I took over as director of Cornell's Center for Applied Mathematics (CAM) on July 1, 2020. With a lot going on at Cornell and in the world, I got into the habit of sending out regular emails. Sometimes, I include a sermon at the end of the message. It's an idea that I happily borrowed from Prof Sandy Mack, who ran the Honors Program at UMD when I was an undergrad, and also sent out such sermons.


2023-12-01

The end of the calendar year brings a lot of happy things, but can also bring a lot of stress. Know the signs of when you are getting stressed out, and how you deal with it. Food, exercise, and social activities help sometimes; or you may de-stress by folding paperclips into the shapes of small animals. Whatever works for you, just be attentive to your own state. And repeating a theme: you are each others’ keepers. If you think you see someone around you suffering, do reach out.

2023-11-04

It was not a great week. PD was my undergrad advisee. These days, I tell my advisees how to get in touch with me, but I don’t chase them down if they never do so, and he never did. Maybe I wish I’d made more effort to do so in this case, but maybe this is a case of hindsight being 20/20. The whole saga makes me sad and upset, and I think it’s probably a good thing that central decided everyone was on edge enough that we should take a three-day weekend to try to reset.

As for the backdrop of the war that had so many folks angry and on edge even before Dai started with death threats – I have a hard time finding anything better to say than a line from MASH. Late in the series, Hawkeye Pierce (played by Alan Alda) objects to the characterization that “war is hell” by retorting that war is war, hell is hell, and of the two of them war is worse because:

“There are no innocent bystanders in Hell, but war is chock full of them – little kids, cripples, old ladies. In fact, except for a few of the brass, almost everybody involved is an innocent bystander.”

A lot of folks around campus are processing. Phil forwarded the information about the support groups and activities to you earlier, if you happen to need to process with other people. And if you don’t, that’s fine as well. Just keep an eye out for each other, OK? I keep writing emails where I say “you are each other’s keepers” for a reason.

And as for keeping yourself, which is also important, I come back to the start of this message. Get enough sleep, eat well, get some exercise, get sunlight when you can. And consider another quote, this one from the philosopher Epictetus:

“Happiness and freedom begin with a clear understanding of one principle. Some things are within your control. And some things are not.”

So start with the things you know how to control – which is mostly you and your local environment. At least, that’s mostly what I know how to influence with any effect.

2023-10-20

Because it is mid-semester, a short sermon in two parts.

Part 1:

We are in the middle of the semester now, and the chances are that this is starting to stress out the people around you even if you are not yourself particularly stressed by it. We are also in the part of the year where the days get shorter, and people with any inclination toward seasonal affective disorder start feeling it. And, once again, the news is heartbreaking and infuriating all at once.

There are many things that you cannot control. But you do have some control over your diet, exercise, sleep habits, and social interactions. Take care of yourself. It won’t make any of the external problems go away, but it will maybe make you more able to deal with them with equanimity. And watch out for each other, too. You are indeed each other’s keepers – that is part of what it means to be in a community. If you see someone around you struggling, don’t be afraid to reach out. And this time of year, if you pay attention when you look around, you will probably find that there are people around you who are struggling.

Part 2:

You’ve likely heard the Einstein quote: “If we knew what it is we were doing, it would not be called research. Would it?” There are jobs where people basically know what they need to know moment by moment – being a researcher is not one of them. When you get started, you at least have structure for learning what you need to know to get started in an area, but at some point you will be thrown into the deep end and asked to figure out what is going on for yourself. And it’s hard! But whether it is in a talk or in your own work, feeling like you are kind of lost but know where to read next, or know what to try to prove next, or know who to ask next – that’s normal, and probably a sign that you’re on a promising path. Put one foot in front of another, keep learning more, and sometimes you’ll get to something pretty interesting.

2023-08-18

Ready or not, here comes the semester! You got this! (I did promise short and sweet…)

2023-08-11

Finally, a short start-of-semester sermon. I usually write something in the middle of the semester to the effect that you are each others’ keepers, and I think that’s true. But you are your own keeper, too! That’s an important thing to remember at the beginning of the semester when you are setting the schedule for what is to come. To the extent that a foot race is at all an appropriate metaphor, research is a marathon and not a sprint – there will always be a next exam and a next paper deadline, but your reputation is determined by the arc of what you can learn and teach the world over a much longer time span. So start as you intend to proceed, set a sustainable pace of work, and remember to schedule some of your time toward friends, food, hobbies, exercise, and all the other things that keep you going.

2023-04-14

Imposter syndrome is the feeling that people perceive you as having more expertise than you actually have (coupled with the fear that they are going to figure it out). A friend of mine in graduate school summarized this succinctly as “help, help, I’m a horrible fraud!” And then there is the Dunning-Kruger effect, where people are too incompetent to recognize their own incompetence. And there is plenty of uncomfortable territory in the middle! This is part of the joy not just of graduate school, but of being human.

One thing I have figured out for myself over time is that I am much less likely to mis-estimate my own knowledge in either direction if I think in terms of very concrete things. Do I know how to state this theorem? How to prove it? Can I prove it in front of a class full of students after a bad night of sleep? Have I successfully implemented this algorithm, tuned it, used it in anger on a problem that matters to me? It’s easier for me to answer those questions “yes” than it is for me to answer “am I competent in X” where X is some broad topic – and when the answer is “no,” it’s easier for me to figure out the next steps to change that situation, should I care to do so.

If you are blessed with the ability to do clear-eyed self-evaluation of your knowledge and skills, more power to you. If, however, you are muddling along with me and are prone to sometimes think “help, help, I’m a horrible fraud!” (or worry that maybe you ought to be thinking that about something that you think you know), I encourage the exercise of thinking on what you think you should know how to do, and how to get yourself from where you are to where you want to be. That may mean going back and spending some time on things that you think your peers learned as undergraduates (note: they likely did not), or it may mean starting on that paper draft and honestly marking some places as “to be figured out,” or it may mean figuring out a super-concrete example for your abstract theorem or trying to figure out how to break the code you just wrote. Maybe there is someone out there who can sit down, think deep thoughts, and periodically blurt out brilliance – but for the rest of us, the road to knowing things involves a lot of hard work plotting the way and figuring things out step-by-step.

2022-11-04

I wanted to write this week, but just a simple sermon.

