Archive for the ‘flavors’ Category

Flavor: Giving a (research) talk.

February 15, 2013

1. What’s going on mathematically?

I’ve been asked to give a talk about my research. After preparing (see Preparing a research talk) for a day or two, eventually I’m standing in front of a quiet room and have just been introduced.

2. What is the emotional and logistical context?

The room is quiet and everyone is looking at me. I may be very nervous, mildly nervous, or not nervous at all. Then I start talking.

3. What thoughts are there?

The mathematical story I start telling is always very integrated with the slides I’m showing, or the material I’m writing on the board. The visuals guide my thoughts, which are translated into explanations and narrations. The translation of my mathematical thoughts to words requires some thinking about the audience, what they might or might not know, what I’ve already said to them, what they’re probably thinking about now. There are also occasional flashes of thoughts that snag on random and inconsequential details during the experience, like I find myself thinking about the color of the board, or where my right hand is, or the sound of a certain word.

4. What quality of awareness?

This is a very, very absorbed state, with little self-awareness. Time doesn’t seem to flow, although I occasionally glance at the clock to notice that it is later than before. I often feel like just a conduit for my thoughts to be spoken, and end up speaking every single thought that enters my awareness (for better or for worse). I feel comfortable but not free, not in control, not myself. My awareness is heightened to an unsustainable level, perhaps like I’m being attacked or about to crash a motorcycle.

The self-awareness I do have is usually about my body movement and tone of language. I wish I was aware of and able to control my eye movement, but I haven’t been able to train myself to do this; I don’t even know where I look, let alone know if I should change where I look.

My level of self-awareness is correlated in an interesting way with my distance from the board/slides versus the audience. The closer I move to the audience, the more I’m aware of being a human who is communicating using body language and eye contact in addition to speech. As I move towards the board/slides, it’s like I get submerged in my own internal monologue.

5. What emotions?

Personally, I enjoy giving talks, and performing generally. I enjoy the adrenaline. During the talk, I’m not very aware of my feelings, except to notice that I feel high on adrenaline. After the talk, I’m always relieved.

6. What does it resolve to, after how much time?

The talk ends and there are questions. During the questions I’m only slightly more aware of my body language and eye contact, and maybe start to feel more mixed emotions (happiness if the talk went well, or frustration if it didn’t). But the heightened awareness and absorption continues. After the questions, I just want to go be by myself and not think about math.

7. How frequent is this flavor?

Every few months.

8. What are good/bad ways to change or follow it up?

Since the experience itself is so singularly focused, I think it’s a good idea to sort of debrief myself afterwards. How did it go? I always tell myself that I should’ve been more mindful of eye contact, but of course there are other ways that the talk could’ve been improved. Giving a talk is an art form, that only improves with practice and reflection (if it improves at all). It’s healthy to acknowledge some successful aspects and some unsuccessful aspects. And there are usually mathematical follow-ups to pursue, from the questions and comments.

There are always imperfections in the performance, and it’s useless to dwell on them. Gandhi said something like: “Freedom is not worth having if it does not connote the freedom to make mistakes.”

Flavor: Wandering around (math) for fun.

December 23, 2012

1. What’s going on mathematically?

I’m surveying some new mathematical terrain, mostly out of curiosity and for fun.

As a child and young student, I remember falling in love with math by exploring, and following my curiosity. Once math becomes a vocation, there’s more at stake and one is less free to just flitter about dabbling and seeking math pleasure. But occasionally, I do it anyways. This flavor of math is the grown-up analog of the childhood experience.

2. What is the emotional and logistical context?

There’s time. Perhaps I’m going to a conference, and want to know more about the talks, the speakers, and the content. Maybe there’s a seminar I’m about to attend, and the title and abstract are intriguing but slightly out of my area. Or maybe I don’t have an excuse, and am just curious about something.

3. What thoughts are there?

I use the internet, and my resources are usually: Wikipedia, papers on the arXiv, personal websites of mathematicians, and the Mathematics Genealogy site.

Like a detective, I start with a few terms on Wikipedia. I follow leads, to read about the people behind the ideas (when and where they studied, from whom; where they are now; who else they work with; what else they’ve done). I try to reconstruct a history of the development of the ideas, while piecing together the theory itself. (I find chronology a very useful tool for unpacking knowledge.)

