Third Year Revelations

Third year taught me about some calculus on funny (non-existent) shapes, and how to draw passable pictures for topology real analysis, but mostly, it taught me to not to take myself so seriously all the time. I have found that things like to fall together exactly when you think they've just about fallen apart. 

o1. Good things come to those who wait... and those who bang their heads against the right walls for long enough.

o2. Perils of being a math major: chalk dust. It will get on all your black clothes, no matter how hard you try.

o3. Sometimes it just takes one. To my mentor: I probably wouldn't still be a math major without your unending patience and support. Thank you for seeing me through, and for always putting more faith in my abilities than I ever did.

o4. Having biweekly episodes of self-doubt and crises over whether you're pursuing the right degree are more normal than you would think.

o5. People are most beautiful at their most vulnerable.

o6. The world actually doesn't revolve around abstract algebra, contrary to not-so-popular belief.

o7. The most interesting things are those that confound you. These are the things that capture the imagination.

o8. Plausible deniability is always your best bet.

o9. People are usually pretty friendly if you ask them for help. Everyone likes to feel that their expertise is needed.

1o. If you're going to prank call someone, don't put your name in your voicemail message.

11. In the toolbox of abstract algebra, the First Isomorphism Theorem is the hammer.

12. And in the toolbox of analysis, it's the Triangle Inequality.

13. You will never, ever regret being a little bit braver.

14. Learn to laugh at yourself.

15. If you've got nothing else interesting going for you, name drop algebraic geometry whenever possible.

16. Learn to accept a compliment gracefully, and it will take you far.

17. People are always more open-hearted after midnight.

18. Sometimes the best way to deal with your problems is really just to pretend that they don't exist. Sometimes they just change, but sometimes they go away.

19. If you're feeling relaxed, you probably forgot about something that is due... tomorrow.

2o. Everything is more beautiful at night. But if it's still sparkly in the daylight, then you know it's for real.

21. Find the people who will walk with you, even if you don't know where you are going or where you will end up.

22. The stereotypes about mathematicians are stereotypes for a reason. (That's not always a bad thing, though.)

23. There is something beautiful about sitting in a darkened room by yourself.

24. Post-midnight driving, feeling like you're all alone in the world with nothing but the stars and city lights, makes you feel like you're on top of the world.

25. The ones who matter are the ones who will celebrate with you over your successes and hurt with you over your tragedies, and likewise.

26. Don't follow emotions; follow truth.

27. Hurting does not mean that you are sitting around feeling sorry for yourself. It means that you cry and scream and do whatever it takes, and then you get out there and love people in spite of it.

28. There's always going to be someone who is suffering more than you. But still—your pain is no less justifiable; your pain is no less real.

29. If you find someone who can see through your mask and your feigned happiness and call you on your made-up disguises, don't let them walk away.

3o. You can't just pick and choose your favourite definition of continuity... you must suffer through them all, because sometimes preimages just won't cut it.

31. Surround yourself with talented people. Sure, you'll suffer from feelings of mass inadequacy, but how else are you going to be better?

32. Just don't ever respond to your emails! You'll just be the eccentric unicorn in the department and people will have no expectations of you, so they'll be pleasantly surprised on the off chance that you ever do respond.

33. Persistence goes a long way.

34. You are infinitely more awesome in a good pair of heeled boots.

35. John Green is, surprisingly, usually right.

36. Campus is stunning at 4:00 AM.

37. Never leave an assignment question blank. Write something, even if it's nonsense. Sometimes your TAs are too hungover to care.

38. It is just as much about who you are as a person as it is about the numbers and title on your transcript.

39. Don't ever let yourself think that you are too good to start from the very bottom.

4o. Go to every single interview that you are offered, even if you think that the job and company are a joke.

41. Just because you wear a blazer and rent office space in a highrise building doesn't mean that you are a real company (ask me about this interview nightmare).

42. The Chinese Remainder Theorem is everywhere. EVERYWHERE.

43. And the Euclidean Algorithm... you can run, but you really can never escape the backwards Euclidean Algorithm.

44. If you can't teach, draw pictures. Lots of them. Preferably with coloured chalk.

45. You are no special unicorn.

46. Sweatpants are—you guessed it—still not okay!

47. Figure out your own standards for ethics instead of listening to someone else's.

48. Learn how to say no without giving excuses. It is always enough and you never need to justify your decisions to anyone but yourself.

49. Everything is really the same thing, except with more or less levels of generality.

5o. It is absolutely okay to be a quitter. Sometimes it's necessary for your sanity.