Today was a celebration of the life of Juris Hartmanis, the founder of the Cornell Computer Science department. Juris was a brilliant scientist, winner of the Turing award for his work on computational complexity, and one of the figures who defined the field. And all of these things were mentioned over the course of today. But what people dwelt on was not his brilliance, but his kindness, sympathy, integrity; his ability to build a collegial and collaborative culture; his mentoring to those around him. I started after Juris’s retirement, and still my memory of my first days at Cornell involves his call of “lunch!” down the halls, the vowel stretched out by his Latvian accent.

What Juris understood, and taught to those around him, is that though there is value in brilliant ideas, there is even greater value in building a department and a culture that allows everyone to live up to their brilliance, not only independently, but also together. It is one of the things I have always valued about my department, and it is also something that I really value about CAM.

At the end of the semester when things get crazy, it’s easy to center yourself and your own trials and tribulations. But I look around and see all of you as people who are kind and brilliant, from whom I can learn and with whom I can collaborate. That is how I see the culture that you are building and living in. I hope you experience it that way, too.

2022-10-06

A thought to take you into the break: I have enormous admiration for all of you. You came here to a new place, willing to try this new thing called graduate school, and you’ve worked at it hard! And yes, you are here to learn to do good research, and you’re doing that – but many of you are equally devoted to just doing good, and that makes me happy as well. You’re learning to answer some questions and ask lots of others, and you’re curious enough about the world that you’ll probably always have more questions than answers. You focus, pay attention, and learn an enormous mathematical vocabulary over time – and you don’t stop there, but turn outward and learn about all sorts of other things as well! And while we’re all sometimes sad, it makes me happy how often I see you be joyous, be silly, be profound. You are awesome, and I’m glad you are here.

2022-09-16

The Canadian writer Laurence Peters said “Early to bed, early to rise, work like hell, and advertise.” I don’t know what all your sleep routines are, though I hope you’ve figured out for yourself how to get plenty of sleep each night. You all know that graduate school is hard work, though maybe hard in different ways from your undergraduate work, and none of you are lazy (if you think you are, consider slowing down and focusing on your values). But most of us could stand to be better at advertising.

What is advertising for a researcher? It’s not about marching into spaces yelling “I am so smart!”; it’s about sharing why you’re excited about your work. That can mean communicating with peers through talks and papers; showing up and asking good questions in other peoples’ talks; talking to a broader audience in a variety of ways; showing up and asking good questions; or even just making sure you have an up-to-date professional web site with a description of your research and links to talks and papers (we can do this on the CAM space, but Github pages and Netlify are also good hosting resources).

You all do cool stuff. Don’t hide your light under a basket.

2022-09-09

Applied math is what the label says. You’re all learning to be mathematicians. You’re also, ideally, all learning about at least one application area, and how to connect that to your mathematical expertise. And learning how to seriously connect math to applications is hard! You need to learn the vocabulary of the other areas; you need to pick up things that the people around you learned as undergraduates; you need to build up from being a beginner to knowing what’s going on, and sometimes you don’t have the benefit of years of time and structured classes.

The good news: you are learning the math skills you need to get started. And the main thing you need to keep going is to not worry that you don’t know what’s going on – it’s a challenge and an opportunity. Put up your hand, channel your inner three-year-old, and start asking “why” and “how” until you get answers you can grab onto. And when you’re stuck, sleep on it and try again the next day.

2022-08-26

I get asked very specific technical questions all the time. My response to the vast majority of these fall into one of three pots:

  1. That’s an interesting question, here’s a book or paper that addresses what you’re looking for.
  2. That’s an interesting question, I think it’s an open research question.
  3. That’s an interesting question, but can you back up and tell me why you are asking that question?

All three types of questions are interesting. Maybe I get asked a lot of uninteresting questions, too, but I forget them quickly – after all, if they weren’t very interesting, there’s not much reason I would remember after answering. But of the three cases, the third type of question is often the most interesting, precisely because it’s where I get the most chance to learn something, and the best chance of really helping. After all, the people who come to ask me questions are usually pretty smart and technically skilled themselves – if they don’t have an answer to the exact question they are asking, there’s a pretty good chance that I won’t either. But if they are stuck, sometimes it’s because they took a hard fork in the road several steps ago, and there is an easier way to get to the thing that they really care about.

It’s exciting to figure out answers to questions. But maybe it’s even more exciting to figure out the right question that is simultaneously answerable and moves you toward an interesting goal. So while I hope all of you have good luck this semester in getting your theorems proved and your computations to converge – but I also hope you have the chance to spend as much time backing up and inspecting your questions as you do answering them.

2022-08-19

Earlier this week, one of the baristas at Gimme told me “you have some of the nicest and friendliest students in your program!” It’s always nice to hear things like this, and one of the great joys of being CAM director is that comments like this aren’t rare. The Cornell style of applied math has always favored good mathematics and good applications both, and the structure of the graduate field encourages this type of work. But bringing together good math and good applications usually means bringing together people from different technical backgrounds in conversation, and that attracts students and faculty who are willing to engage in such conversations – and encourages them to build their skills in talking across areas. And I tend to think that this is part of the reason why I get such nice comments about how friendly you are as people and how effective you are as teachers and collaborators from across the university.

Of course, part of the challenge of being in an inherently interdisciplinary field is that you’ll likely spend a lot of time trying to understand someone who seems to be speaking a completely different language. I always figured that this means a big part of an applied math PhD involves learning to be comfortable with feeling a bit lost, and growing to feel secure in your ability to learn what on earth someone is talking about if you only listen, work at it, and keep coming back with questions. So the moral of my first sermon of the new academic year is: as you make your way through the PhD and grow in expertise, I hope you also keep growing in your ability to be a beginner. Be curious as you are confused, keep asking questions and trying to understand, and you’ll learn a lot of cool things about the world – and, with luck, make some friends along the way.

2022-05-27

Here I sit, with draft graduation remarks on a notepad before me. And on my screen, next to this window, is a mail from the Graduate School with guidance on leading during trauma. I celebrate the conclusion of another academic year, the successes of our students, good news and recent victories for myself and my loved ones. I mourn shooting after shooting, a million lives lost to COVID, a world in turmoil and at war. I feel I should say something about it all, but the whole of it seems too much to deal with directly, and metaphors are not much better. The glass is half full, and it’s half empty, but mostly there is too much glass and water and air. I endure. But until I’ve recovered some more, I can’t even seem to celebrate or rage against the world properly. I just get exhausted.