Certain words, terms, and theorems keep appearing, and I try to pin down precise definitions, as well as get a gist of main properties and consequences. Gradually, a rough map of ideas comes together. It is superficial, to a larger or smaller extent, depending on how familiar I am already with the ideas.

The exploration is not completely aimless, unlike the times I start reading the news about Syria, then end up scouring the internet for information about the millions of pounds of chemical weapons the US has dumped in the ocean, then reading about underwater landslides and the currents they produce, and giant squids, etc, etc… I stick to math, and stick to the rough topic I started with, and if necessary I abandon an intriguing thread and return to the starting point.

4. What quality of awareness?

A productive session has a good dose of self-awareness, to keep pulling myself back to the central idea(s). There are periods of absorption, when I try to let my curiosity lead me, as unfettered as possible. These alternate with stepping back, checking in, closing some browser tabs, and returning to somewhere familiar, to head off in a different direction.

There are also good periods of spacing out. After skimming one too many papers, my eyes glaze over and my mind detaches from the reading, to go out on its own adventure. I catch myself staring off into space, like I’m listening to the new ideas resonate within the context of everything else that I know.

5. What emotions?

Getting lost in curiosity is delightful. There’s a bittersweet tug every time I stop myself and return to the central idea(s). The space-out periods are also pleasant, the pure joy of absorbed thought. I think there is value in this type of unconscious percolation, although it is hard to quantify or describe.

There’s a feeling of irresponsibility, that is enjoyable. As I piece together an understanding like a detective, a narrative emerges. I can enjoy the characters and what they’ve gone through, without feeling accountable. It’s like watching a movie of mathematics. I can relate. It is meaningful to hear the human story, and understand the conceptual inter-relations. Even if the content is different in substance, analysis instead of algebra, say, the architecture of the content is still logical and rigorous, and the humans responsible for the development are still members of the same community. I relish the taste of this mathematical essence.

Interestingly, there’s always a gradual trend within me towards anxiety, that I watch and try to keep in check. Inevitably, I’m confronted with the vastness of Math That I Will Never Know, or with things I used to know but have forgotten, or with a long list of articles that I really should read and understand. Traveling quickly and superficially around the mathematical terrain is frightening, just like traveling quickly through any unfamiliar terrain for too long. What’s tragic and somewhat fascinating is watching this anxiety (which I never had during the childhood periods of mathematical exploration) sneak up on me, every time.

6. What does it resolve to, after how much time?

There’s really no concrete end, since one can always go farther or deeper. So I just decide to stop at some point. Usually after an hour or a few hours. Most times, I will have found some papers that I genuinely want or ought to revisit in more depth, and these get saved as PDFs and put in a certain spot.

7. How frequent is this flavor?

Maybe once or twice a month. I ought to do it more often.

8. What are good/bad ways to change or follow it up?

In the best cases, I even write out a quick outline or sketch of the ideas that I’ve mapped out; this helps me internalize the exploration, and remember some of what I’ve learned. This could be an outline, a chronology, or an idea map.

This flavor is a great sort of intermission, to working more seriously on some project. So afterwards, hopefully, my mind is relaxed and I feel happy, and I can dive back in to “work.”

In the worst cases, the anxiety catches me and I can’t get perspective on it, so I’m left in a sort of panic, facing the overwhelming deluge of information.

Flavor: Pondering.

December 23, 2012

1. What’s going on mathematically?

I decide to try to see (mathematical) things differently. It’s a relaxed, playful attempt to play with math. Similar to an “intentioned immersion” but looser and less aggressive.

2. What is the emotional and logistical context?

Usually I’m riding on public transit, commuting, in a car, waiting for something, or taking a long walk where I won’t be interrupted. I’m alone. I won’t be able to work very rigorously, so I have low expectations of what will happen; still, there’s an intention to engage math.

3. What thoughts are there?

There’s a range of pondering modes, or games you can play. Here are a few.

Sometimes I take a specific object or idea and try to visualize it. I try to describe its essence. I imagine seeing this image or description for the first time, and see what questions arise.

Sometimes I juxtapose two things via a nonsensical premise, and see what happens.

Sometimes I imagine that I can turn any statement I want into a true statement, like I had a magic truth wand. What would be the most beautiful situation in a given context? What do I really want to be true? And then what are the relevant hypotheses?

Sometimes I construct an internal dialog with an imaginary colleague, or pretend I’m teaching a class.

