Wolstenholme also wrote up his perspective on this excellent process here

2 years ago, both me and Wolstenholme attended AMSP Cornell 2013. Since everyone knows how incredible I am at geo, I took Geo 3 (aka "Cosmin murders you"). Wolstenholme took this for dumber reasons (i.e. he actually knows geo).

Anyway, I got pretty murdered throughout that class, but that's not the point of this particular post. At some point during Geo 3, we talked about the excellent topic of inversion, which Wolstenholme knew and I did not. So I was asking him how inversion worked, he explained it to me, and I asked him whether this was limited to 2 dimensions -- i.e. can we invert about a sphere? He responded "yeah... we could invert about a 4-sphere if we wanted to". Little did we know...

Fast forward 2 years to MIT orientation, part of which involves taking ASEs (Advanced Standing Exams) to test out of classes you already know the material for. In my case, since multivariable calculus is pretty boring and I didn't really want to bother with it for an entire semester, I decided to take the 18.02 (multivariable calculus) ASE without knowing multivariable calculus.

Perhaps that wasn't a particularly great idea, but I still had a week or so to learn the subject, so it was probably going to be ok. Also I was taking the makeup version of the ASE, because at the time it was scheduled I would be taking the 8.01 (Physics I) ASE (which I didn't end up actually taking, but that's a story for another day...). On the other hand, most of the math crew here (including Wolstenholme) had already gotten credit for 8.01 through AP Physics, so they took it the day before I did.

Alright, so 2 weeks pass, and it's time for me to demonstrate my extensive knowledge of multivariable calculus. The day before, Wolstenholme mentioned how easy the ASE was, and that it didn't actually have questions on most of the harder material (e.g. surface integrals), so I was pretty chill. So I breezed through the first ~9 (of 20) questions, struggled through the next few, and finally reached #14 (ok maybe not #14 but w/e), which I was completely stumped on...

Also I should mention that spherical coordinate problems made me very sad, because there was a lot of computation, so I basically skipped them during my hardcore training.

Anyway, so first of all we have to figure out what this thing means, which is basically saying we have a sphere of radius centered at . Ok that part's done, yay. Unfortunately, the rest isn't too easy to deal with: we can do the standard substitution of , but unfortunately the bounds here aren't so nice: we still have , but bounding involves some semi-annoying trig that results in a pretty ugly integral.

So I figured there was probably a better way, especially considering the answer choices (sidebar: why the hell are there answer choices???) were of the point where was rational ( and were the only reasonable ones). Unfortunately I couldn't find said better way, burned 40 minutes, and just moved on to other problems (eventually I made up some garbage like the answer was where is the expected distance from the ball centered at the origin with radius [which comes out to ], but it's totally wrong).

Ok, so the ASE ends, but I can't really get this problem out of my head because I'm so certain that there must be a nice way to do it. So after some unsuccessful conceptual ideas, I go ask Wolstenholme, whose first reaction was "that's 100x harder than anything we had on our test". Darn. So we briefly try this, conclude there's probably no good way, and go off to lunch.

At lunch, we meet Christopher Shao, who's also pretty good at math so I give him this problem also. Unfortunately, the three of us still can't find a particularly great way to do this problem. Finally, at some point I'm like "guys, what if we like invert about the sphere". I was actually serious (more out of desperation than anything), but Wolstenholme just started laughing before he realized I wasn't trolling. So at first we're all like "ok this is dumb", but then gradually we realize "wait........ does this actually work"

Indeed, inversion is actually quite motivated here: the ball in question is sent to a half-space (this took a while for us to work out though), and eventually we realized that this half-space doesn't actually start at , but instead the half-space is bounded by the plane containing the intersection of the two spheres (since the inversion sends the "top" of the ball in question to that plane). So we end up with the triple integral from the definition of inversion, which seemed relatively promising.

So anyway, we couldn't really work this out without paper, so we went to go do other stuff and eventually Wolstenholme and I reconvened to solve this problem. After many, many, many failed computational attempts, we finally came up with the following excellent solution...

Writeup credit to Wolstenholme

The great thing about this solution is that it works in effectively the same exact way for other dimensions, which means that -- after 2 years -- "invert about the 4-sphere" is finally a legitimate strategy for solving a problem. I'm unreasonably happy right now.

So it turns out that time is not, in fact, infinite, and in something like a week and a half I'll have officially left the realm of high school.

I'm not entirely sure how to feel about this: on the one hand, I'm mildly excited (at least to the extent that I get excited, which is not very much -- I'm a pretty emotionless person in general) to be "moving on", but at the same time I sort of already miss the prospect of another year of high school.