And so, with too tenuous a grasp on the world as a whole to try to figure out any over-arching wisdom, I return to the basics that I’ve written before. You are your sister’s keeper, and your brother’s. We are social creatures, and we are stronger in community than we are alone. We build that community when we show up for each other, whether to celebrate or to mourn or simply to share a cup of coffee and a whiteboard of math. As we celebrate graduates going out into the world and new students arriving with fresh ideas and perspectives, we build and rebuild that community anew.

Our goal as academics is to have an impact on our intellectual community and on the broader world beyond. That impact can take many forms, and there are as many approaches to impact as there are people. For my own part, I have always sought impact on the world by reading widely, bringing together tools and problems from wherever I come across them, and connecting ideas across areas. I never fully figured out to be when I grew up, and I still don’t pretend I really know what I’m doing. But I know that I like the play of mathematics, the design challenges of engineering, and particularly the conversations that help me learn the languages of other areas of science. I try to have an impact by solving interesting problems myself, and by teaching students how I think about problems. And, though I am still mystified by humanity as often as not, I like the challenge of trying to figure out how to design an environment where humans can thrive – maybe through my scientific work, maybe by helping build or advocate for better processes.

My path is just one path, and there are many others. You will all have your own successes and failures as you walk your own paths. But I believe many of you share with me a broad curiosity about the world around us, not only in the “big issues” of the day that jostle us all for good and ill, but also in the details of how and why the world works the way it does, and maybe how it can be engineered to work better for all of us humans. And I hope you will all keep thinking on how to craft your impact on the scientific world and on the community around you to be as positive as possible.

I wish you all a thoughtful, restful, and restorative summer. With any luck, this will be the last edition of Friday notes until August – I need a break, too! But I will be around, by email even when not in person, and you should reach out to me if you need anything (or if you just want to talk).

2022-03-18

This is less a sermon than a reminder of a few things that I hope you already know:

You’re at Cornell because we wanted you here. “We” here includes me, but I’m going to include the field and the Graduate School in this. All of us want you to succeed in your time here, and are working to try to support you (though sometimes subject to constraints that may not be at all obvious). And when you do face issues that I might be able to help with, I’d much rather you tell me about them early than late – preventive maintenance is almost always the least expensive option for everyone in time, money, and general grief.

2022-03-11

We’re halfway there! (Woah, living on a prayer…)

The halfway point of the spring semester is often a pretty stressful time. It’s midterm time for some classes; spring is coming, but the weather hasn’t turned around yet; and everyone is feeling ready for a break – but it won’t arrive for another couple weeks.

But: spring is coming (and so is spring break). Days are getting longer. You’re working hard, but there is a payoff in learning cool stuff. And I hope you feel like you’re getting the support you need to succeed even in the middle of the semester. If you need help (or just want to talk things through), you know where to find me and Phil. And please do talk to us if you have concerns – as with vehicles and medical care, preventive maintenance saves everyone a lot of time in the long run.

2022-03-04

When I took over as CAM director, Cornell was reconfiguring policies on the fly almost daily, and we weren’t able to see much of each other because of the pandemic. I started writing “Friday notes” both to make sure that you were able to keep up with the local changes that affected you and to try to provide some measure of support when everything was crazy and everyone was feeling isolated.

We’ve had a few weeks now with Cornell operating almost as normal, and little in the way of new policies you need to know about. And I think we are less universally isolated now. I was glad to see many of you at today’s colloquium and at the refreshments after, and I hope you are looking forward to meeting with some of the admitted students next week.

At the same time, the world does not seem to be getting less crazy.

After last Thursday, I struggled to say something in this space that would be at all helpful. I failed, and so I chose not to send a Friday email. But I have been thinking about it this week, and have at least a one thought to share. It is an old thought, and not one that I came up with, but it is timely:

The chief task in life is simply this: to identify and separate matters so that I can say clearly to myself which are externals not under my control, and which have to do with the choices I actually control. – Epictetus

In the pandemic, we have had only a little personal control, though we do our bit by getting vaccinated, keeping our mask up, and following public health guidelines. None of us have even this little lever of influence over what is happening in Ukraine and Russia. Epictetus lived well before anyone invented the term “doomscrolling,” but he and the other ancient Stoics would surely have recognized the phenomenon, and recognized it as both very human and as counterproductive. Where we do have control is in our own environments: how we tend to the things about us that are also important, and how we support each other. That is where I at least try to focus my own energy and effort, though I don’t always succeed.

A second thought is one I’ve written before: you are each others’ keepers. You are adult humans who have seen ample examples of people acting terribly and of people showing kindness and compassion. Most of us manage both over time. But to the extent that we can find creative ways to be kind and compassionate to each other, we usually are able to make at least one part of the world a little better. And I think that is worth doing.

2021-12-03

It’s a time of the year where everyone is getting crunched a little, so let me remind you:

  • Watch your sleep, diet, and exercise. It’s hard to do your best if you’re tired, hungry, and haven’t moved from your computer all day.
  • Keep your big picture in mind. Sometimes you’ll have to choose between things you focus on, and that’s OK.
  • It’s easy to fall into the trap at the end of the semester of only being in question-answering mode. But remember: you’re here partly to learn how to ask questions, too! Don’t let that get lost in the churn.

Good luck to all of you as we enter the semester end game. And I’ll see you at colloquium!

2021-11-19

First, I want to acknowledge that this time of year is a crunch time for a lot of us, faculty and students alike. You’ve got this – which is to say, I wish you many successes, and to meet the failures that happen from time to time with equanimity. All of us stumble, and a lot of life is just about incorporating those stumbles into your stride.

Second – I was getting ready to send this when I heard about the Rittenhouse verdict. I am angry and disappointed, and a little bewildered and numb. I wish I was shocked. Some of you may feel the same, or more so. Some of you may just not have been following. But I assure you that if you are teaching, you have students for whom this is going to land hard. Take care for each other. Talk to me if needed.

Given the season we’re entering, I wanted to say a few words about community and service. But that might be a discussion for the next week.

2021-11-12

I struggled with what to write here this week. Between the return to standard time and the ramp-up of homework and exams that inevitably happens around this time of year, this was never going to be an easy week. Bomb threats and police pursuing a gunman, atop the ongoing strain of pandemic life, has only made things harder. Some of you are also teaching this semester, and dealing with students who are processing this trauma in their own ways. That can also be a challenging exercise, particularly if you’re still processing some things yourself.

