Well, folks, this is it. Today’s the day.
And guess what?
We made it.
As you might imagine, we’re going to do something a little special to wrap up it all up.
In the 100th post, I mentioned that @absurdseagull told me I should follow Day’s model of having “My Life of Starcraft” but for math. I made a half-joking comment about maybe doing it for #1000, and that’s exactly what I decided to do :)
As I started writing this post, I realized that it was going to get very, very long. So I’ve written an abridged version, which I hope hits the highlights. The full version can be found here, if you’ve got some time to spare :)
[ Reader beware: the full version is really a document I wrote for myself. It’s not quite done as of this writing— you can see I have some notes in the text where things should be added— and it has some unformatted LaTeX and missing pictures. On the other hand, I did write it as if were going to be read, so it should be respectably entertaining :P ]
It All Started When…
In the summer of 2009, after my sophomore year of high school, I attended a program called the Summer Institute for Mathematics at the University of Washington (SIMUW).
The fact that this happened at all was, to be frank, nothing short of miraculous. My parents learned about SIMUW when they failed to find the podcasting class that I had heard was happening at the University of Washington (because, you see, I was Very Serious™ about podcasting at the time). After suggesting to me that math camp would be kind of like podcasting, I submitted my application.
Even if I had been in the region of the country that they were targeting, it was not a very convincing application: several weeks late, and incomplete to boot. But they accepted me anyway for some reason, and so I joined 23 other high schoolers in Seattle for a six-week program that would completely change the trajectory of my life.
Briefly, SIMUW was six weeks long. Every weekday except for Wednesdays, we spent 4 hours in class; with half going to the morning course and half going to the afternoon course. Every two weeks, we would get new courses, so we had six different courses over the whole program. These were:
- In the first set, both courses were on group theory. The morning class was focused on the wallpaper groups and also the math of Escher, and the afternoon class was about the group theory in Rubix cubes.
- In the second set, the morning course was about combinatorics and the afternoon course was about algebraic geometry. Both were very well-taught, but I was never able to find a narrative in the geometry class.
- In the last set, the morning course was graph theory and the afternoon course was a real mixed bag: I remember covering complex numbers and quaternions, ostensibly in service of understanding the Hopf fibration.
Wednesdays were special: both classes were shorter to make time for a long special lecture on more or less whatever. I remember these less well, but two were about game theory, one was about P vs NP, and one of them was about cardinality (which actually motivated it in a very unusual way that I’ve never seen since; I wish I had kept my notes).
But there was also the homework. Oh boy, the homework.
The homework was, in my opinion, the secret sauce of SIMUW. And key to its success, the sauce of the sauce, if you will, was that the homework was really hard. For instance, one of the problems on the first day of the (morning) group theory course was to classify the groups of order 8. They did not fuck around.
[ Looking back on it, the professors must have been explicitly instructed to do things like this. There is no way that all six courses spontaneously decided to make the homeworks so consistently hard. ]
Of course, collaboration was encouraged, and we figured out pretty quickly that it was de facto mandatory. The most stubborn of do-it-myself-ers held out for about three days.
And this pretty much worked as intended: we learned a lot from each other. When I talk about the community of SIMUW, I of course am referring to the friendships formed over breakfasts and board games and sneaking out after bedtime. But I am also referring to the “professional community” that developed among the 24: the accepted standards of proof, the relative value assigned to various problems, the divorcing of individuals’ disagreements from their mathematical collaborations.
In fact, as tremendously mind-expanding as the mathematical content of the program was, the impact of SIMUW on my life was very deeply related to the sense of community that was fostered there. At that time in my life, I was beginning to thirst for a community to call my own, and SIMUW provided it. So for me, from the very beginning of my “committed” mathematical life, learning and doing mathematics has always been a community endeavor; this understanding only increased when I went to a small liberal arts college. Longtime readers of the blog know of my love for Polymath and the Collaborative Research Project, and those feelings certainly have their roots in the six weeks SIMUW.