Obviously, this a big part of this relates to competitions. I've consciously made the competitive math scene the biggest portion of my life for what will, in a few months, be a full decade, so leaving it behind is closer to the "bitter" in "bittersweet moment". It's not even accurate to say some of my best times have happened while at one of these competitions; rather, almost all of them were (they were generally only tangentially related to the math though ). The realization that I will literally never participate in one of them again is one I had a while ago, but the full magnitude of which is just starting to hit me.

But probably more pertinently, the prospect of "growing up" is frankly pretty frightening, since I've never actually paid much attention to how to... well, live. My parents instructed me to put together a list of things I'd need to get before college, but I realized I had absolutely no clue whatsoever: how exactly does a Kat live a life? There's also a weird flurry of "wait, I can vote", trying to work out how normal people transport themselves from place to place beyond "Dad, I have to go somewhere tomorrow", "what's a tax form??", and other things that I definitely should have paid more attention to when I was younger.

On the topic of things I should have paid more attention to when I was younger, I'm quickly discovering that my conscious strategy of not learning a whole lot of higher math in high school ("I'll do competition stuff now; I can always do higher math stuff in college!") is sort of imploding in my face. More specifically, multivariable calculus is just really annoying to deal with, and I really don't want to have to deal with it for a semester, so I really wish I had gotten this out of the way at some point in the past (for those of you with some familiarity with MIT, my end goal here is to take 18.701 which is actually interesting math). I guess we'll see if my "study an entire subject in a week" manages to hold up as well for MIT as it did for all the standardized testing (my guess is... no).

There's also one final factor to this whole complex of emotions: college is, "traditionally", effectively the death of a chess career (besides those who go to colleges with strong chess programs such as Webster/TTU/UMBC/etc.), both because there's little time to devote to study (which, frankly, wouldn't affect me much because I rarely studied seriously) and because actually playing in events is problematic -- both because of transportation issues and the fact that serious chess tournaments last ~5 days, which doesn't work very well with school schedules. So while I plan on staying sort of into chess in the future, from a realistic perspective it's not going to be a serious pursuit anymore.

So that's where I've been for the last couple months or so: willfully ignoring the fact that everything I did in high school is -- more or less -- no longer a part of my life, and dodging the fact that I'm actually responsible for myself now and I should do things that responsible people do. Ok, this is a bit strong -- I don't plan on terminating involvement with the math competition community (far from it in fact, as you HMNTers will find out ), and I don't plan on abandoning chess completely -- but it's somewhat true in spirit.

Anyway, I don't make posts just to rant about my life being non-ideal; there's actually something of useful substance to follow One of the interesting things about going to MIT is that pretty much everybody knows what the place is -- its name recognition seems to be almost as good as e.g. Harvard's. I was on a plane back from Arizona, working on writing HMNT questions, when a couple next to me asked me what type of math I was working on. Of course, the usual difficulty in explaining competitions to laypeople followed, and basically everyone within the row (who was, of course, listening in because America!) was pretty confused. Eventually, though, they asked where I was going to college, I told them, and then everyone seemed to be suitably impressed and no longer confused (I, on the other hand, was extremely confused). A few months back, I was playing at the Philadelphia Open, when some parents came up to me and asked variants of "I heard you got into MIT, any tips?" without any real prompting (I still have no idea who most of them are, or how on earth they even heard of this). Then, finally, at the World Open I had a rather lengthy discussion with a friend's parent about the subject of college admissions, which was eventually followed up via e-mail.

Now, I'm not exactly an expert in the fortune telling business of optimizing for college admissions***, but I guess I did something right considering I got in to the best school on the planet (intentionally inflammatory ). Also, the world of college admissions has a ton of totally inaccurate information being thrown about (a search for closure, perhaps?), some of which seems to be genuinely misguided, some of which is straight up stupid, and some of which is... indicative of other motives. What's particularly interesting, however, is how much of this misinformation passes through AoPS, a community that should really know better. So, I figured I'd touch on the topic a bit on here, because I think the subject gets way more attention than it deserves and people should get back to doing useful things (like math). I also want to have something to copy and paste when I get more of these questions MY MOTIVES ARE ALTRUISTIC

First of all, there are a ton of threads about quantitative stats, especially "chance" threads, that crop up all over the place -- even on AoPS (if you want to kill a few hours of your life, you can see tons more these on collegeconfidential). These threads, almost invariably, completely miss the point. Let me tell you something that any admissions officer will tell you, but students choose not to believe for some reason: there is essentially no difference between a 2200 and a 2400 on the SAT (obviously, this applies equally well to other tests). Ok, perhaps there's some argument that the lower bound there should be closer to 2250 or whatever, but the point is the same: past a certain relatively low score, there is literally no benefit to devoting a ton of time to the test, and there is definitely no point to retaking a test to improve on a 2250 or whatever. I know people who retook the SAT after getting a 2370; some of them ended up getting their 2400, but basically wasted that time.

