1. What mathematical activities? What level of rigor?
These blog posts attempt to describe the common experiences of a research mathematician… all of them. Most mathematical seasons seem to involve hard work, even overwork. This post is about the necessary seasons of rest and gentleness. They occur during vacations, or after significant accomplishments (e.g. passing qualifying exams, or finishing a PhD). It’s a time to recharge the batteries, but there may be some light math — reading blogs or news, checking out what others have been working on, maybe attending a conference as a participant. However, of utmost importance is allowing oneself to “do nothing,” which is hard! Low rigor, high relaxation (hopefully).
2. What relevant interactions with other mathematicians?
Almost none, except perhaps social interaction. If I’m interacting mathematically with someone, I’m not resting.
3. How does it feel, what is the mood?
4. What state of mind? stable vs. chaotic? focused vs. dispersed?
Any state of mind that is a release, or distancing, from mathematical states of mind. This is a chance to get some fresh air, and in my experience this means not just thinking about non-math things, but actively experiencing fresh and different states of mind. So I often go traveling, which often induces a chaotic, dispersed being in the world. Or I focus on friends and family, which is a chance to stabilize and concentrate on meaningful non-mathematical things.
5. What type of self-reflection during the experience, and did it help?
Mathematicians need to develop not just mathematically, but also emotionally, morally, politically, culturally, etc. For me, a period of rest is an important time to ask, “Who else am I?” and “How else can I engage the world?” So there is self-reflection about the world and my place in it.
There is also much reflection about my mathematical lifestyle. When I rest, I reflect that my life in math mode seems unsustainable, in one way or another. How, besides taking periods of rest, could I change to make it more sustainable? Should I do less (one fewer math-art collaboration?), or do things differently (more sleep, less coffee?), or shift priorities, or change my short- or medium- or long-term mathematical goals?
Furthermore, there is usually some good self-reflection about the threads of mathematical content in my life. Was that last proof really the best one I could find? What do I think is really going on with that circle of ideas? I have some of my best mathematical clarity during vacations, or in the first few weeks after I return to working. I’ve learned to gently introduce this pondering, towards the end of a rest period.
In a sense, I rest precisely because I need to self-reflect in these ways. If you’re not self-reflecting, you’re not resting properly.
6. An everyday metaphor for the experience?
Of course, everyone knows what rest is. Imagine how you feel after staying up late, or through the night, or staying up for two nights in a row — that closed, confused, muddy state of mind and rigid, almost non-sensical, way of thinking. Imagine then the surrender to deep sleep, and then the wonderfully free and light mind of waking up, really rested. So important! Don’t let anyone convince you otherwise!
7. An example of a good day and a bad day?
On good days I am gentle, and allow myself to rest. Maybe it’s even a “productive” rest, in which I can contemplate the bigger picture of my mathematical doings. On bad days, I don’t allow myself to do this.
8. What did you do when you were stuck?
If I catch myself working when I should be resting, or not allowing myself to rest, I remind myself that gentleness is a virtue, too. Although it might not be easy, it’s something worth striving for.
9. When and why did it end?
Vacation is over.