I feel like I’ve learned so much more than theorems in these years of earning a B.S. in Mathematics.
Lesson 1: Things aren’t always what they seem.
2 + 2 doesn’t always equal 4. In the ring of integers mod 3, it’s the multiplicative identity; in integers mod 2, it’s 0. (Math is weird, people.)
Lesson 2: You have to start somewhere.
The way to start a proof is this: Write P-r-o-o-f.
If you’re still stuck, write, “Let ε > 0 be given.”
Lesson 3: If plan A doesn’t work, try plan B. And plans C, D, and E.
First, you try proving a theorem directly. Then you go for induction. Then, when all else fails, you assume it’s false and contradict yourself (hoping the universe doesn’t disappear from existence in the process).
Lesson 4: Know when to give up.
If it’s 1:13 am on Wednesday night and you’ve tried plans A through Q with three of your closest friends and whiteboards and none of you can speak English anymore (though you still understand each other), it’s time to give in and ask your professor in the morning.
Lesson 5: If you write strange things on whiteboards, you will get strange looks.
(Maybe this one isn’t so much a life lesson as a study in library anthropology.)
Lesson 5: The squeaky wheel gets the oil.
“But Dr. Professor, the undergrad contingent just left your office asking for homework help, and we haven’t had time to write it up. Can we have an extension?”
Lesson 6: Sometimes, you’ve just got to dance.
I mean, really, Abstract Algebra occasionally requires that you break out into the macarena. You may get strange looks from other people in the library, but what can you do?
Lesson 7: Humility.
“What are you working on?” “Advanced Calculus.” “Oh, is that like Cal 3?”
No, honey, no.
And certainly not least:
Lesson 8: If you look, you can see God everywhere.
Everywhere, even in math theorems (the false etymology of which is theo- -rems: God things). Parameterizations remind me of worship songs. Mathematical truths are true because, somehow, their truth glorifies God. My friend Austin sees God’s existence in the proof that .9999… = 1.