I’m writing this post to impart, to future undergraduate students, my most valuable advice. That advice is to study what you love. When high school is coming to a close, it’s common for one to be interested in a few things. It is, however, important to distinguish between a novel interest and a career choice. The line between these may at first be blurry, but there are several considerations which can help sharpen it.
For each candidate major, think about whether you are truly captured by that subject. This is usually a deep-rooted gut instinct which either is or is not present. We may, of course, deceive ourselves into believing we harbour a passion that we don’t. This can be highly detrimental; majoring in a given subject is, well, a major commitment, a four to five-year declaration of fealty: your collected undergraduate course work will certainly be no trivial accomplishment!
Also, reflect critically on your high school life, and your exposure to the subject in question, or relevant material, to date (you certainly should have had some — one usually does not, for example, contemplate attacking a physics major if they took minimal science and math courses throughout high school!). If your performance in those areas was poor or average, you should probably watch your step, and seek advice. This may sound harsh, and admittedly it is sometimes unjustified. For example, due to extreme laziness during the first two years of high school, my math grades were awful, and hence my teachers were quite reluctant to even permit me to take “university preparation” (U-level) mathematics in the third year. However, they gave me the benefit of the doubt, and I subsequently excelled in those U-level courses (yeah, sometimes grades can lie). I wonder what their reaction would be if I told them I was now taking graduate courses in pure mathematics.
When I was about 16 or 17 years old, I was an avid (and also employed) programmer. Waterloo was my target, and studying anything other than computer science in university had never occurred to me. Before high school ended, I discovered abstract mathematics: a breathtaking vista of profound wonder which recently, in a repugnant act of what I believe is sheer misanthropy, has been excised almost completely from the Canadian high school curriculum (other countries, of course, have not been so stupid). Computer science plummeted on my priority list, and I applied to nanotechnology engineering, physics, and pure mathematics programs. I received offers for all of them, but chose to accept mathematical physics as my major. After a year, I realized I didn’t really care about the science as much as I cared about the math (I was already taking “a lot of math” as it was — specifically, I switched into advanced math in my 1B term despite being a science major — but it still damn well wasn’t enough math), so I transferred faculties and became a pure mathematics major. I also declared a second major in computer science, with an eye toward job security, since I felt like I was interested enough in it.
To make a long story short, this configuration lasted for a few years, until I realized that a dominant majority of CS courses seemed to be badly organized, be badly taught, and/or deviate very strongly from what I expected computer science to be. At this point, I decided to accept the simple fact that I inherently lack what it takes to be a successful computer science major here, and drop CS before it does any more damage to my real goals. Perhaps my idea of computer science was too ideal, but many weeks I found myself immersed in frustration as I was prompted with tedious grunt-work that I really didn’t care about, and which moreover was tainting my performance in pure mathematics courses, which I do actually care about. “What about the tedious grunt-work in pure math”, you ask? It virtually doesn’t exist, and even when you think you’ve come across it, there are 2 possibilities: it’s been very well-motivated and arises naturally, or you’re missing a clever silver-bullet observation that will almost immediately shatter the problem and expose its inner sanctum. Usually the latter.
In retrospect, when I look back at who I was in late high school, where my interests really lied, and where my performance truly distinguished itself, it comes as no surprise that I ultimately ended up where I am today, devoting all my time and energy to pure mathematics. Despite the fact that I was very nervous about getting rejected from nanotechnology engineering (I thought, at the time, that I wanted to be one of the engineers behind quantum computers), upon getting an offer of admission to it, I ironically accepted physics instead (still with a view towards quantum computing, however). While mathematical physics didn’t turn out to be for me, I still feel like I made a better decision than going into engineering, because I have never been very interested in concrete, tangible things, and my performance in corresponding high school courses showed this. Perhaps I would have survived in physics, but certainly would have found myself bored by engineering.
Finally, things are right. The glowing jewel that has been present throughout my entire undergraduate career, to which I have always remained faithful, from which I have never been able to escape, has now slid into the role it deserves. Please think very carefully before you accept an undergraduate offer of admission. IF YOU CAN FEEL THE PULL OF SUCH A JEWEL, PLEASE DO NOT IGNORE IT. Good luck.