Thursday January 12th
Week 4 : Chapter 12
- Right now, if you asked me who my three favourite mathematicians are, I would probably say:
- This was in regards to their work and their perspectives, but I had not realized until recently how much they had in common!
- I read a Quora post today on the difference between advisors who publish a lot, across a bunch of fields vs those who publish deeply (the post was in fact about two specific mathematicians who I will not call by name, since that seems to be a lot of my feed). I had a conversation about this interestingly with a mentor I have in industry, and it made them think that they had had a similar experience such that one of their advisors was like the first, and the other was like the latter. I think that there is space for both in research, but it doesn’t seem to be the case (and they agreed with me on this) that industry in particular values this. For example, I spoke with someone who was part of the evaluation process of a certain really well-known industry fellowship for students in grad school, and they admitted the they originally had a cut off of about two papers for 2nd year to third year-ish students (that is, your application would be rejected and your proposal would not even be considered below this threshold). I remember hearing it and thinking that I would probably not choose to work there because it really flabbergasted me at the time (I had several Maths friends who didn’t begin publishing until their later years, for example, and Shannon himself spent 10 years working on a paper alone), but it was very insightful to hear that as a student, and I knew that something / someone had put it in my path so that I could be in that room and hear these things as a student.
- Even back then, I thought it was really silly, and it would discourage them from discovering students who were doing the work of the latter type; in particular, the Quora answer had said that the person who worked in the latter way was someone whose work rocked the boat, even though they didn’t publish as much (meaning that their work revolutionized the field, or some space when they did). So they would completely be disregarded if they applied to that fellowship or research internships, unless they attended a prestigious institution with professors who could leverage their reputation to “talk up” the student’s potential. So yeah, that’s definitely a failing of the system, I guess.
- I thought about this as someone who moved from an area where people CHURN out papers, to one where this is less likely the case (mostly because the community was more supportive and less back-stabby (lol) and I found the work more interesting / up my alley. I didn’t think I wanted to spend my time in a field where I would be miserable navigating things while trying to produce work). I’m not sure what would be a better way of assessing this. Perhaps something like just interviewing students based on how they would break a problem down, digging deeply to find out the depths of their knowledge and their creativity in problem-solving? Or perhaps industry was never made for that kind of work? I don’t know, as I possibly will not be a fit for that sort of thing as I don’t fit the criteria anymore (i.e. has lots of publications with lots of citations in trendy field, and attend fancy school).
- I was always kind of struck by how early in my degree, one of my strengths (i.e. my creativity) was not leveraged. That was always shocking to me. I have generally excelled at things that are creative (e.g. I topped my class in undergrad in a creative discipline, as an example, and easily won those kinds of competitions and challenges growing up and generally struggle with having too many ideas and find connections between things constantly, asking myself “has anyone looked at…”? Something I thought about my first year was only published over summer this year by a top research lab, even though my idea was brushed off when I had a discussion about it to one person in my department. When I explained it to someone else in another (Econ at the time), it blew their mind and they said they could imagine a tonne of possibilities for it), but it wasn’t something that was acknowledged as a student, for some strange reason, once I was in the CS side of things. It felt like I was starting over in many ways, and when I tried to express these things, it was met with a lot of tone-deafness. It was only when I noticed that they weren’t necessarily acknowledged but they were being extracted (usually without my consent and in much simpler, shoddier form that did not quite catch the subtlety of what I was proposing) that I realised that yes, it is the case that I’m still very naturally creative. I say this to make a point specifically about why this is the case. I am creative out of necessity and the environment from which I came, and my life experiences.
- In undergrad, this mystified a lot of my peers. They didn’t know where some of the things I said came from. I was mystified by how things worked in the United States when I first came here; we didn’t have some of the machines they had for doing things like painting traffic lines in roads and we didn’t make buildings the way they did, with their technology. We used other methods; this is how we understood the world.
