## Last day at Willamette

Today, we wrapped up the REU (on-site, anyway). Each group gave their final presentations, and then we had a final round of root beer floats and games.

It’s been a lot of work to be an REU mentor, but it’s been equally fun.

In the next week, I’ll wrap up a few thoughts about the REU and post a link to our final product.  But for now, it’s time to get to the airport and start my trip back to Hamilton.

## The art of feedback (a treatise on my own artlessness)

Let’s be blunt: I’m not good at giving feedback.  I tend to lay things out with little (read: zero) padding.  My former linear algebra* students will understand what I mean immediately.  Did you include a meaningless sentence?  Did you try to prove linear independence and instead show me that 0 = 0?  Here’s what I think of that:

I’m lucky to have an REU group that takes my criticism in stride.  They realize, I think, that it’s the math that matters.  My comments, though critical, are not judgments of the students.   Anything that obscures the math (or worse, misrepresents it!) is a problem.  Too much detail is as bad as too little detail, but these are subjective norms decided by the mathematical community.  Yep, proof is a social construct.  What makes a proof good is much different than whether it’s a proof.

There are many ways in which I think I’ve been a solid REU mentor, but the place where I give myself the harsh feedback is in my transmission of this sense of style.  Partly, this is because every mathematician has a personal aesthetic.  One’s criteria for “goodness” comes from reading papers (and liking the style of the papers that he or she finds easiest to understand), from writing papers, from having papers refereed (and then refereeing papers).  And there’s a difference between a paper that’s pleasant to referee and a paper that contains useful (again subjective!) mathematics.

So, I’m left with this unresolved question: How do you begin to help students develop their math paper writing skills?  It’s much harder than just writing up proofs that happen to be true.  I don’t really feel like I’ve been helping the students learn anything except how to use the “todonotes” package in LaTeX.  Your comments are welcome.  Feel free, too, to rip on my writing.** If I can dish it out…

*At Hamilton, linear algebra is also the “intro to proofs” class.  As such, it’s writing intensive.  This designation means that I grade proofs assignments once or twice a week.  At my lowest point, I’ve written “duh” on a paper (and I won’t do that again in linear algebra; senior theses, however…).  I have not yet written “aardvark barf” on a paper, but I do remember that particular biting comment making several appearances on drafts of my dissertation.

** I specifically avoided using my Grammarly plugin and my spell check so you’d have plenty to criticize!

## Writing it up

Writing up results is the worst part of math (in my opinion). It’s where you run into snags like, oh, hey, that case doesn’t work, or worse. No different for us. I’m less worried than my REU students because I think there’s a good chance the “problem” is not a math problem but instead an issue with how we formalized something.

I left two weeks for writing, anticipating these hiccups, but it still seems too short.

Irena Swanson, of Reed College, is visiting us today. She’ll give a lecture on free resolutions. I’m excited! Irena is much more than a kickass mathematician. She’s also an ideal role model for anyone who hopes to be good at all parts of the profession.  She has a robust research career while also being an excellent teacher at an elite liberal arts school. She’s done a ton for the mathematical community, especially commutative algebra.  She’s advised more undergraduates that I can count on my hands and feet (along with a handful of Masters and Ph.D. students).

Having the chance to talk to Irena about their research will be an excellent opportunity for my group.  And learning about free resolutions and Groebner bases will be super for the other REU participants.

## Starting to end the REU

There are only two and a half weeks left of the REU. How did that happen?!

My REU students are still making progress. We established that the active writing will commence (and thus the research will end) on Monday.  My students assure me that they’ll work on tying up the loose research ends on over the weekend.*  They know that I’d like to see one more theorem from them by the end of the week, and I think they’re slightly afraid of me.  Ergo, I have high hopes.   Oh, yeah: They’ve also got some blogging to do. (← see what I did there?)

As usual, I have only good things to say about the REU students. All nine of them, plus the other Willamette students that have been haunting the math building, are friendly, well-adjusted people. It’s nice to see the “awkward mathematician” stereotype erode with each generation.  At the same time, it’s almost boring.  They could at least pretend to have some drama in the ranks.  You know what they say.  Every happy REU cohort is the same…**

While the REU’s end looms ever closer, I can’t help but remember that MathFest is right around the corner.  I need to extract my talk from my brain on slap it on some slides for the session “Concrete Computations in Algebra and Algebraic Geometry.”  Shout out to UNL alum and former office mate, Mike Janssen, who’s talking in the same session. While I’m advertising talks: Don’t miss Karen Smith’s Hedrick Lecture Series!

There’s plenty more to do, too!  Since I passed off my big project to my coauthors, I’ve made small headway on a couple minor projects (one expository, one research).  I’m struggling to write the broad strokes of a grant proposal before the summer is over (there’s no time during the semester to get something like that written).  It’s hard to believe my first sabbatical is close enough that I have to start planning now.  It’s exciting to pin down goals and questions, but it’s also frustrating to reflect on all that I want to accomplish.  The process has been painstaking and slow.  I have to remind myself that, although it feels like I’ve been a math professor forever, it’s only been a couple years.  There’s been a huge learning curve.  Now that it’s less steep, I look forward to being more productive.

Speaking of productivity, I see that my allotted blog-time has run out.

*”We’ll work through Sunday night if we have to!” one of them exclaimed.

**Sorry, Dostoyevsky.

## Surrounded by inspiring people

The two other REU mentors, Erin McNicholas and Colin Starr, are incredible people.

Erin is one of the PIs for the grant that’s funding the REU for the next three years. Colin has had this role in the past, too. Aside from the obvious responsibilities that come with that job, there are hidden mountains of paperwork and bureaucracy to summit. Erin is a portrait of productivity. She’s doing the extra work on top of mentoring her algebraic voting theory group, learning new math alongside them, organizing the occasional picnic or outing, and keeping up with her research agenda! Colin spends most of each day working with his students, which is a big time commitment considering everything else a professor has to do over the summer. My only complaint? Erin and Colin haven’t gone to karaoke with me yet. It might be the only activity in which I have a chance of keeping up!

However, I’m not just writing about Erin and Colin because they work so hard for the success of the REU. What impresses me is that they also manage to be excellent parents and spouses.

When I think about my future family, I’ve always got a bjillion career objectives that push the event-horizon further into the future. When people ask about my work-life balance,* I shrug. What balance?

At this stage in my life, as a 30-something junior faculty member, it’s inspiring to be around people who have found that balance. I don’t get the sense from either Erin or Colin that they have compromised or that they have sacrificed being “real” mathematicians or being good parents. When I see them at work and with their families, it’s clear that their successes in each realm amplify their successes in every realm. I am slowly shedding my skepticism of the “You can have it all!” ethos that defines my generation’s values. Maybe it is possible, after all.

Still, tell me to “Lean in!” at your peril. Enlightenment doesn’t happen overnight. 😉

*I will tell you another time how much I resent that this question is put almost exclusively to women!

## Whoa!

I had resolved myself to the idea that we might not prove our theorem in full generality. I accepted that we’d settle for writing a paper where we made a conjecture about the general case and wrote proofs for, I don’t know, up through n = 6 or something.

Note-to-Gibbons: You shouldn’t doubt your incredible REU group like that! We riffed on the general ideas in our proof and about 10 minutes ago, we proved the general case!

Now, I know it’s dangerous to declare that you have a proof right after coming up with it. However, it’s important to celebrate immediately after proving something just in case it isn’t an actual proof. Pro tip: this technique will maximize your personal happiness in the field of mathematics.

But the best part of all of it is that I don’t have to write any more code!

## #win1

My students won the minisymposium conference this time!