Again, the basic idea is to play. Rearrange, experiment, start again… but in a light way.

Usually I don’t write, or don’t write very much, so my lines of reasoning can’t get very far. If the game I was playing was like a chess game, then I don’t try to strategize out four moves ahead, but rather just imagine different possible vague developments in the layout of the board.

4. What quality of awareness?

It takes effort, to stay focused on my pondering, and to think in ways I’m not used to. There is a strange juxtaposition of the mathematical headspace and the real world. My perception and awareness jumps back and forth, usually in a disjoint way, between these two realities. So my hearing of the ambient surroundings cuts in and out, perhaps alternating with the sound of an internal mathematical narrative. Or my spacial sense of where I am cuts in and out. Or my visual perception of what’s in front of me gets interrupted by mathematical imagery.

There have been a few times when the two realities sort of coalesced. Rather than a juxtaposition, or cutting back and forth between the two, there was a synthesis. I don’t quite know how to describe these experiences, except as a kind of integration of mind and body.

5. What emotions?

It’s usually fun, and sometimes funny. Sometimes it’s too effortful though, because I’m too distracted. It never feels like I’m getting anywhere, and so it often feels pointless and dumb. But there’s a pleasant feeling that comes with bringing some cognitive depth into a somewhat numbing situation like riding the metro or waiting on line.

6. What does it resolve to, after how much time?

Often I do get some new idea (of questionable worth). Or a new perspective, or a new question. I think I need about 15 minutes of stable pondering, if I’m going to settle into it and get anywhere.

7. How frequent is this flavor?

Mathematical pondering doesn’t come naturally to me, but I feel like it should. (I ponder other things much more effortlessly.) Maybe once a week, unless I intentionally practice it.

8. What are good/bad ways to change or follow it up?

I always think that pondering will become easier, or more fruitful, eventually. It seems like the transitions from being in the real world to being in the math headspace, and vice versa, should become easier and easier to traverse. It seems like there’s a lot of insight in being able to enter the math headspace in different ways, at different times, and so pondering is a way of practicing this transition.

I try to write down any insights I gain from pondering, no matter how vague. But other times I give up pondering because it’s hard and doesn’t feel productive, or even fun.

Flavor: Natural inspiration.

November 28, 2012

1. What’s going on mathematically?

Mathematics is overlaid onto a nature experience. Nature seems to present a vague metaphor, that inspires some mathematical insight.

2. What is the emotional and logistical context?

I’m out in nature. Maybe walking, sitting and looking, or traveling. I’m relaxed, and not particularly thinking about math at first, except for some pondering perhaps.

3. What thoughts are there?

It starts with an acute focus on the natural experience. Maybe watching and listening to wind blowing in trees, or looking at clouds, or looking at interference patterns of raindrops in puddles. I’m absorbed in the sights, sounds, smell; it’s a full experience.

As the scope of my awareness expands (see #4), I start to overlap the nature experience with some math idea. This is usually not an explicit direct metaphor (maybe it would be for a physicist, or a mathematician studying geometry or dynamical systems; the math I do is too abstract, too structural to ever really correspond to anything in physical reality). Instead it’s a loose structural metaphor, a vague feeling like nature is presenting me with the secret I’ve been looking for. Often I have the thought that I’m looking at, or experiencing, the Answer, I just don’t quite see how to interpret it.

Mathematicians are only as good as their imagery and metaphors, which allow them to fasten abstract ideas to commonplace intuition. In these moments of natural inspiration, it feels like I’m getting hints of new images, metaphors, and structures on which to hang my math ideas.

4. What quality of awareness?

First there’s a strong focus on physical sensations, and then absorption into those sensations. This brings an expansion of awareness to a totality, engaging all the senses in one singular experience of the moment. Bringing in the math requires a small conscious intention to do so, to bring some math ideas into my awareness. And then I just hold the two flavors simultaneously: the natural experience and the math ideas. Sometimes this juxtaposition takes effort, sometimes it seems effortless.

5. What emotions?

At the start I’m usually relaxed and happy, then become more happy and slightly less relaxed, and towards the end I just feel peaceful, and a feeling like everything is going to be okay.

6. What does it resolve to, after how much time?

There’s usually no concrete insight, just a sort of spreading out and a new perspective. I hold the juxtaposition for five minutes to 45 minutes (if I’m on a hike, for example), then let go of it. I usually leave it and do non-math things afterwards.