What do I have to offer at times like this? For this week, I think, I’d like to offer three thoughts.

First is that sleep, diet, and exercise make a difference. It’s hard to deal with life with equanimity if you are tired from trying to pull all-nighters, skipping meals (or eating poorly), or not moving around enough. For those of you who have spent most of your life in more southerly latitudes, be aware that seasonal affective disorder (SAD) is a real thing, and kicks in for a lot of people as the days get shorter – there are strategies to deal with this, including light therapy, but it helps to first recognize the issue:

https://health.cornell.edu/sites/health/files/pdf-library/winter-blues.pdf

Second, be reasonable with yourself. Many of us treat ourselves differently than we would treat others, and that often plays out as overly harsh self-criticism. I think it’s pretty normal to have moments where you feel like you’re drowning and everyone else is doing better. If we were completely rational creatures, we could think ourselves out of such moments; but then, if we were completely rational, we might not have those moments to start with! If you’re in such a patch and can recognize it in yourself, take a step back. Take a few deep breaths, go for a walk to clear your head, talk to someone else, have something to eat, do whatever it takes to help get yourself unstuck. And then, yes, you can make a plan. You can do this.

Third: you are your brothers’ keepers. Support each other! We say the university is a community of scholars, and part of what community means is that we watch out for each other in times of trouble.

2021-10-29

I haven’t sent a sermon in a while, and feel like I’m overdue.

So how about this one: none of us are mind readers.

We form more- or less-good mental models of each other through our interactions, and maybe your model of your best friend is so rich and detailed that you can predict their next sentences – but move away from those I know well, and my mental model for most people in the world is cartoonishly bad, and I’m guessing that the same is true for most of you.

What does this imply? Well, I’ve always figured that it means the exclamation “I have no idea why you’d think that!” should be read as a statement of fact rather than a condemnation. I have no idea why lots of people think what they think, up until I start talking to them – and sometimes not even then. But even close to home, it implies that those around you might not know what is going on with you, even if they should.

I’ve used this slot before to tell you all that you are each other’s keepers, and that you shouldn’t feel shy about making sure those around you are OK. That’s still true. This week, I’m going to tell you the converse can also true: if something is not right for you and you need help, consider reaching out and saying something about it! If I’m the right person to listen, I assure you that I’d rather hear from you now that you are having a minor problem than to hear from you in a month when it has turned into a major emergency. But the advice holds as well for reaching out to your advisors, your mentors, your professors in classes. Don’t assume we can somehow intuit your problems, because most of us probably can’t, even though we’d like to help if we could. Speak up!

2021-10-22

I might be able to marshal my thoughts into a sermon next week, but for this week I’d just like to point you to a resource that I think is useful, the “mentor map” guide from the National Center for Faculty Development and Diversity:

https://www.facultydiversity.org/ncfddmentormap

None of us enter new roles having it all figured out – indeed, academic life consists largely of being thrown feet-first into situations where we have no idea what we’re doing! But we’re social creatures, and you can pick up a lot of support and wisdom from asking the right questions of the right people in your circles. Everyone’s support network and needs will look a little different; but thinking through who you have available to ask different types of questions, and what types of questions you’re asking, is a good way to help yourself stay centered and happy.

2021-09-10

I got a wonderful email this afternoon from the teacher of one of my kids about how the class is “learning the core values of the classroom through discussion, artwork, reading, sharing, play break, and other activities.” The values she listed are:

  • Above All, Be Kind
  • Different Is Good
  • Learning Is Not A Race
  • It’s Wonderful To Be Wrong
  • Be Smart - Ask Questions
  • I’m Exactly Who I’m Supposed To Be
  • Fair = We All Get What We Need

The details change, but I hope the core values you’re embodying in CAM as umpteenth-graders have a pretty strong overlap with the values being taught in second grade!

2021-09-03

One day, I hope to start by talking a sermon by talking about how great the news was! But the news this week was again full of both natural disasters and human ones, piled atop the fears and uncertainties brought on by the pandemic. But these things are largely out of my control. What I can choose, and do choose, is to find actions day by day to try to improve the part of the world around me where I do have some control.

2021-08-27

I have a hard time doing better this week than Martha Pollack’s message: “Respect knowledge. Be kind.”

2021-08-20

Just a short thought today: The start of the semester often brings a measure of excitement and a measure of terror. But you’ve got this. Go and do good work, reach out if you need help or see someone who needs help, and remember that mistakes need not be fatal (and if we knew what we were doing, we probably wouldn’t be doing research!).

2021-08-13

Though I hope you are all excited to be back at CAM (or be in CAM for the first time), we are still entering another uncertain semester. I remind you again, as I did a few times last year, that you are your brother’s keeper – keep an eye out for opportunities not only to do good work, but to do good for each other, and for the world. Or, to steal from a conversation on the CS faculty Slack right now, I hope you can all “follow the PUCK” this semester (PUCK = Patience, Understanding, Compassion, and Kindness).

2021-05-14

Some wag once quipped that a PhD is about saying more and more regarding less and less until one is able to say absolutely everything about nothing at all. But I’ve always held the ideal of a T-shaped applied math grad student: someone who goes deep in some specific area, but also becomes technically broad. The summer is often a fantastic time to pursue both of these goals, whether by making progress on a research thread that got stalled during the semester or opening a textbook for a subject you always wanted to learn more about. I’m personally looking forward to doing both of these things this summer, and hope you are as well.

More broadly: I am looking forward to the summer in particular as a chance to step back and remember how to play! Partly that is going biking, tossing a frisbee, going out on a kayak, or maybe playing a video game. But I also mean playing at work: writing a bit of clever code, understanding a proof, digging into a computation, setting up a little experiment. A PhD is a long commitment, and a lot of it is hard even in the best of times – we all get paper rejections, have lectures that go awry, get totally lost in classes and colloquia, and find critical errors in our proofs and programs. But it can also be a tremendous playground, and summer is a great time to remember that.

This summer, I wish for you what I wish for myself this time every year, and this year even more so: a break, a chance to decompress, a chance to play, and a chance to deepen and broaden your knowledge. And when the summer is done, I look forward to welcoming you all back to the CAM space!