51. Just aim to be irreplacable.

52. At some point you will begin to feel lucky, even if you don't believe in luck. Never let yourself forget that moment.

Second Year Revelations

I go to school for mathematics, but second year has taught me about so much more. Here are the things that I learned, inside and outside of the lecture halls. 

o1. People at university like meetings. They like holding meetings, talking about holding meetings, and talking during the meetings that they hold.

o2. Oh, and emails. People at university love emails.

o3. Sometimes your professors see the potential in you that you can't see in yourself, and for that I am grateful. I owe a world of thanks to the math professor who told me that my dreams are worth pursuing when I had convinced myself otherwise.

o4. Some of the classmates that I sit beside today are going to be great tomorrow. They are going to be mathematicians and doctors and teachers and physicists and leaders, and they are going to be amazing.

o5. Sometimes the most useful thing someone can do is not to give you any advice at all. Own your decisions, the resulting consequences and the gifts.

o6. It makes a world of difference if you do the readings and problem sets before class as opposed to after class.

o7. "If you think about it", you can come to any conclusion in the world. (This one's for you, Calculus 2502.)

o8. A sharp pencil makes all the difference.

o9. You don't have to be a genius to do math.

1o. If the problems that you're doing don't make you want to bang your head on the desk and scream and quit and cry, then you're not working on hard enough problems.

11. The people get stranger as you progress deeper into academia.

12. It's easy to forget about your own ability when you go to an incredible university and are constantly surrounded by so much talent, but never forget why you are here in the first place.

13. Sometimes you have to say no to people. That's okay.

14. University is just a big game as to who can be the most overcaffeinated, underslept, stressed and still make it on top.

15. Being ahead of the game is the best feeling in the entire world.

16. Your health really does come first. I learned this the really, really hard way. Don't do that.

17. Well-lit study space is the ultimate commodity.

18. Waking up fifteen minutes early in the morning can change your entire day for the better.

19. Never underestimate the incredible power of the perfect little skirt.

2o. Sweatpants are still not okay.

21. Everyone always needs a stapler, and no one ever has one.

22. It's about the experience. You're missing out if you don't have a sleepless night once in a while.

23. Context is everything.

24. You never see the whole story. The people who appear to be the most put-together are often those who are the most stressed out.

25. You don't always have to talk. Sometimes silence speaks louder.

26. The hardest decision is to take the high road, but it is one that you will never regret.

27. Wikipedia is an incredible math resource when you have the knowledge to comprehend what it says. Otherwise, it's just a bunch of nonsensical strung-together symbols and accurate yet ridiculously convoluted proofs.

28. If there exists a textbook, there exist solutions somewhere.

29. Cute cats make every PowerPoint presentation instantly better, no matter what the topic!

30. Everything in the entire world can be reduced to systems of linear equations if you try hard enough.

31. Being kind to perfect strangers will take you far in life.

32. You can only eat so much pizza before you have to start eating real food.

33. Stop substituting infinity into equations; nothing good ever comes out of it.

34. Punctuality is impressive, but it shouldn't have to be. We live in a culture that makes it okay to be late as long as you let someone know, but really, you still wasted fifteen minutes of someone else's life.

35. No one ever thinks "Oh, I wish I'd spent more time on Facebook." Ever.

36. The most important trait for success in math is not mental arithmetic, hard work or even talent; it's creativity (and sometimes a little bit of luck).

37. It isn't until you get deeper into school that you realize how vast the world is, how limited the scope of human knowledge is, and just how much you still have to learn. But the moment that you make that realization is quite enlightening.

38. You are more certain of your path at fifteen (fueled by blind confidence) than you are at twenty (fueled by the revelation of your own ignorance).

39. Some professors will teach you about math. Some will teach you about so much more.

4o. When in doubt, proof by induction. Also, thanks to one Discrete Structures professor, I will never again write, "Let P(n) be true."

41. The really cool thing about math is how you can take two seemingly unrelated concepts and come up with a beautiful relationship between them.

42. Real life would be simpler if we worked exclusively over the field of complex numbers. (Because then your characteristic polynomial would always split!)

43. Everyone here has something to teach you. Whether or not they're fun to talk to—well, that's a different story.

44. It is still only, ever, all about the chase.

45. It turns out that you can't just change the question to suit your needs, you actually have to answer the question.

46. Never underestimate the power of a well-placed "if and only if" statement.

47. There are all sorts of infinities (thanks, Real Analysis), but finiteness is just as essential, for humanity is finite.

48. Sometimes it's simply figuring out the right questions to ask. Everything else will fall into place.