The Aftermath of SIMUW
The blessings that allowed me into SIMUW would follow me after the program as well. My interest in math was sparked by SIMUW, but it was kindled by three events which happened almost independently and simultaneously, right after coming back to school.
First: I discovered that my friend Ryan was taking an independent study of Multivariable Calculus through MIT OpenCourseWare. So of course I asked him to jump in on that, and he agreed.
Second: I was “hired” for the first time as a mathematical consultant. Two of my friends had been playing a game when they met up over the summer, and one of them was on a very long loss streak. By the time school started, she was sick of it, so she asked if I could analyze the game and show her how to win. Why she thought I could do this is anyone’s guess, but it turned out that I could. And it turned out that their little game intrigued me, and I puzzled over a generalized version for the better part of junior year. (This was my first foray into truly independent mathematical investigation, sometimes called research.)
And third: I discovered, essentially by accident, Paul Lockhart’s A Mathematician’s Lament.
The Lament rocked my world. It was love at first sight.
SIMUW had taught me that mathematics was something so completely different than anything I had encountered in my public education. And Lockhart, it seemed, is the only one who actually gets it. It was Lockhart, not my math classes, who confirmed that proof plays a central role in mathematics. It was Lockhart, not my teachers, who understood that “…mathematics, like any literature, is created by human beings for their own amusement…”
And he did all of this through a rant— eloquent it may be, but the Lament is definitely a rant— that gave voice to an idea flowering in my own teenage mind: How dare these “schools”? How dare they hide this beautiful, wonderful subject from me and my friends— for years!— in favor of this ridiculous dribble called “Math Class”?
[ Over time, of course, I came to have a more accurate, nuanced view of the situation. But Lockhart would be instrumental in developing my interest in math education, which unfortunately I won’t spend any time talking about here. ]
Each of these things turned out to be instrumental to my mathematical life continuing outside of the community of SIMUW, in different ways: thanks to Lockhart I wanted to continue with math, thanks to Ryan I was still learning math, and thanks to Candace I was still doing math.
The Wonderful World of Math Talks
One of my first orders of business when I got to Harvey Mudd College, before I really had any idea how much work I was going to have, was to track down every single seminar I could find, about anything at all. Yes, folks: I’ve been a talk whore from pretty much the beginning.
But the only thing that actually matters for us (and, in fact, the only thing I attended with any regularity) was the mathematics colloquium. I distinctly remember the first talk I went to: Quartic Curves and their Bitangents. I also remember finding it almost completely incomprehensible. I dutifully took notes, which I could not understand, and were probably riddled with errors. But even at the time I enjoyed it: someone else who gets it! And all these people in the audience; this is amazing!
I enjoyed it enough to continue going to colloquia, including The Legacy of Ramanujan’s Mock Theta Functions: Harmonic Maass forms in Number Theory— which I did not find completely incomprehensible. Indeed, it was and would remain my favorite math talk that I attended for almost two years.
In this way I found myself, suddenly, and in a way that I had never experienced before, immersed in the world of professional mathematics. I would continue regularly going to Colloquium and the “Algebra, Number Theory, and Combinatorics Seminar” (yes, really). And as I did this more and more, I began to grasp the enormity of this world.
But nothing at Mudd prepared me for the winter of sophomore year, when I attended my first Joint Mathematics Meetings. If Colloquium was my first light on the scope of the mathematical world, that first Joint Meetings was the friggin sun.
You’ve certainly heard about the Joint Mathematics Meetings (JMM from now on) if you have been reading this blog for… well pretty much if you’ve ever read this blog at all. JMM posts (or posts about the JMM, at least) account for 103 of the posts on OTAM, so literally one out of every ten posts I’ve written here have been about these conferences. So I don’t think I need to tell you that I enjoyed myself.