2021-05-07

This year has been hard, and it has been hectic. But I continue to find joy in the time that I’m able to sit down and think long thoughts: plans for projects and programs that I do not expect to wrap up within a month or two, but that I think are likely to engage me over years. That is true of my research, of course, but it is also true of other things – like CAM. And, as with most of my research, CAM is a long-term collaboration, both with the faculty and with all of you.

Summer is a great time to spend some dedicated time on long-term thinking, and one of the things I would really like to do this summer is to think through the types of things we can do together to make CAM a better place. I have to write some of this up in the form of a graduate field manual, and I am looking forward to your thoughts about things that should go into that. But more than just writing down a document that describes where we are, I hope to write where we want to go next. What should we do more of? What should we do less? How can we best support each other? What can we take from this COVID year that will make future years better?

I need your help with this, and I’m looking forward to hearing your thoughts.

2021-04-30

No sermon this week, just my encouragement to get outside tomorrow while there is sun. Lots of rain expected next week.

2021-04-23

This was a trying week, in a trying semester, in a trying academic year. But while I was staring at the ceiling and waiting for sleep last night, I thought for a bit about the AA prayer, the one that talks about “the serenity to accept the things I cannot change, courage to change the things I can, and wisdom to know the difference.” It’s a good dichotomy for the current moment.

There’s a lot out there to accept, and there’s a lot out there to change. But it’s hard to be wise about the difference when you’re exhausted. So go take care of yourselves as best you can for the remaining three of these four days of break. Get some sunshine, some exercise, a conversation with a friend. Give yourself the break you need to be wise.

2021-04-16

No sermon this week, just a reminder: this time of the semester is rough most years, and this year isn’t most years. People are feeling it across the university: faculty, staff, grad students and undergrads. Take care of yourselves, and check in on each other.

2021-04-09

In April 2014, I visited Nick Trefethen at Oxford, and we went out for a walk together. I was thinking while walking and talking, and fell into my everyday habit of looking down at the ground as I figured out how to frame what I wanted to say. And at some point, Nick exclaimed (in some exasperation), that I really should look up! I don’t remember the exact words he used, but the sentiment was that the sidewalk in Oxford was not so dissimilar from what I’d find anywhere else, but I was missing out if I didn’t look at the buildings.

I still remember this seven years later, so clearly it made an impression.

Routines and rituals are a fine way to keep organized, to keep moving forward, to keep a sense of regularity to life. But it is also worth remembering, especially in the middle of a pandemic semester as we mostly try to get by, to look up! What is making you curious? What are your dreams and aspirations like right now? If you look at your to-do list, why are the items there – to keep you fed and healthy, to help someone out, to take care of something that it seems important to take care of, to move toward a long-term goal, to have fun?

2021-04-02

There are a lot of things I miss about being on campus: consulting my bookshelf, hallway conversations with students and colleagues, the little conversations that happen before and after classes and colloquiua – the list goes on. One thing I miss for all of us, though, is what we learn from watching our very human peers and mentors get confused, make mistakes, and think things through.

From afar, I tend to look at colleagues and assume that they are more knowledgeable than I am, or at least much quicker – see how many things they know that I don’t! Of course, the fact that everyone around me knows things I don’t ought to suggest to me that the converse might be true as well, but it was well into my own graduate training before this really began to sink in. I observed the people around me in seminars and colloquia doing the things that people do in talks – following closely or falling asleep, making connections or getting confused, and usually struggling a bit to digest topics outside of their everyday routine. And I talked to people after lectures who thought it was great or terrible, watched people give me confused looks when I talked about my own area, and generally got to build mental models of the people around me. What do they know? What confuses them? Understanding that everyone else spent a lot of time being confused, too, helped me a lot at the beginning when I was trying to figure out how on earth everyone else seemed to know so much more than I did. And later on, when I got over that feeling (mostly – I still relapse regularly), it helped me be a more empathetic teacher and speaker than I was when I began.

This year, you don’t get to watch people fall asleep in front of you in seminars. You don’t get to watch your friends look totally baffled in lecture. You don’t get to watch your students get that “aha!” expression that suggests they had a moment of insight. But you should realize: all those things are still happening. If you don’t get it, you’re probably not alone. If you have a question, you’re probably not alone. You are not imposters. You belong here. You are all students, and getting confused (and then unconfused) as you learn is a big part of your job. If you’re not getting everything in your classes and seminars but are gradually getting more over time as you keep showing up and working at it, you’re making progress.

2021-03-26

No sermon today. I started one, but it got too long and muddled. Instead, I’ll just give my normal advice: get up and get outside this weekend if you can. No amount of self-care and mindfulness is going to make this an easy year, but it’s easier to take things as they come if you can get proper rest and exercise.

2021-03-19

The news this week was hard, the pace of our spring-break-free semester feels relentless, and the change to Daylight Savings has disrupted sleep schedules and made it harder than normal to take things with equanimity. I’m speaking for myself, but I know I’m speaking of experiences that many of you share. And we all face our own personal issues as well – to misquote Tolstoy, “all happy graduate students resemble one another, but each unhappy graduate student is unhappy in their own way.” So while I originally planned to write in this section about the value of talking broadly and “T-shaped” research, instead let me end with an evergreen statement: you are each other’s keepers. Check in on each other.

2021-03-12

Cornell shut down for COVID on March 13, 2020, a year ago tomorrow. We are in a better place now than we were than, in many ways. We have a better notion of what we can do safely until there is a vaccine, and vaccinations are proceeding apace. Eligibility letters for those of you who are eligible (anyone with on-campus duties, though in-person class as a student doesn’t count) should be available a couple days after you submit your attestations. Get your vaccination when you can. But while we all wait, stay safe. You have all likely seen the modeling predictions – we are likely to have increased prevalence in the student body for the back half of the spring semester as the new strains arrive. We expect things to remain under control, but we are not yet in the clear.

No sermon today, just my encouragement to you to hang in there. We knew coming in that spring would be long, but at least we now have signs that spring is arriving. It’s supposed to be clear tomorrow, if not as warm as it has been for the past few days; I hope you have a chance to go outside. And remember to set your clocks forward on Sunday night.

2021-03-05

I started to write something longer, but decided that I could say what I wanted with fewer words: Some of you, like me, may have ambitions to catch up after a crazy couple of weeks at the start of the semester. I hope that this will not keep you from spending some time away from your computer screens as well. March is when Ithaca starts to thaw out. For those of you who can get outside, I encourage you to do so. If you can see others while outside, all the better.

