Several years ago I published my favorite kind of paper: it took a problem that was hard to solve by hand, and solved it using 20% cleverness and 80% brute force. The details don’t matter here, but the solution had scalability problems. Therefore, the next iteration of the work (done primarily by a very smart student) was more like 80% cleverness and 20% brute force. The student, Usit, disappeared into Microsoft after getting an MS degree, leaving me to give the talk about his work. After giving this talk I spent a while talking with a member of the group that produced Astree, a team that contains some of the heavy hitters in the program analysis world. Of course, they had encountered similar problems to ours in constructing good transfer functions, and they also had some ideas for solving these problems. Not long after this conversation, I decided to drop this line of research. My impression then — and five years later I still think it’s true — was that while I could have continued to publish in this area, my contributions would not have been very deep or interesting ones. Basically I realized that (1) the problems in this area were highly mathematical and (2) any math power I could bring to the table was insignificant compared to groups containing people like the guy I talked to.
I take a positive and a negative lesson from this little story. The negative one is about the state of math education in the US. Why am I so often outclassed by people (who usually don’t have a degree in math) educated outside the USA? It’s ridiculous, and I actually do have a degree in math. I’m not saying that I’m supposed to be a math genius because I took some classes (I chose to go to grad school in CS instead of math for a reason) but the difference is pretty noticable. Looking back, I only learned real mathematical thinking in a handful of upper-division classes for math majors only. In contrast, the math classes that were in service of an engineering degree emphasized cookie-cutter methods for predefined problems.
The positive lesson is that I found it very freeing to realize that a research area is covered by other people who are more capable than I am. This has happened to me a few more times since then and it’s always a relief. As a researcher, life is good as long as there exists just one important problem that I’m most capable of attacking.
6 responses to “Outgunned”
> Why am I so often outclassed by people (who usually don’t have a degree in math) educated outside the USA? It’s ridiculous, and I actually do have a degree in math.
Selection effect? To learn a new language like English, to decide to come here, to even just be admitted (with or without math degree)… all these seem like they would skew the class of said people upwards.
Hi gwern- The people I’m talking about who were educated outside the US still live outside the US, so I don’t think that particular selection effect is a factor. Of course there are many other selection effects…
It is a selection effect. You are generalizing from a few individuals.
I have met many Asians and Europeans who are very weak at math.
@Daniel, In general Asians are better at maths when compared to Americans, that is one thing you need no selection effect to realize.
Hi John,
from my experiences with the German system, we had a more thorough math background than most unis in the US or Oz or somewhere else; this has changed a lot in the last 10 years. Whereas CS students were forced to take almost the same curriculum as math students in the first two years, this is very different nowadays, so we’re heading into the same direction. 🙂 Anyway, talking about the topic of transfer function synthesis: The math required is so much simpler nowadays than it used to be back then; and I’m happy about that so I can work on the topic 🙂
There are also significant cultural differences between countries. In some countries, becoming a professor is so far removed from any practical issues that there is a strong concentration effect. Many talented people who may have become good ‘applied’ professors would simply be doing other things in those places. So, when you speak to the academics from these parts, you see a very different distribution from the one you are used to.
The converse effect in such places is that strong math skills compensate for weaknesses in the interface between theory and practice. Just being able to do complicated math is not the same as doing good math aimed at some major issue. I don’t think the US has much to worry about at this interface.
I say this as someone originally from India, trained in a good US graduate school and currently teaching in UK. So, somewhat based on first hand experience…