that everyone faces in life, people in marginalized groups also have to face the feeling that society wasn’t really designed for them; that it considers them an afterthought at best. People in dominant cultural groups are used to rejection, but they’re probably not used to that kind of rejection. And they’re probably not used to being forced to pay attention to all the little social cues and codes that others pick up when trying to navigate a society that isn’t inherently made to fit them.

It’s not easy to deal with shame, hurt feelings, or fear during these kinds of cultural clashes. But particular spaces or identities are rarely the most productive things to blame for the strife. Inside or outside of safe spaces, the real problem is usually a failure of empathy, and the real solution is treating others with humility, respect, and compassion and being willing to learn from our own mistakes.


The non-academic job search (Part 1)

10 Aug

This may come as a surprise to you, but I’ve decided after much soul searching this year that I will not be applying for postdocs this fall and following the steps to success in mathademia.  Please do not take this as an indictment of academia (though I also feel that;  each of those words is a separate link about academia & motherhood), and I highly recommend postgraduate study in math if you’re interested in it (so does Evelyn Lamb on Slate!)

I have loved my time doing something I love on a flexible schedule which gave me lots of time to spend with my son, organize conferences, travel, blog, bake, exercise, and have the life I wanted.  It’s also been very difficult to have the highly unstructured environment, little oversight, and lack of regular collaboration.  Also very little money, but I married a person with an actual job so he can support the kid, and as a young 20-something I didn’t need much money (especially with math conferences covering travel and accommodation costs!)  So I love math, I love mathademia, but I don’t love teaching enough to do it full-time yet, and I don’t love research enough to want to move my family only to move them again 3 years later, and possibly 3 years after that again.  Hence I am starting my non-academic job search, and I thought y’all could join me on my journey.

When I first started toying with leaving academia, a friend of mine who also has a Ph.D. in math told me: the hardest thing about leaving academia is deciding to leave academia.  It’s been several months of pro/con lists, discussions with friends and family, and days of feeling sad and hopeless vs. days of feeling inspired.  You can’t help but feel like a failure when you make this decision, because all the exemplars of success that surround you are academics.  And that’s not even true for me; I try to know a range of people who do different things, but still in my day to day life and work it’s all professors etc.  Anyways, I got through this stage but it was rough.

Next I got some books!  Specifically, In Transition and What Color is Your Parachute? + Workbook.  I’d heard of Parachute, and I talked to a friend on the phone who used to be in consulting who said that everyone who left his company was given a copy of In Transition.  So I spent a few weeks working through these, which was mostly about soul-searching and there’s some practical advice in there about informational interviews.  In those weeks I also contacted career services at Yale (they have someone dedicated to alumni) and UT Austin and got some short and helpful advice.

I rejoined Amazon affiliates so I could put these pictures in this post.  Buy the books from links above, I get money!

After using the books and career people and narrowing down to a few fields that might interest me, I used LinkedIn and the internet to find companies in those fields in the locations I’m interested in (Austin, where we are now, and where our families are).  After a few days of searching, that got me a list of 50 or so companies in a file I called “first impressions”, which I then went through again and checked out all of their websites which took another several days.  I deleted all the ones I couldn’t imagine working for or which didn’t exist anymore, which brought me to a list of about 20 companies.

I figured once I started contacting people they’d google me, so I updated my website and made it pretty and fancy!  Then, using my CV as a starter and a template that one of the career counselors sent me, I wrote a resume targeting these fields.  Based on that, I updated my linkedin.  The website took me an afternoon several months ago, the resume took me two weeks.


How many pictures of myself did I put on my website?  A lot!

In the meantime several more companies got added to my list: I’m on several email lists and one alum sent out a note that his company is hiring, I looked on which ranks consulting companies on lots of metrics, including “work-life balance” and “least amount of travel” so that added a few companies, and I added a few dream companies (AAAS) which are not where I want to live but why not explore them and figure out what makes them dreams, and what things I want in the job I end up getting?

So about two weeks ago I added another sheet for contacts to this growing excel file which still has the name “first impressions”, and I used LinkedIn to find people who work at and people who used to work at each of those companies who are in my 2nd degree networks, and I wrote down their names and the name of my connection to them who can introduce us.  I also used LinkedIn to find people who were alums of any of the schools I’ve been affiliated with.  Now I’m starting to do informational interviews with those people- I asked for half hour phone conversations, but after the first one last week I think 15 minutes would suffice.  To get introduced, I write an email to our mutual connection and include at the bottom of the email an introductory note to the person I want to connect to, so our mutual friend can just forward it instead of having to write a whole long thing.

What’s great about informational interviewing people who used to work somewhere is they have no skin in the game if I end up at that company.  They can tell me why they left!

If you couldn’t tell this has been a summer-long project that I started at the end of May (at least, that’s when I redid my website).  I didn’t start out the summer knowing any of these things, neither what the tasks were nor how to do them, but I talked to that former consulting friend for an hour in May and he made all of these helpful recommendations, and I talked to the Yale alum counselor for a half hour in June, and I met with the UT counselor in July who gave me concrete advice as well.

I’ll keep you updated every few months with the progress of this!