- A friend of mine in Los Angeles joked that I “always misunderstand everything”. I realized later on it was because things assumed to be understood by people who share certain levels of understanding are quite perplexing to those who do not. Imagine if you gave a problem to the latter kind of person to solve? How would they imagine the problem or its solution? Once I learned the context within which I had to understand a problem, I could usually determine what the logical steps to a solution they wanted should be. But even something as simple as “what kind of cheese do you want on your sandwich?” in America, can be perplexing to someone who isn’t from that place. Maybe “cheese is cheese” where you are from. Growing up, this was the case for me. There wasn’t an assortment of cheeses (although there is today).
- Growing up in a place where we had to be creative to solve problems also facilitated that; we didn’t always have the tools that countries like the United States had. I also think about this when there is evaluation of grad students on these fellowships or opportunities or even admission to grad school; why don’t they see this, because nothing in their metric measures this (do you come from a place where you had to be, out of necessity, more creative and resourceful?)? I saw a documentary on (Claude) Shannon years ago where someone said this about him; that it was important that he grew up where he did, because it was a place where people had to build things growing up as a child, and that influenced who he was. Perhaps this is why we should advocate even more for persons who don’t come from the typical background that we expect of PhD students (honestly, I think the textbook definition of how we choose who gets in to be especially boring and uncreative; we don’t look for those kinds of students!); by necessity they have to be more creative and stubborn (ha) to even consider such a thing!
- I struggle with this a LOT in my current institution. It has been my experience that many of the students in grad school are filtered up from undergrad; that is, they also have attended undergrad there, or in a handful of the states nearby. So in many ways, for an advisor (or fellow student peers), they might feel “familiar” in a way that it is easy to discount the ability and potential of someone who is not. Interestingly, there is a fair mix of grad students in Pure Maths who are from the other coast, or all over the country (and who are internationals from continents like Asia and Africa), and even though I did not immediately pick this up, I almost immediately found a better fit with them. I would argue that having a mix of students is key to challenging assumptions of students who have only exposed themselves to a limited world view, a limited expectation of what navigating ambiguity and solving a problem looks like.
- Everything about the structure of the institution, and how classes are taught, and how research is encouraged, I often think, must feel familiar to someone from this region, in a way that someone who isn’t will have to navigate and initially struggle. And so, it makes sense that persons at this place often stay within this region, and set roots down here, whether they continue in academia or they do not.
- I was also thinking recently about differences in advising. I really like the kind that feels more like a conversation, where the student can sort of graze through a field of information, rather one that is too “top-down”. If the student has the right mindset (i.e. that the whole point of this is so that they can engage in research independently), they can experience a much deeper understanding of the field and with more drive for a problem at hand rather than being assigned one. But that also takes a degree of trust from an advisor, and a degree of maturity on the part of the student, and well, time.
- This chapter (12) covered Seymour’s Splitter Theorem. It’s a fairly shorter chapter; I read it in a doctor’s office today, while waiting for a health check-up, if that helps any. Interestingly, that particular office is very comfortable for reading and the consistent hum of the air conditioning unit is such that it’s very easy to focus. Not sure why that is, but here we are. I vowed to take a nap and read it again in the evening, though.
- I also got through some of the papers from yesterday in the wee hours of the morning this morning. They were super interesting!
- Seymour’s Splitter Theorem is a generalisation of Tutte’s Wheels and Whirls Theorem. The Wheels and Whirls Theorem determines when we can find some element in a 3 connected matroid M to delete or contract in order to preserve 3 connectedness. The Splitter Theorem considers when such an element removal is possible that will not only preserve 3 connectedness, but will also maintain the presence of an isomorphic copy of some specified minor of M.
- I will actually not be covering this chapter today here, although I did go over it on my own. I just wanted to write my thoughts today, and will continue with notes as usual on chapter 13 tomorrow!
- One neat thing I did find is while ago that I forgot to mention is that the Appendix has a whole glossary of graphs, which is super helpful!
And that’s it.
Written on January 12, 2023