Archive for October, 2012

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.

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Season: Applying for jobs.

October 23, 2012

1. What mathematical activities? What level of rigor?

The math job application process is described in more pragmatic detail in many places, for example here or here. This post will focus on the interior experience of applying. You must write a research statement, which is a sort of demonstration of ability with rigorous logic. You must write a teaching statement, which is less rigorous and more personal. There is a lot of non-rigorous soul-searching, about what job would be best, what the future might hold, is mathematics really worth doing?

In a way, you apply your mathematical problem-solving skills to the problem of getting a job. This requires researching different mathematical lifestyles, asking yourself good questions, methodically clarifying your wants and abilities, and articulating these in the application materials. It’s a sort of math problem, but with your life.

2. What relevant interactions with other mathematicians?

As a grad student, it’s not clear what life is like as a postdoc, or a professor, or someone working in industry. So there’s lots of question-asking. Getting career advice is also fun. Maybe editing and proof-reading help.

3. How does it feel, what is the mood?

For me there were lots of ups and downs. It’s necessary to balance an artificial, constructed hubris with humility and longing. I could work myself up into a high mood of idealism, dreaming about the future, being excited for change. I could also exhaust myself with low moods of fear, competition, existential crisis, and administrative fatigue. It’s important to be passionate and indifferent at the same time.

4. What state of mind? stable vs. chaotic? focused vs. dispersed?

In fact, my mind was focused on the applications, a determined focus to make the best applications possible. There was not much clarity about my desires and hopes for the future, more of a two-month tunnel vision centered on application paperwork. I figured I could apply first, and then think about what I wanted; I don’t know if this was the best strategy. Gradually, this determination and focus left my mind confused and drained.

5. What type of self-reflection during the experience, and did it help?

It was extremely helpful to recognize that I would have to balance artificial, constructed hubris with my more genuine and self-reflective longing and confusion. Holding this contradiction in my awareness, I could present myself as passionate, confident, and all around really awesome, and could get excited for a range of possible futures, while also recognizing how humbled and confused I also felt. In a sense, I could self-reflect on the self-reflection that the job application process was stirring up, and give it a space to unfold. Gradually, on its own schedule, some clarity did emerge about what I wanted for my future.

6. An everyday metaphor for the experience?

Everyone (hopefully) knows what it’s like to apply for a job. However, applying for an academic math job is a little unique. I applied to over a hundred positions, and received rejections that explained they had over 600 applicants for a single opening. So chances there were worse than flipping a coin and getting 9 heads in a row.

Furthermore, the job cycle is almost a full year. So applying for an academic math job is like writing someone else’s application for a job that starts a year later. Who will you be and what will you have actually accomplished by the time that job starts? That’s who you must present in the application.

7. An example of a good day and a bad day?

On a good day the application material looks good and well-written. On a bad day, it feels like I’m spending hours applying for jobs I don’t want.

8. What did you do when you were stuck?

It was always nice to return to doing actual math, research or teaching, rather than just writing about it. I found it really helpful to discuss plans, and vent, with friends and family who knew me well.

9. When and why did it end?

No matter how exhausting and nerve-wracking the application process is, at least it has specific deadlines. You know it will end at some point, hopefully with an accepted job offer.