7. How frequent is this flavor?

About once every 2 months.

8. What are good/bad ways to change or follow it up?
As I said, there’s usually no specific insight or answers that arise. Just a vague feeling of fresh perspective and harmony. I think it’s a mistake to try to squeeze some insight out of these vague, almost subconscious, mental interactions. It’s also a mistake to try to hold onto the delicious peace that accompanies them. Better to not try to understand everything, and enjoy the moment as it passes. I’ve always trusted, blindly perhaps, that these experiences make me a better mathematician.

Flavor: Filling out results.

November 28, 2012

1. What’s going on mathematically?

This is a mathematical flavor that happens during a “Pulling together and writing up” season. I have some collection of results that I’ve pulled together, and I’m trying to turn it into a coherent paper or talk. To turn it into a whole, instead of a bunch of pieces. In a good paper, the results are “complete” in some sense. But most of the time, math sprawls continuously off to the horizon. Choosing a paper-size chunk of terrain, and trying to develop it into a coherent whole, is what I call filling out the results.

2. What is the emotional and logistical context?

There’s usually some excitement that things are coming together. For me there’s always some confusion about what’s interesting, or rather what will be considered interesting to others. There’s usually time pressure from a deadline.

3. What thoughts are there?

There’s an element of logic, maybe even necessity. On the one hand, I need to know where to draw the line. To make up an example, imagine that I proved something is true for every positive value of some parameter n. I could stop there, or I could work for a few months longer to try to prove it for every negative value as well, or every real-valued n, or complex-valued n, etc. At a certain point, I draw the line somewhere. This decision takes into consideration the background required, and the proof methods used, and is usually a straightforward decision. On the other hand, maybe I know n can only take values 0, 1, or 2. If I’ve only addressed the n=0 and n=1 case, there’s a feeling of necessity that I should consider the n=2 case. If it is significantly harder, or different, or uninteresting, I should at least mention that this is the case. I think every mathematician would agree that omitting any mention of the n=2 case would be a shortsight.

But mostly the thoughts are centered on aesthetic considerations. The paper needs to “flow”, to be “complete”, to go “far enough” but not “too far” (not to mention the proofs must go “deep enough”, but not “too deep”). These are all culturally-defined aesthetic qualities, that nevertheless most mathematicians would, for the most part, agree on. You know it when you see it. When filling out results, the challenge is that at first you don’t see it. The results are incomplete, and your job is to complete them.

4. What quality of awareness?

Very fluid and open. I’m trying to step back and see the collection of results as a whole, possibly for the first time. It takes an open, flexible mind to see the best way to organize the ideas. Or rather, it’s more like the ideas self-organize into a natural flow, if I can only hold them all in my mind at once, in a big open awareness. Filling out the results means, while holding that big awareness, also noticing all the dark areas that need to be explored, or at least addressed, to complete the whole.

5. What emotions?

Manipulating my own results is always emotional. Often some hard-won proofs are subsumed, or irrelevant, or improved upon. Filling out results means identifying holes and small-minded reasoning, in other words, flaws. This is the phase when the ideas and proofs are depersonalized and objectified as much as possible, and it can be heart-wrenching.

Also, probing the aesthetics engages my emotions, as I try to decide when enough is enough, when results are interesting or complete rather than irrelevant or partial. In general, mathematical exposition is really an art form.

6. What does it resolve to, after how much time?

Personally I haven’t had many hugely climactic results. So after I’ve filled out the results I do have, there’s a feeling of having drawn an arbitrary line somewhere, and there are always copious new directions to pursue. See also the post on “Pulling together and writing up.

7. How frequent is this flavor?

This happens in the lead-up to every paper, write-up, or research talk.

8. What are good/bad ways to change or follow it up?

I’m not very good at drawing a line and deciding enough is enough; I’m more inclined to keep proving and proving, until I really get a big tangled mess. Recognizing some necessary arbitrariness is healthy, then.

The aesthetic judgement part is not easy either, and I can get confused and frustrated. It’s helpful to step back and appreciate whatever nice flow of results is already there, and recognize that the sense for mathematical aesthetics is only grown slowly, through practice.

Flavor: Making a big mistake.