2021-02-26

Let me steal a few words of advice this week from one of my many academic heroes, Prof. Fan Chung at UCSD: http://www.math.ucsd.edu/~fan/teach/gradpol.html

2021-02-19

Vaccinations are in sight, and we all hope to have a mostly-normal in-person academic experience next year. For now, though, we have only just started with the marathon that I expect will be the spring semester. I hope the semester might get easier in some ways, as the cold and snow creeps back and we get the first hints of spring. But while we wait for those days, I thought it might be useful to share an adaptation of one of the old sermons that I got as an undergraduate, sent in mid-December of 1997 by Professor Sandy Mack (you can probably figure out for yourself which item I changed!).

How to Handle Stress:

  1. Pop some popcorn without putting a lid on it.
  2. When someone says, “Have a nice day,” tell them you have other plans.
  3. Make a list of things to do that you have already done.
  4. Dance naked in front of your pets.
  5. Tape pictures of your teachers on watermelons and launch them from high places.
  6. Walk to class backwards.
  7. Read the dictionary upside down and look for hidden meanings.
  8. Stare at people through the tines of a fork and pretend they are in jail.
  9. Make up a language and ask people for directions in it.
  10. Remember that we only ever walk one step at a time, whether it is through the 14 weeks of the spring semester, through the course of a graduate program, or the course of life. We can do remarkable things through steady progress and time.

2021-02-12

You are all getting mentoring of some sort, I hope. At least, you should be. But one of the things that I think about a lot in this weird year is whether everyone is getting the type of mentoring that they need. Do you need help navigating courses? Preparing for job talks? Finding an advisor? Starting research? Navigating your teaching? In a normal semester, there would be a fabric of informal interactions to help support these. But for this academic year, you may need to be more deliberate.

I’ve written more than once in this section that “you are your brothers’ (and sisters’) keepers,” but you also all get to advocate for yourselves. And one part of that is finding a network of people who can help you with advice and guidance. If you think you are headed on to an academic career, you will want several faculty to know you well – maybe even collaborate with you on research – in order to have the letters that you need for your job applications. But even if you have no interest in academia, talking to lots of people about the things you think they’re good at, and getting the perspective and advice you need, can be one of the great pleasures of being a graduate student.

So: if you have a committee put together, find excuses to talk to your committee members! And if you’re still taking classes, go visit faculty office hours in whatever form they may have! Think a bit about what you want to know or where you want guidance, and then go out and find it.

Some mentoring resources:

2021-02-05

Spring semester is always a time of beginnings and endings. For now, we are at the beginning of a new year; the beginning of a new cycle of life; the beginning of new classes. The end of this semester will be a time for several of you to move on from Cornell, out into the broader world. I hope it will be the end of this COVID-centric educational experience, though some elements of it will doubtless be with us for a while.

But in between the beginning and the end, we have 14 intense weeks. There’s no spring break this year, and nobody ought to be traveling anyhow. I hope you are making plans now for how you are going to sustain yourself through this semester. Should you need help with this, check out the Cornell Quaranzine. And I remind you again – yes, you are your brother’s keeper, and your sister’s. Check in with each other.

Good luck with the start of classes.

2021-01-08

Faculty sometimes get reminders that natural or political catastrophe are affecting some group of students, and maybe school work and deadlines are justifiably less important to them at the moment than the safety and well-being of their home and family. Given that you are all spending at least a part of your life here, insurrectionists storming the US Capitol with the encouragement of sitting politicians is the type of political catastrophe that could reasonably rattle any of us. It has certainly rattled me — enough that it’s hard to keep track of other stuff.

In normal times, I think any one of the elections in Georgia, or the no-charge decision in Kenosha, or the continuing drumbeat of bad news about COVID and the economy would be the dominant story of the first full week of a new year. Or maybe we would still be getting filler pieces about the psychology of sticking to New Year’s resolutions, or analyses of the first days of the post-Brexit UK. But while 2020 is over, we are still not in normal times.

For the most part, academics get the privilege of thinking long-term thoughts — certainly much more so than many of our peers in business. That doesn’t mean we’re immune to short-term chaos. If you’re having trouble focusing, be gentle with yourself. And, if you are able, turn off the news, take a walk, talk to a friend, do the laundry, and remind yourself of the everyday.

I’m looking forward to seeing you all when classes start back up in February. I hope to return to radio silence until late January, but of course will send a note if things come up (hopefully related to Cornell logistics). But I’m back at it myself, and you know where to find me if you need anything.

2020-12-11

Well, you’ve survived the rolling ball of disaster that was the Fall 2020 semester. It was deeply weird, upsetting, and unsettling, for me and for many of you. It was not what I thought I was signing up for when I agreed to the role as director — and probably not what any of you thought you were signing up for when you decided to come here for graduate school!

And yet: amidst the struggle, I saw many of you grow.

I saw you grow technically. Everything takes three times as long as it would in a normal year, but I kept seeing you learn new things — and I learned new things from many of you. We asked you to suggest speakers for the colloquium, and there were some phenomenal choices. I asked you to tell me about your research in late September, and you provided one of the most fascinating afternoons I had this year. And despite the chaos of the year, when I talked to you — for twenty minutes at a time in scheduled meetings, for a few minutes after colloquium, for an A exam or setting up a committee — I mostly just got to enjoy thinking about math.

I also saw you grow as humans. I saw you supporting each other. I saw you caring. I saw you challenging yourselves not only to pick up new technical skills, but also to think about the broader world in new ways.

Universities are funny places. They are old, tradition-soaked, conservative to the point of being hide-bound. We still celebrate our major events by donning medieval robes! And yet, through our students, we are constantly reinvigorated, and our programs ever re-built. As with anywhere else, the room to grow and rebuild is greatest when the world has conspired to tear down the old. Well, here we are, at the end of what may be the most destructive year I’ve ever personally witnessed. And here you are as well, continuing to build.

I am proud of all of you, the work you are doing, and the place you are building.