Do I remember a single talk I went to at that conference? Yes: I remember that I went to a talk where a guy was basically shilling his book wherein he used group theory to prove the existence of God. Beyond that, I only remember the broad outlines: quantum random walks, Coxeter groups, lots of graph theory.
But mostly, I remember coming back to my brother’s friend’s house, completely wired but trying desperately to get to sleep because it’s not like I’m gonna miss that 8:00 talk tomorrow; and I remember flying home in a haze of bliss; and if there was any doubt in my mind that I had wanted to be a mathematician, it was certainly wiped out at the 2013 Joint Mathematics Meetings.
[ Future JMMs were less intensely exciting, which is saying something if you have ever seen me at the Joint Meetings, because I still get pretty damn excited. But the JMM has been remarkable in my mathematical life if for no other reason than that they offered me the best and second-best talks on any subject that I’ve attended: Mathematics for Human Flourishing by Francis Su, and The Lesson of Grace in Teaching… also by Francis Su. ]
Discussing research is difficult (that’s why talks are long!). One certainly doesn’t want to spew a bunch of incomprehensible technicalities, but also, one often doesn’t have the time required to build an intuitive picture. Still, in a post such as this, it feels wrong to completely omit my research experiences— since of course they were a damn big part of my mathematical life! (Even if they were fairly small, and none of them have produced very much.)
I will therefore content myself to just say a few words about each of the projects I’ve been part of:
I was blessed to do a lot of undergraduate research.
- As a frosh, I did some vaguely researchy directed study about posets. The research outcomes weren’t very good, but I did get from it a lot of working experience with point-set topology.
- As a sophomore, I applied to work on campus researching with Professor Su and I ended up getting it. When we proved our major result, I called my mom to tell her the good news. Later, she would say about that conversation, that she had never heard me so happy.
- As a junior, after some unpleasantness with an internship, I again did research on campus under Professor Omar. We were not a good fit, and I got very far off track, and basically stopped working entirely for four of the ten weeks. The outcomes were of course bad, but considering the circumstances they were really not so bad.
- As a senior, I wrote a senior thesis. This was supposed to be a research experience but ended up being not that; I’ve written about this on OTAM.
- What did end up being an actual research experience in senior year was the Collaborative Research Project. The outcomes there were also bad, but pretty darn good considering that we did them over a month when school was also in session.
Since I started grad school, I’ve had a lot less formal (or even semi-formal) opportunities, but I did do the Graduate Research Workshop in Combinatorics. I am about to start writing my oral paper, which will hopefully lead to me doing research in earnest. And I hope there is plenty more to come :)
In various places on this blog, I’ve mentioned my favorite class, and I’ve mentioned my favorite talk, and I’ve mentioned my favorite teacher. I think I wrote enough about the class, and the talk speaks for itself. But I haven’t said much at all, and certainly not enough, about Winston Ou.
I don’t generally know how to describe people’s appearance, but Ou is the single person that I’ve met who I would describe as “slight”. He is, by all accounts, high on the awkwardness scale, even when normalizing for being a math professor. And this is no small part of the appeal.
(source; if you can’t tell which one is Ou then both the cameraman and I have really failed at our jobs :P)
Another part of the appeal is that Ou very much cares about his students— but not only is the caring great; his whole demeanor simply makes it look like he cares. For example: when people ask questions in class, he lowers his arms slightly, leans in (seemingly instinctively), and he looks— no, stares— directly at you, with this look of expectation (it is actually a little intense the first few times). You really get the feel that he is deeply listening to you, with his whole self.
And then there are the stories. There are so many of them, usually doled out once every class or two, but here is the one I remember best:
I first met Ou in the fall of sophomore year, because he was teaching a class called Fourier Analysis, that I decided to audit. Ou wore to that class, every day without fail, a white or blue button-up shirt.