October 23, 2012

1. What’s going on mathematically?

Someone points out that I’ve made a very big mathematical mistake. Perhaps in a paper that I’ve submitted, or during a research talk. Mathematicians are devout truth-seekers, and mathematical truth can be harsh.

2. What is the emotional and logistical context?

The context is social. I’m presenting what I believe to be correct, with confidence. Someone points out a serious flaw.

3. What thoughts are there?

The flaw is usually presented with a counterexample. So first there is cold certainty (of the mistake), and then along with an unpleasant emotional response there are non-mathematical thoughts about the non-mathematical implications. Does this mean the paper is junk, or the theorem fails? Maybe I won’t get a good letter of recommendation then? Does this mean I’m actually an idiot and should quit mathematics? How can I acknowledge the mistake and recover in a way that saves some face?

4. What quality of awareness?

There is a shock and a vivid immediacy. I feel acutely aware, but with an instinctual fight-or-flight quality. My thoughts actually move very slowly, and I find myself focusing acutely on a single symbol on the blackboard, the texture of my seat, or my breathing.

5. What emotions?

There is usually an unpleasant mix of embarrassment, terror, panic, and disgust. Once there was a feeling of being betrayed. There is also a strong feeling of surrender and letting go, which is maybe the silver lining of this mathematical experience. I’m forced to surrender my pride and a bit of ego, in the face of incontrovertible mathematical truth.

6. What does it resolve to, after how much time?

It’s necessary to immediately admit that a mistake was made. There may be an effort to fix or learn from the mistake, but it might be clear that there is no fix. Some face-saving gestures, some wound-licking.

7. How frequent is this flavor?

Maybe once or twice a year for me. Of course, there are smaller mistakes all the time. I wonder if there are mathematicians that have never made such a big mistake.

8. What are good/bad ways to change or follow it up?

There can be something very freeing, about surrendering pride and ego and accepting reality. Mathematical truth is uncompromising and absolute, and mathematicians are harsh truth-seekers. When I can step back from the frustration and embarrassment, I can watch my ego dissolve a little, and find new freedom in the experience. When my mathematical world has just broken so dramatically, it seems like the real world is going to break — and yet it doesn’t.

The worst thing to do is get caught up in the emotions, to the detriment of others. Sometimes I find myself getting angry and trying to place blame on someone else. In the end, however, it’s absolutely clear who is responsible for the mistake: me.

I’ve had mistakes pointed out graciously and ungraciously, and there’s something to be said for compassion and understanding in these moments. Doing mathematics means being stuck, confused, and wrong most of the time. It is our job to clarify and get to the bottom of things, even if that means pointing out a fatal mistake to a colleague. By going through the process of making a big mistake and having it pointed out, I’ve developed a little more empathy for others in the same situation.

Flavor: Finishing the PhD.

September 30, 2012

1. What’s going on mathematically?

I graduated with a mathematics PhD.

2. What is the emotional and logistical context?

Many years (for me, six) had gone by since I signed up for this. The last few involved working for hundreds, probably thousands, of hours on writing a dissertation that a handful (really!) of people will ever read.

3. What thoughts are there?

For me, “I am invincible” and “It’s over.”

4. What quality of awareness?

Sublime, peaceful, and quiet. My mind was light and free, as a huge burden was gone. For the first time in six years, there was no work to do, and I could let go.

There was also an extreme intimacy with my own mind and being. Remember the scene in Star Wars, when Luke Skywalker is the last hope for destroying the Death Star, and at the last minute he disconnects himself from his radio and homing equipment, to just use the force? During that last act, he is alone with himself. I thought of this scene often, and it captures my mindset from the time right before my dissertation defense, up until the graduation receptions I attended.

5. What emotions?

My operational metaphor during years 3 – 6 of graduate school were that of a pine tree in the Cascades during winter, burdened with snow but beautiful. Finishing the PhD, the snow fell to the ground and the bough rebounded and oscillated with uncertainty. I felt expansive elation and lightness, and spent hours crying. There was a lot of deep sleep. Eventually, there was several weeks of stratified relaxation, during which I realized just how tense and focused the lead-up to graduation was.

Handing in the dissertation, there was a feeling of invincibility but also a sort of creative ecstasy. Condensing so much effort into a creative act and object brings a deep joy and feeling of meaning.

6. What does it resolve to, after how much time?

There’s more work, eventually, and next steps. After emailing out my thesis to folks I thought might care, I took a few months off.