2020-11-20

The tradition of harvest festivals is hardly unique to the US, but we have our own peculiar take on it, even apart from the traditions of turkey and cranberries and pumpkin pie.  As a kid in school, we learned about the myth of “the first Thanksgiving,” and even that version of the story involved the survivors of an awful lot of death and disease.  Reading history as an adult, the whole episode feels even grimmer and sadder.  In the early part of our history as a country, the holiday was celebrated intermittently (e.g. Thomas Jefferson, a deist, declined to declare a Thanksgiving holiday while he was president).  It was Abraham Lincoln who declared Thanksgiving as a regular, official holiday, in the middle of the US civil war; and the current date (the last Thursday of November) was nailed down after a bitter fight between Franklin Roosevelt and his political adversaries among the Republicans in the midst of the Great Depression.

And now, we approach the Thanksgiving day as we reach the end game of a deeply weird and unsettling semester in a year rife with tragedy.  I find it hard not to feel sadness and anxiety about a lot of the current situation.  And yet, I’m grateful: for the fact that all of you are still alive, for the continued success of our local community in managing the epidemic, for the opportunity to continue learning new things every day.  And I’m grateful for a day that I will spend at home with my family without the pressures of lecture prep, meetings, and getting the kids to their classes.

So while I wish you all success in your semi-finals and end-of-semester projects, let me also wish you the vision and courage to try to help fix some of the things that are wrong with the world, and also gratitude for the things that are right.

2020-11-13

We pay attention to milestones and big goals, but we get there day by day. So get enough sleep, eat right, try to get out and move around if you can. Be patient with your students, your professors, yourselves. Try to learn something new every day. When something goes wrong, roll with it as best you can, and ask for help if you need it. You know how to do this.

2020-11-06

A big, messy, ongoing election; in excess of 100K/day infections — what times we live in.

Even in a normal year, this is around the time of the semester that lots starts coming at everyone.  This year, of course, it’s easy to feel like the world is happening to us, and we’re just trying to keep up.  For good or ill, none of us are where we are without a good bit of luck playing a role.  But don’t underestimate your own agency, either, and keep looking for chances to make the world a little better, whether through your technical work or through a kindness to a student, a friend, a random stranger.  Or, per Robert Louis Stevenson: “Don’t judge each day by the harvest you reap but by the seeds that you plant.”

2020-10-23

I have a job where I do things I like to do.  I play with math and computers, sometimes getting others to join in, and then I get to tell students about the stuff that I love.  I think this is great!  For me, the joy of it isn’t in papers or prizes, it’s in the day-to-day figuring out.

There are lots of external milestones in undergraduate life: homework, quizzes, exams, projects.  Most of them are on the time scale of semesters.  Grad school has some milestones as well: finding an advisor and committee, A exam, B exam.  But these milestones are fewer and farther apart.

As graduate students, by and large, you are responsible for structuring your days and figuring out how to keep moving forward.  That’s not always a simple task, even in less turbulent times!  And sometimes there is the temptation to just bull forward with the concrete tasks that the world has set for you: grading homework for your class, running experiments prior to a paper deadline, doing the laundry and feeding the pets.  But while these are all important things (certainly your pets think so!), I hope you all are able to take advantage of the rare privilege of exploring what interests you, I wish for you all the mental space to enjoy going to play with your research.

2020-10-16

One of the things I remember from my pedagogy course in grad school is Vygotsky’s idea of the “zone of proximal development” (зона ближайшего развития) — the set of tasks that a learner cannot yet do unaided, but can complete with appropriate guidance, the space between “I already know how to do this” and “this is totally beyond me.”  Part of the idea of the ZPD is that learners need to be challenged by things that are just at the edge of their capabilities — or even just beyond their capabilities without help! — in order to make the best progress.

None of you chose to go through a pandemic.  That’s just bad luck.  But you did choose graduate school.  And even in normal times, as we get into the middle of the semester, it’s easy to think “why did I agree to this?”  Classes are hard; research progress feels slow; it seems like you’re struggling with things that those around you are getting.  The first edges of the gray Ithaca winter don’t help.  But you are not alone in any of this.  You made a choice to go into graduate school, pursue mathematical research, live in the zone of proximal development, and take on these challenges “not because they are easy, but because they are hard.”

And remember that part of the idea of ZPD is that you’re tackling problems where you might still need help, whether from an instructor or a peer or just a reference book.  So talk to your advisors and talk to each other — and don’t worry that your ideas might be half-baked!  The only way to get something to be fully-baked is heat and patience.

2020-10-09

Get your flu shot.  Make a plan to vote, if you’re eligible.  Go outside and get some exercise.  Get some sleep.  Celebrate your victories.  Talk to a friend.  You know a lot of the things that you need to do in order to keep yourself and your circle moving forward.  Take some time today to do them.  Yes, that homework, paper deadline, etc is important, but you’ll be able to deal with these things more effectively if you are also able to take the time to take care of yourselves.

2020-10-02

The first news I read this morning was about the president’s COVID diagnosis.  This came on the heels of diagnoses for people I care about rather more on Thursday night, and other bad health news for my extended family earlier in the week.  The combination reminded me that, though it’s harder with those I don’t know and those I violently disagree with, I aspire to being able to wish happiness and freedom from suffering to all.  In days of anger and upset, finding compassion takes work - it’s easier to see disagreement than to see common humanity.  But for all that, the effort to move toward compassion still seems worthwhile, at least to me.

2020-09-25

No serious charges in the Breona Taylor case, and riots after. DHS seems to be proposing a regulatory measure to make life hard for international students again.  The pandemic continue.  And yet: COVID numbers in Ithaca seem under control.  The weather has been beautiful.  It is a strange world at the moment, but many of you are making the best of it.

All these things are true.  It is not a normal time, and seems unlikely to return to anything like normal for a while.  It is OK to be behind, to be frazzled, to not be on your game.  If you can, though, it is also OK to appreciate a sunny day.

2020-09-11

No sermon today, but I did want to say a few words about Paul Steen, who passed away unexpectedly one week ago.

In the first year that I was at Cornell, Paul gave one of the talks for the CAM visit day.  I’d met him briefly before, but I remember that I got to talk to him after his talk to the prospective students, because I thought the stuff he was talking about sounded really cool.  I interacted with him several other times in the first couple years about other CAM things, too.  He helped organize the colloquium one year, gave the visit day colloquium another year, and was always around for the field meetings, picnics, and events.  And I saw him on proposal efforts, and at the SCAN seminar, and on student committees.  We never did any research together, mostly just from timing; we shared a number of interests.