But when he first started teaching, he wore only white button-up shirts, every day. This went on for years, and it became a bit of a meme for his students. But one day, he comes into class wearing a blue button-up shirt, and the class is stunned. Eventually, one student asks, “Why are you wearing a blue shirt? Is there an occasion?” And he does this sort of taken-aback-blush thing, and says “Yes, actually, there is an occasion. I received tenure today.”
It is from stories like these that I came to learn my two favorite Ou quotes: “The key to learning is shamelessness” (which is original to C.P. Chou), and “At each step, you must ask yourself: why is this completely obvious?”. And it is in no small part because of stories like these that I resolved to actually take a course from him if at all possible.
Not until spring of my junior year would Ou teach another upper-level math course. Knowing I might not get another chance, I signed up immediately.
This course was affectionately known as Analysis IV, because it was the second semester of the graduate analysis sequence at Claremont Graduate University. It was also, by light-years, the hardest course I took at Mudd: I basically ruined my academic life that semester trying to complete the homework assignments. And I did not complete a single one of them, despite going to every office hour and tutoring session that was offered.
At one point, I asked Ou point-blank if I was going to get an A in the course, because if not, I was going to drop it. He said: I wouldn’t worry about your grade, but if you are still worried on Thursday, we can talk after class.
I was, and we did.
Ou bared his soul to me that day. He began by talking about grad school. By this point I had already been all over the internet, and I’d heard all of the horror stories that I cared to hear, and I was a little skeptical about where this was going. First, grades. He said:
What you’re going through in this course, this happened to everyone I knew. All of us, we worked and we worked and we worked, and we never finished anything, but in the end we all did just fine. So I assumed that this is how a math class is supposed to work. When I came to Scripps, you can probably guess, I was not very popular. (We both smiled weakly.)
And then he talked about being stuck. He said:
As a mathematician, you spend most of your time stuck, he said. I nodded; I (thought I) knew that. Yeah, about 99.9% of your time stuck, probably more. And you don’t have any idea what to do, or what you’re doing, or why you’re doing it. And then that .1% comes along, and suddenly you’re soaring high. It’s a drug, it really is. But that happens when? Almost never. You spend most of your time unhappy. And that doesn’t change when you leave grad school. That’s just what math is.
One thing I’ll never forget is this: he didn’t try to end our conversation with something even remotely optimistic. He didn’t cheapen it with some trite thing like “You have to really love the high to be willing to deal with the lows!”. He didn’t even say that it gets easier to deal with the lows as you get more experienced with them. He could have— because it’s true— but he didn’t.
Because this wasn’t a pep talk. It wasn’t a talk about whether or not I would succeed. It was a talk about how I was, 100%, absolutely, certainly, going to fail. And it was a question: knowing you cannot change that, what now?
I decided to stay in the course. I worked and I worked and I worked, and I never finished anything, but in the end, I did just fine.
One night in March 2013, taking a break from topology homework in the computer lounge, I got a crazy idea. And I wrote this paragraph, which the very longtime followers of OTAM may find familiar:
It’s simple, really. To read and understand everything on this page would require a great deal of specialized knowledge. You might have it, you might not. But you do not need to understand art to appreciate it. If a proof is beautiful enough, the words on the page are as elegant as the ideas they chain together. I am not a master artist; I cannot always provide these beautiful proofs. But on some days I peer deeply into the abstractions which on others I carelessly banter about; I want you to be there on those days, that you may share my joy. Not all art provokes the same emotion, not all pieces touch the same people; so it is with proofs. Don’t get discouraged if the first three don’t work for you. Rather, read proofs until you know how to appreciate them, then seek out the one that you can feel.
Hence was born Not Only Truth But Supreme Beauty, aka NOTSB, aka @proofsareart, aka the blog that started it all.
NOTSB, unlike OTAM, was a very low time-commitment affair. I proved the theorem, I took a screen shot, I wrote an artsy paragraph, I wrote a technical paragraph. Boom. Besides the time I was writing up the proof for homework anyway: 20 minutes, easy. And I wrote about three posts a month.