7. How frequent is this flavor?

Once, unless you really want to do it again…

8. What are good/bad ways to change or follow it up?

I think you’re entitled to do whatever you want, no questions asked, for a little while.

Flavor: Preparing a (research) talk.

September 28, 2011

1. What’s going on mathematically?

Often I have to give a talk about my research, or a survey talk about relatively advanced mathematics. This post is not about giving the talk, but preparing it.

2. What is the emotional and logistical context?

Before starting to prep, there’s always some degree of nervousness and anticipation, depending on how important the talk is and how comfortable I am with the material.

I’ve experimented with a wide range of logistical contexts for prepping talks. This is one experience for which the math culture permits a significant amount of flexibility and alchemy. Among mathematicians, “He/She has to prepare for a conference talk next week” translates to “he/she is going to be acting a little strange; give him/her some extra space.” I’ve tried locking myself away until it’s done, or prepping during a long hike without writing anything down, or sitting in front of a waterfall and practicing my words for hours. There isn’t much common context.

3. What thoughts are there?

The goal is to develop a human connection to the content of the talk, in order to figure out how to communicate the content so it can be best understood by the range of people in the audience. There is usually some learning and relearning of material, piece by piece. But the biggest challenge is in reorganizing the ideas into a story that is linear enough to flow as a narrative, but nonlinear enough to convey the robust intuitive interconnections. The second-biggest challenge is aiming for your audience – including the right balance of detail and metaphor, rigor and exposition.

A good starting point is immersion in the subject – getting comfortable with all the important ideas, the different perspectives on those ideas, the history of the ideas. I recently spent 15 hours preparing for a one-hour talk. Then it’s necessary to zoom out, try to see the big picture, and from a good vantage point to construct your story. Towards the end of the preparation, the talk becomes more gestural in my mind – it has organized itself into parts, with transitions, and an engaging structure and flow. The talk is ready when I can see it all in my head – all the information batched into articulate clumps, which are batched into sections, each section occupying a place in a conceptual outline whose shape I see clearly in my head.

4. What quality of awareness?

The hardest, but perhaps most important, task is to constantly and consciously shift between the different levels of detail. Zooming in, zooming out – the talk needs to work on multiple levels, so that the audience can comfortably engage the talk and follow it, from a range of backgrounds and focus. It’s easy to passively let the math lead you, while prepping a talk, but the result usually lacks perspective and is boring.

I try to see the content for the first time, to be my own audience. I try to forget that I already know how the story ends, so I can perfect the story-telling. It feels like trying to hear your own voice, from outside your head.

Each expository challenge starts with a tension, which is broken by a moment of freshness and newness, which then rearranges itself into an enjoyable obviousness.

When the talk is ready, I feel like I’ve transcended the math/non-math boundary. I’m holding, in my mind, an object (the talk) that is mathematically rigorous and true, but crafted to interface with the multi-dimensional, non-rational, colorful and robust real world.

5. What emotions?

There are the emotions associated with the impending performace – fear, adrenaline, excitement, nausea. The preparation itself is, while usually an anxious experience, also very pleasant. It is a gradual shift from confusion to certainty, confidence, familiarity, and friendship. They say that you don’t really understand something until you’ve tried to explain it to someone else.

6. What does it resolve to, after how much time?

It might take 30 minutes or 15 hours to prep the talk, but it’s clear to me when it’s done. I stop thinking about it, move on to something else.

7. How frequent is this flavor?

About four times a year. There are lots of lectures to prepare when I’m teaching a course; the experience is similar to prepping a research talk but much more mellow, since I’ve only taught 300-level courses.

8. What are good/bad ways to change or follow it up?

I have a strict post-talk-prep routine, which consists of actively doing nothing. I’ve found it’s important to rest, not worry, get sleep, do enjoyable things like listen to music or eat, maybe meditate or get some exercise. The talk is prepped; there’s nothing to worry about. It’s out of my hands, and now my job is to be the best performer I can be. If the talk was prepared well, the performance of the talk is really fun. The worst thing to do is to indulge in nervousness and anxiety.

Flavor: Mathache.

September 20, 2011

1. What’s going on mathematically?

I’ve been doing lots of math, maybe too much: research, writing up a paper, teaching, applying for jobs, other projects. There’s a lot more to do. I stop to self-reflect.