Phylogenetic trees

2 Aug

I just listened to a two hour talk on phylogenetic trees, and they seem fun enough that I thought I’d share them with you!  Sorry I literally forgot to post last week, and then I realized I did not take notes on the stuff I wanted to post about (more pictures by Aaron Fenyes)- here’s a photo that I took and wanted to explain:


Something twisted representation something skein algebra something unit tangent bundle

Instead, you’ll read about the basics behind the research of my friend Gillian (no website), which is being supported somehow by people who want to know about cancer.  First, some background: the field of study of phylogenetic trees is inspired by and informs applications in evolutionary biology.  All of the life-forms today (or at some slice of time) all trace back to a root life-form at time 0.  Each current life-form follows a series of branching away from the root to get to where it is now

Then we can represent this evolution via a labeled rooted binary tree: the root represents the root life-form at time 0, and each branching of the tree represents a different evolution.  The labels mark which life-form is which.  Of course this model isn’t perfect (I can’t find the word for it but it’s a thing where two different species evolve separately from the same ancestor, then meet again and make one species.  If we were to represent this information in a graph, it’d make a cycle and not be a tree), but it’s been fruitful.


The rooted binary tree of the wikipedia picture: node 0 is the root life-form, then 1-7 are the life-forms at our current time.

Now let’s mathify this.  We’d like to encode the evolutionary information into our tree.  We’ve already decided that all life-forms will end at the same time (now), so if we just assign lengths to each of the non-leaf edges this will automatically determine the lengths of the leaf edges.  A leaf in a tree is a vertex with only one neighbor, and we call the edge leading to that vertex a leaf-edge.  Let’s call the non-leaf edges interior edges.  In the picture above, we have 5 non-leaf edges, which determine a tree with 7 leaves.  Using this exact configuration of labels and edges, we have five degrees of freedom: we can make those interior edges whatever lengths we want, as long as they are positive numbers.  So in math-terms, the set of phylogenetic trees (aka rooted, binary, labeled trees) in this configuration forms a positive orthant of \mathbb{R}^5.  You can smoothly change any one of the edges to a slightly longer or shorter length, and still have a phylogenetic tree with the same combinatorial data.


This is from the paper I’m writing, but it does show that in 3D, there are 8 orthants cut by the three axes (red dot is the origin).  The pink box represents a single orthant.

What about phylogenetic trees with different combinatorial data?  Say, with different labels or different branching, but the same number of leaves and the same number of interior edges?  First we need to figure out what we mean by ‘different’.  For instance, the following picture from the seminal paper in this field shows three trees that don’t immediately look the same, but we don’t count as different:

Why aren’t they different?  Because they encode the same data for each life-form: reading from node 0 we see that first 1 branches off, then 2, then 3 and 4 in all three cases.  There’s some combinatorics here with partitions that you can do (one can label a tree with a set of partitions).  However, changing the labels so that first 2 branches off, then 1, then 3 and 4 will be a different phylogenetic tree.  In fact I can smoothly go from one to the other in the space that we’re creating: first I shrink the length of the green edge below to zero, which takes us to the middle tree (not binary!), and then extend the blue edge.


Shrink the colored edges to get the same tree in the middle (not a binary tree)

We’re going to add these non-binary trees with one less edge length to our space.  Remember the tree on the left has an entire positive orthant, and the tree on the right has an entire positive orthant.  Shrinking the green length to zero means that we’re moving to one side of the left orthant: so we add this axis to our space (we have \{x,y\in \mathbb{R}^2: \ x,y\geq 0\} instead of strictly greater than 0).  We can glue the green and blue orthants together along this axis.  Here’s a picture from the paper:


Notice that they also have the origin filled in, with a tree with no interior edges.  This is the cone point of this space.  Now we’re finally ready to describe the space of phylogenetic trees: within each combinatorial structure/labeling, we have a Euclidean orthant in (n-2) dimensions.  Then these orthants are glued together along their axes in a specific way, and all of them are connected to the cone point.  This is called BHV(n), short for Billera-Holmes-Vogtmann space (in the paper they call it T(n) but that’s confusing to everyone else).  Here’s the picture of T(4):


Each triangle represents an infinite orthant

There are 15 different orthants glued together in this picture, because the number of labelled rooted binary trees on vertices is (2n-3)!!.  The double !! means you only multiply the odds, a.k.a. (2n-3)(2n-5)(2n-7)… This is also known as Schroeder’s fourth problem , which as far as I can tell was open for 100 years.  Pretty cool!

If you truncate BHV(n) so it’s not infinite (just pick some compact bound), then it forms a nonpositively curved cube complex, and we love those!  CAT(0) cube complexes are great.  I haven’t blogged too much about them (first terrible post and then those truncated Haglund notes) but they are the basis of all that I do and the number one thing I talk about when I give math talks.  Whoops!  The gist is that you glue cubes together in not-terrible ways, and then the resulting complex has great and fun properties (like you can cut it in half the way you want to).

That’s about all I have to say about this!  Gillian is working on some stuff about putting a probability measure on BHV(n) [you can’t do it with certain conditions], embedding it into a small enough Euclidean space that still preserves some of its features, and finding an isometrically embedded copy of the phylogenetic tree inside BHV(n) instead of just the coordinate point.  Also, fun fact to prove to yourself (actually please don’t scoop my friend), find the automorphism group of BHV(n)!  It’s just the symmetric group on some number that has to do with n (n+1 or something like that; I can’t remember and didn’t take notes).

Again, the main reference for this is the seminal paper that should also be accessible as it’s meant for biologists and statisticians.

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