Fast forward to November: I’m in Budapest, and on a whim I logged into my alternate email account— you know, the one that you have that you give to websites that you think are going to spam you with alerts. And I had an email from tumblr saying: “Hey, proofsareart, you have 253 new followers!” My reaction to this was amusement: I was like “lol silly tumblr, you mean that I have 253 total followers”, because that was about the number that I had at that time.
Although… it did sound a little higher than I remembered, so I logged into tumblr. And that is when I discovered that my little rinky-dink blog, where I basically just posted screenshots of my homework, had become Featured on tumblr mobile, and suddenly had 1,400 followers.
I never really did much with these followers, except for converting a few of them to OTAM readers a year or so later.
And, speaking of which… let’s talk about OTAM, now that it’s almost over :)
But what do I mean by ‘over’? If you think about it, what exactly I’ve accomplished here on OTAM is not so easy to say.
I mean, yes, OTAM contains 1000 posts. That’s just a fact: you can count them. But a “post” can be pretty much anything.
What does it actually mean to have made 1000 posts? It certainly doesn’t mean I’ve written up 1000 talks. It also doesn’t mean I’ve written 1000 pieces of mathematics: there are posts which are blog recommendations, or life updates. It doesn’t even mean I’ve written text in 1000 separate artificially-partitioned entities, since some of the posts are just reblogs (and some are reblogs with the most perfunctory of text). So what does it mean?
This issue has been on my mind for a long time.
And the truth is? I’ve never resolved it. When people ask me about OTAM, I’ll say, “I wrote 1000 posts, and most of them were writeups of talks I went to”. And I’ll cross my fingers that they won’t prod any deeper into the ontological nature of a “post”.
How can I sleep at night with an answer like that?
My solace comes from a post I wrote over two years ago. It’s a post that’s not about math. Not really, despite my efforts to spin it that way at the end. It’s one of those posts that, had I ever come up with a good criteria for “what is a post”, would probably not have made the cut. I was just about to start grad school, bright-eyed and bushy-tailed, but I had somehow just… completely lost my motivation for blogging. I was thinking about quitting. But in the end, I didn’t.
I decided to stay with the blog.
I worked and I worked and I worked,
and I’m not sure I ever finished anything.
But in the end, I think I did just fine.
How to Come Out of Dead Week Alive
As dead week begins, students everywhere are searching for the few last bits of sanity that are left. As stressful as life can become as the semester comes to an end, it’s so easy to drown under the piles of homework that never seem to end.
Dead week and finals week (especially your first one) can seem so overwhelming and at times unsurvivable. But here are some tips to help survive (and possibly thrive in) this dead week while still staying both physically and mentally healthy.
As tempting as it may seem to pull an all-nighter to finish your homework, many have learned the hard way that it’s not the smart thing to do. Although staying up all night may help you finish that six-page research paper, the lack of sleep will catch up with you later. Plus getting rest will help you function and focus better the next day.
2. (Try to) Eat Healthier
It’s so easy to load up on junk food and snacks from Paws n Go when you don’t want to wait in a 30 minute line at the Den, especially when you have the giant freshman dining plan. But eating healthy will not only help your body from getting sick from being so stressed, but it will also help you feel better.
3. Take Breaks
Studying, writing papers, and compiling portfolios can all seem like daunting tasks. Doing them all at once can seem even more overwhelming. Don’t try to do everything at one time. Aristotle even says that “even studying is occasionally harmful to health.” Every so often, take a walk with a friend or go grab something to eat. Try setting a timer to work for an hour or two and then take an intentional brain break to relax.
4. Have Some Jesus Time
This may very well be the most important tip of all. In times of the impending stress and anxiety, remember that you can’t get through this by your own strength, but rely on God’s. Spending time praying and reading the Bible can be one of the most refreshing and reenergizing things you can do in the midst of a stressful day.
Always remember that God’s got you and He will help you get through what may seem unsurvivable.
You got this!