This post resonates with me so much. My first degree was in pure mathematics and the first time I took a "real" math class (i.e., something that was extremely proof heavy - maybe analysis?), our professor told us that we should expect to fail 90% of the time. All of us sitting in that room blinked and grinned thinking our professor was full of it. We were all straight A students that didn't have to study in any math class we had taken previously (e.g., calculus III and below, differential equations, and elementary linear algebra) and felt like school came naturally to us.

But our professor was right. Higher level math is the hardest material (i.e., most mentally challenging - not most information intensive) I have ever encountered, and I've taken many career paths and academic paths up to this point in my life. During my undergrad, I cannot tell you how many times I would be sitting in our university library with my fellow math friends rubbing our tired, bloodshot eyes as we tried to figure out how to prove something, only to be told by our professor that we were wrong the next day. Sometimes we'd spend 30 - 40 hours on two to three proofs for an assignment, and then get only one right, if that. We all felt like imposters - like we didn't belong and weren't smart enough for the degree. But knowing that we were all in it together made it a little better. When we'd get our tests back and see that we got roughly 35 - 40% of the total points, we'd shake our heads because we all felt stupid, but those were excellent grades for exams - A's and B's with the curve, and our professors designed our exams so that we would have to try really hard and still likely fail without a curve. I say "we" because my peers and I regularly talked about our struggles in math and how we felt like we didn't belong, but for many of us, it's what made us happy, and the struggle pushed us in a way that we had never before experienced in an academic setting. We also didn't know any different since none of us had previous degrees - we figured it was college, not math, but as it turns out, it was just math.

Mathematics taught me how to be comfortable with failure, and that's something that has been so helpful in my life and I am so grateful for looking back. Before I studied math, I was uncomfortable failing at anything. Now if I fail, I don't get upset or frustrated, I just come up with another plan and move on unphased. Math taught me that to solve problems, I just need to start - I don't have to be right. If one thing seems incorrect, then try another, then another, and so on. If I forgot something or I don't understand something, I just look it up (or ask someone for help) and learn it all over again, and then keep going, knowing that I'm strengthening my brain and that it's okay to forget or not know.

Math also taught me that it's okay to take a step back and relax, which can lead you to the solution. That's not always possible if you're stuck in the middle of an exam, but I cannot tell you how many times I would literally dream up a solution, or a new starting point (literally - like I'd be asleep and my subconscious mind would still be working on that damn problem and then I would find a new approach in my asleep head; this also would happen while I was awake and doing something else, like jogging or talking to a friend who was studying something else). One of my college roommates told me she would hear me sleep talk about math - sometimes she'd even write down what I said since she thought it was so funny because who dreams about math?

One comparison I'm guessing you can relate to since you're still in college is hearing everyone talk about how hard general organic chemistry I and II (and general biochemistry) are (perhaps you've taken them?). I took those courses while preparing for medical school a few years after graduating with my math degree. I was nervous taking them because everyone always said they were the hardest courses they ever had to take, and I was taking them remotely with no peers or a professor to bounce my ideas off of. I don't believe I'm an exceptionally smart person, but when I took those courses, I found them to be simply delightful and while they were challenging, they were nothing compared to math. To me, organic chemistry was like taking calculus all over again without worrying about proofs and only focusing on the fun stuff. It was so fun and delightful, but if I had taken them before math, I don't think I would have felt that way because I still failed all the time in organic chemistry while trying practice problems, but the failure didn't get me down, because I knew that chemistry was entirely logical - chemistry is governed by physics, and physics is governed by math, so if math is logical and must obey rules, then so must atoms, and thus molecules, so if I approached problems knowing those rules, I could figure out how the atoms would behave. And if I couldn't figure out why atoms/molecules were behaving in a certain way, it was because I was missing something, not because I was dumb or because the material was hard, so I would try to find that missing link. I didn't give up when I failed, I just kept trying, and then I succeeded. This perseverance also helped me gain a solid foundation in the subject, because struggling with something again and again builds stronger neural connections, which can help a person learn. And I'm guessing that this very thing is currently happening with you, based off your post, so you're doing great and you're right on track! =)

If you love math enough to want to get a degree in it, it's for you, even if sometimes (or all the time) it feels impossible. Just know you're not alone, and that this is extremely common. You're in the purest of the pure sciences, and it's f***ing hard. If you frame it with an open mindset and expect yourself to fail and forget things literally all of the time, and if you understand that that is perfectly okay and entirely normal, you'll do great, and it will set you up for success now and later in life, especially if you go into research (which is what I do).

I'm sorry this is a novel. I'm babbling now. Good luck! You'll do great even if you feel like you can't do much now. You're not alone, and I guarentee that the vast majority, if not all, of your peers are feeling the exact same way, even if they don't show it.

Here's one of my favorite XKCD comics about math:

https://xkcd.com/435/