Why doesn math make sense anymore?
There is no shame in realizing that you aren’t the smartest person in your major at a prestigious university. Also, as someone who has run the grad school gauntlet (though not in math), some of the feelings you describe are pretty much endemic in any person with an ability to realistically assess themselves. When I was in grad school the “macho posturing” you describe was palpable. When I decided that I needed my interests and hobbies outside my discipline (i.e. a life outside the ivory tower), and started pursuing jobs at regional state colleges, all the bigwig professors in the department wrote me off. And you know what? Screw them. Do I publish in my discipline’s flagship journals? No. Do I have groupies that follow me around at academic conferences? No. Does my research light the world on fire? No. But I’m an excellent teacher, I publish regularly, and I enjoy turning my earnest but average middle-class students on to the ideas that matter to me. I also have smart, well-rounded col
By this time, you may have heard of the infamous Impostor Syndrome within grad students. As someone who suffers from a sickening dose of that, let me tell you that most people seem like they know more than they actually do. Don’t let that bother you. Deep inside, everyone is worried about the same thing. I once had a very similar question on metafilter, and the wise told me something in the lines of, “you may not be the best chess player out there, but that doesn’t stop you from playing. You play because you love the game”. My only advice is that if you like math, do math. Don’t do grad school as means to an end (i.e getting a better job), because you can get equally good jobs with an undergrad degree. Grad school can be a en end to itself. If you like learning and enjoy the stuff, then this place is for you, even if you’re not the next Andrew Wiles. Just remember that nothing good comes easy. If you don’t want to end up at a mind-numbing job at a desk 5-9, you have to put effort, even
“How did something this beautiful turn into a bugbear?” Simple. You formalised its role in your life by studying it and assigning an enormous amount of importance to it beyond mere enjoyment. It can happen to anything. Hell, you could be the biggest Star Wars fan in the world, but if you were to suddenly start studying it so that you could write essays that needed to be in by a certain date to ensure you earned enough passing grades to allow you to study the next set of subjects in the following term, and then devoted three or four or more years of your life to it, repeating the process every one of those years for however many years… I guarantee you that you’d hate Star Wars, and not just because you’re sick of listening to Jar Jar. The only solace I can give you is that once you leave the structured world of University and enter into the adult world of working and using what you’ve learned to earn you money, you’ll find a certain amount of joy returning to you.
but in these upper division classes I feel like I don’t get things as fast as my peers. They can follow a conversation on harmonic analysis while I have to scramble to write down notes and take several hours after class to understand. One more thing: different people learn differently. If that’s how you learn, then that’s best for you, who cares how others do it? I personally always have to take notes too, and study them afterward. In any case, I’m sure your other peers also have to spend hours learning the material, upper level math is no joke. Knowing how to talk like you know your stuff when you don’t is just a skill. It doesn’t mean anything. Don’t let it bother you.