2. What is the emotional and logistical context?

Maybe after a long day of conference talks; or a frustrating afternoon of getting nowhere with research; or late at night when my brain has stopped working and I should be done by now, but I have more to do.

3. What thoughts are there?

My head feels saturated with information, strained from too many self-imposed cognitive tasks. I keep thinking of how many more things I have to do. Often there’s a frustrating problem that I’m stuck on but can’t seem to give up. Usually my body is struggling as well as my mind, and I start to think about my physical aches and discomforts.

4. What quality of awareness?

I’m existing very shallowly. Even if I do non-math things, there’s such a loud noise in my head, of math ideas chasing each other, that I can’t focus on or process life much. The noise has a wide spectrum of frequencies – some of it conscious math thoughts, some of it low-frequency “percolation” (my word for when a math idea hijacks mental bandwidth for an indeterminate amount of time, for mostly-subconscious learning and processing). I’m very aware of physical discomfort and fatigue.

It reminds me of the drained and saturated feeling after a long day of socializing and talking to people, when you want to lock yourself away and listen to silence. But it’s hard to lock the math out of your head.

5. What emotions?

I feel pain, tightness in between my shoulders, often a headache or stinging eyes. Tired, drained. Disconnected from real life emotions and experiences. I feel behind, and sometimes like I’m drowning. It is a particularly physical math experience, and an unpleasant one.

6. What does it resolve to, after how much time?

Eventually things get done, or I sleep, or take a break. somehow my cup gets emptied a little. But it might take a while, and it might get worse first. There have been points of graduate school that really tested me, with burnout or breakdown a nebulous possibility.

7. How frequent is this flavor?

Sometimes for days or weeks on end. As a flavor, it usually comes in the late afternoon, maybe five times a month.

8. What are good/bad ways to change or follow it up?

One thing that helps is physical rest – laying down, consciously fixing my awareness on my breath and on relaxing my body. Meditation is one of the best things to do, although depending on the state of my practice and the degree of mathache, sometimes I fail at dissolving the anxiety. Sometimes a good cry seems necessary, and makes me feel better.

The worst thing is to let it take over, and to wallow in mathache. My cutoff point is societal: if I start to become a mean person, then it’s gone too far.

Flavor: Discussing with a colleague.

September 12, 2011

1. What’s going on mathematically?

A live conversation with a colleague, about research. For example, with my PhD advisor, or someone at a conference.

2. What is the emotional and logistical context?

The context is pleasant. We’re sitting together, with paper and pen or at a chalk/whiteboard. I’m mildly prepped, with comments or questions. There might be coffee. There is always time, and patience.

3. What thoughts are there?

A dynamic back and forth, sharing and building, going beyond either individual. We express old ideas, new ideas, shared ideas. Sometimes there is a bit of translation involved (e.g. topologists say “finite” and “smash”; algebraists say “compact” and “tensor”), or effort in communication. But overall the thoughts themselves seem to move unhindered in our shared collective mind, via common mental imagery. There is a lot of mathematical “body language” – conceptual shorthand, written scribbles and diagrams, and physical gestures that convey so much.

4. What quality of awareness?

My awareness is always sharp, like lightning. I feel like I’m reading someone else’s mind, seeing inside their head. Often I’m simply absorbed in the moment, without self-reflection; there’s nothing else around, no time, no bodies. When I talk with my advisor at our weekly meetings, I have enough perspective to reflect on the experience while it’s happening, to witness the mind-meld from outside as well as inside.

5. What emotions?

These discussions are usually exhilarating; I’m on the edge of my seat. There’s a deep, deep pleasure in connecting and speaking the same esoteric language, especially with someone who is a stranger in so many other ways. The math is a strong bond, of a common research philosophy (of how to think about things), common research modes (of how to go about doing research), and common upbringing (of learned content). The precision of our language allows us to go very deep very quickly, in spite of other cultural differences.

6. What does it resolve to, after how much time?

There are usually some of the following: new answers, new questions, new directions, and/or new perspectives.

7. How frequent is this flavor?

Usually once a week, with my advisor. Possibly twice a day, at a conference. During my recent Solo Math Intensive, I only video-chatted once a month.

8. What are good/bad ways to change or follow it up?

It’s helpful to quickly review any notes from the discussion, to document the new ideas, add things to a To Do list, or hunt down new references. Getting frustrated, intimidated, or discouraged is very unproductive.