Living Proof

I am going to add my voice to the others talking about Living Proof (which was originally brought to my attention by a biology professor at my school, of all people).

This is a (free) book on what it is like to struggle with mathematics. It features 41 mathematicians who describe their struggles in becoming a mathematician, with some of the chapters on how they overcame such struggles.

I think that the sections really vary in their usefulness to any particular student, but that is a feature. I will likely use Living Proof in some of my classes, but I will assign students to read, say, any $n$ of the chapters. Students can then pick which topics resonate with them.

I struggled a lot with my qualifying exams, which for me were 6-hour written exams. I had to take them in two areas, and I chose algebra and logic. You could take them twice per year, and you had to have one passed by the beginning of your third year and both passed by the end of your third year.

For me, this basically meant that I had to pass one of the two exams in my first three tries (so one exam in my first six attempts at an exam, or one exam in my first 36 hours of exam-time). In my second year, I took each exam twice, and I studied hard for them. I got a “Masters Pass” on three out of my four attempts (I failed the fourth), which means that my work was good enough for a Masters degree but not for a Ph.D. I was going to get kicked out of the Ph.D. program if I didn’t pass one of the exams on my next attempt.

This was very disappointing to me, and I thought that I wasn’t good enough for graduate school mathematics. I applied for a couple of community college jobs, who fortunately turned me down because of lack of experience.

The happy end to the story is that I got a full, Ph.D.-worthy pass in logic at the beginning of my third year when I really needed it (along with another Masters Pass in algebra), and I passed the algebra exam with a full pass four months later. It was do-or-die twice for me in that third year, and I managed both times.

In retrospect, I didn’t really know how to study. I learned a lot, but I did not really know the level of dedication and immersion that I needed to really learn the material. I definitely learned the material well enough to pass, but I don’t think I learned the material well enough to guarantee that I pass—I think that I was partially lucky with the choice of questions.

I think about this experience a couple times per year. It reminds me how some of my students feel. I also want to try to tell my students what I learned about how to study, but I haven’t yet figured out how to put it into words.

I am glad that this exists, and I am grateful that Henrich, Lawrence, Pons, and Taylor made this happen.