What is linked here is mostly my story as a math major, but I want to share this as a warning to the type of prospective math major whose math background is not very strong or the type who has asked questions like “would I be good enough for math”, “do I have the ability to become a mathematician”, and so on. If you don’t want to read my story, just jump to my advice at the end (reproduced below in this text post). The reason I wrote out my own story at such length is for prospective math majors of the type I referred to earlier (hopefully that’s you) to read and understand that what I’m going through is a possible future for you. Please understand and learn from my mistakes so you don’t make them yourself.
The Advice I Have
If you are unsure about being a math major or mathematician or about your ability to do well in math, double major in something else. Engineering, computer science, and physics are good options. But don’t just be a math major. Everyone asks me if I’m double majoring, because (as I learned all too late), it’s informally expected of math majors to double major unless they are sure of going to grad school or are working to become teachers. Advisors never told me this. I wish someone did before it was too late.
Get job, internship, and research experience ASAP. It’s awful that these aren’t graduation requirements. What I learned at my simple restaurant job one summer was more valuable than almost anything I had learned in class. And I should have never let embarrassment get in the way of getting research experience. In the worst case, you’ll be told “no,” in which case, try again. Or, maybe you do research and realize that you shouldn’t do research. That’s actually great if you learn this early on, because you know now how to adjust your career plans.
If you are currently struggling in whatever math you’re taking, don’t expect things to change much when you get to more advanced courses. There’s this common statement that gets told to people who want to be math majors but have a shaky background in lower level courses. It goes something like this: “Proof based math is very different, and your performance in lower level courses doesn’t say much about your ability to be a math major/do math/go to grad school/etc.” Frankly, I call bullshit. Maybe, if you simply didn’t study well or didn’t try at all, you could fail calculus and still be a successful mathematician. But if my math background sounds anything like yours, it may not be true for you. Don’t bet your future on it being true for you. Lower level and upper level math courses all require the ability to think abstractly. If you’re like me and you’re not exactly the brightest crayon in the box, things aren’t going to get any easier for you when you get to real analysis. And I know, talking about “intelligence” isn’t the most politically correct thing, but I think it’s awful to convince a person that “they can do anything” when that is not always true. No one in their right mind would recommend a person with an exceptionally low level of intelligence to try to become a research scientist. You would be setting them up for failure. Not everyone is good enough to be a mathematician. It’s just the way it is. I’m not saying “give up”, I’m saying make sure you have something to fall back on if you ever (and I hope you never) come to the realization that you’re just not cut out for it.