Paul was at the top of his field, and was also very down-to-earth.  I never knew him as anything but kind and cheerful.  He laughed easily.  I looked forward to seeing him.  I found out about Paul’s death at the same time that I was responding to an email from him.  He’d written on Aug 28 (two Fridays ago) to say that he was glad to help out with CAM in whatever way he could, that he was enthusiastic about the idea of a “SciML at Cornell” push, and that there might be some eigenvalue problems that would be interesting to chat about (with paper references!).

I am sad that I’ll never get the chance to explore those ideas with Paul.  I think I would have enjoyed it.  But beyond his body of technical work, I think he lived well, laughed often, and will be remembered fondly by many.  So he leaves a great legacy in many senses, and I suppose that is all any of us can hope for when we go.

2020-09-04

Today’s inspiration is again borrowed from Sandy Mack (from http://honcol.blogspot.com/2014/11/former-honors-director-sandy-mack-is.html):

Committed realist or idealistic romantic — showing up alert, sane, and compassionate seems more and more to be at least Woody’s 85%, maybe more.

It’s thrilling — because there is almost always room for change, adjustment, repentance, improvement, ecstasy, magic.  It’s exhausting — because we never seem to outgrow the need to grow, fail, learn, and try again.

And isn’t that just the right note to start this semester?  We’re all making it up as we go along, even more so than normal, and it is both thrilling and exhausting.

2020-08-28

This week we saw fires in California, hurricanes hitting Louisiana, COVID deaths passing 180K, and the news of police shooting Jacob Blake in the back.  The drumbeat of bad news is a constant background in 2020, but any given piece of bad news is probably hitting some of us disproportionately hard.  For those of you who are teaching this fall, that might be a student in your section.  Or it might be a friend, or it might even be you.  And the year is not over, and we know that there will be more bad news in store.  Fall will turn to winter soon enough, and for many of us it gets harder to cope as the days get shorter and colder.  This will, for many, be a hard year.

So what are we to do?  I have said it before, but it bears repeating: you are your brother’s keeper.  Lean on those around you, and let them lean on you in turn.  Schedule regular check-ins with your friends now, so that those routines will be in place when trouble hits.  Learn about the formal and informal mental health and counseling resources that Cornell offers.  And while I encourage you to strive, to learn as much as you can, and to good research — also be gentle with yourself, your friends, your students, and your mentors.

This is not a normal year, but we’re all in it together.  Good luck to all of us in the coming week as we set to it.

2020-08-21

When I was a kid, I used to watch “The Red Green Show” and then “Red Dwarf” and “Doctor Who” with my dad on Friday nights on our local public television station.  Our reception was terrible, but it was a good excuse to laugh together, and some things stuck with me.  One of those was from an episode of “The Red Green Show” (a Canadian comedy), in which the main character is explaining how to make some type of living space out of an old refrigerator.  “Don’t measure too carefully before you cut,” he advises, “because you’re going to need some cracks to get breathable air in!”

None of us are under much illusion that our long-term plans for this year will unfold in exactly the way we hope.  There is too much uncertainty.  But even the best of times have plenty of uncertainty to them.  As academics, we have the privilege to think long thoughts, and to work on projects that might not see fruition for several years.  But just because we are in a position to plan things out for several years, that doesn’t mean that it will work out as we expect.  And so…

For new students: grad school is a confusing place!  Plan to talk to faculty, and to get involved in research.  But realize you may not end up working with who you expect to, and you may find inspiration in a direction that you never even knew existed before coming here.

For old students: with graduation no longer on the infinitely-far-off horizon, you might well be worried about what comes next.  Network, make connections, plan — and realize that eventually you’re rolling the dice.  Have an idea where you want to go, but keep a broad awareness.  Applied mathematicians can go in an unusually wide number of directions, inside academia and beyond.

For students in-between: plan your research, your papers, your A and B exams.  And realize that it wouldn’t be research if we knew what we were doing, and you will almost surely have to abandon a plan or two in order to make progress.

And for all of you — plan to be gentle with yourself and with each other this fall.  Even if you sometimes fail in that plan, having made the plan in the first place might remind you to breath, cope, and lean on your friends when you need to.

2020-08-14

No sermon this week, but did you know: On this day in 1894, the first summer meeting of the AMS was held at Brooklyn Polytech (now NYU Tandon).  A 126th anniversary isn’t quite as auspicious as a 125th, but it’s 2020 — let’s take what we can get!

2020-08-07

That’s more than enough official business for one mail.  So I’ll wrap up this week with a snippet of another of Sandy Mack’s “sermons” from my undergrad days (from Dec 16, 1997):

How to Handle Stress:

  1. Pop some popcorn without putting a lid on it.
  2. When someone says, “Have a nice day,” tell them you have other plans.
  3. Make a list of things to do that you have already done.
  4. Dance naked in front of your pets.
  5. Tape pictures of your teachers on watermelons and launch them from high places.
  6. Walk to class backwards.
  7. Read the dictionary upside down and look for hidden meanings.
  8. Stare at people through the tines of a fork and pretend they are in jail.
  9. Make up a language and ask people for directions in it.
  10. Remember that when we next meet it will be a new year. With new chances for improvements. With new terrors. With new hope.

Have a great weekend.

2020-07-31

It has been another terrible week in the news, and many of you are facing additional, personal hardships.  It’s a lot sometimes.  I’ve taken to dealing with that by sitting with our bunny rabbits and watching their antics (and sometimes they nibble on my toes).  It doesn’t make the world any better, but it at least cheers me up.

It promises to be beautiful weather here in Ithaca this weekend.  I hope those of you who are in town have the chance to enjoy it.  For those of you elsewhere, I still hope you have the chance to take a break this weekend.

2020-07-17

When I was an undergraduate, I was part of the honors program at the University of Maryland.  At the time, the director was Maynard (“Sandy”) Mack of the English department.  He sent out an email about once a week, and always said the same thing at the start of the semester — and often in the middle of it:

I’ll always repeat at the start of each semester: in many ways we are our brother’s/sister’s keepers. If someone seems troubled, reach out. The worst you can get is yelled at, and you just might save someone’s semester…or life. Be kindly nosey, please. This perilous uncharted journey called life can be terrifically exciting in its freedom, and it can be overwhelming, in its freedom, too. Take care.

Yes, I still have those “sermon” emails, now from more than twenty years ago.  And I still think about them at times like this.  So obviously the message stuck with me, and I still find it helpful.  I hope the same thought is also helpful to you in these T-6 weeks until the fall.