Similarly, there's not a great deal of difference between anything above a 3.7 GPA or so (i.e. mostly As with some unusual Bs); use the time you would otherwise spend agonizing over fractions of points doing something useful instead.

The point here is that colleges view quantitative data as a simple question: "are you academically qualified to be here?". If your scores show that you are, then how much you exceed the threshold by is largely irrelevant*. This is the source of the numerous threads that pop up sometime around decisions date positing something like "how did I get rejected with a 2400 SAT?? Affirmative action kappa", dumb stories like students sending colleges rejections of rejection letters, or dumb actions like actually suing a college over being rejected. If only people understood this really simple point...

By the way, you will get sufficiently decent scores without a whole lot of specialized studying as a result of doing useful things. I didn't study for the SAT at all (for real; I'm not fishing for respect here), but I've read voraciously and written often throughout my life as a matter of choice; as a result, when I actually took the SAT, I did perfectly fine (apparently I got a 2290, but I had to look it up to see what score I actually got). Here's a group of ten words ostensibly classified as "SAT words":

Abhor
Bigot
Counterfeit    
Enfranchise    
Hamper    
Kindle (not by Amazon...)
Noxious    
Placid
Remuneration
Talisman

I can't tell you anything resembling a dictionary definition of any of these ten, but I've used all of them in some form before (though to be fair, I've probably only used "talisman" in this context). The point is that these are things you should pick up through common usage; actually sitting down and trying to study these things is a huge waste of time and effort.

So what does actually get someone admitted? The overwhelming factors are qualitative data -- things you can't put a standardized number to. These are both things like accomplishments that can't be directly compared (e.g. AIME qualification is good, USAMO qualification is great, national debate team is great -- which one of the latter two is "greater"?) and the most dreaded part of the application: the essays.

First, some words on accomplishments/extracurriculars: if you don't care about it, neither will the college. I know it sounds overly romantic, but don't do things solely for the benefit of a college application: you'll end up viewing it as an obligation, and it probably won't end up helping your application that much anyway. That said, value to colleges is definitely a valid criteria to pay attention to -- just don't let it become the main one.

What colleges really want to see is a passion for a subject. Passion is something that's technically possible to fake, but frankly it's easier to do something you're passionate about in the first place. Besides the criteria of tangential relevance, there's not a whole lot of difference between activities (e.g. passion for video games is not interesting to colleges, but passion for math and passion for sports are probably weighted nearly equally). Obviously, the level of achievement matters as well, but the passion and dedication to something is far more important. Many people were surprised when I told them I basically only did math and chess in high school, since the stereotypical picture of a top applicant is one with a ton of different clubs/activities; what they presumably didn't realize was that I was putting the equivalent to a part time's job worth of hours into those activities. That's far more important than getting your name on the NHS membership rolls for application season.

Ok, on to essays. College essays are not very well understood by students in general (probably myself included), but it seems like this issue is exacerbated on AoPS (which is understandable, since most AoPSers prefer math to writing). The highly subjective nature of what makes a "good" essay -- let alone a college essay -- doesn't help either, especially since almost all applicants have no real formal training in writing (high school English doesn't count).

So what makes a good essay? Paradoxically, you don't want to describe yourself to the reader -- despite this being the whole point of the section. Instead, you want to tell them about youself, and let them fill in the blanks. This is a very subtle difference that's not too well understood by many (again, myself included); the most obvious place where it applies is telling a story illustrating something, rather than just saying that thing immediately. For example, here's the first paragraph of one of my essays (the prompt for which was "What attribute of your personality are you most proud of, and how has it impacted your life so far? This could be your creativity, effective leadership, sense of humor, integrity, or anything else you’d like to tell us about"): (copied verbatim to preserve historical integrity, feel free to rip it to shreds)

This type of paragraph is infinitely better than something bland like Hopefully you can see why. Anyway, you can get a better illustration of this concept here. This second of the two paragraphs is more or less the reason why you occasionally hear things like "SAT perfect scorer rejected from [Ivy]", usually accompanied by passive-aggressive use of the media ("I don't want to brag about my achievements, but...") and straight up dumb comments ("...I feel I would have gotten in if colleges were a meritocracy, because that girl over there only got a 2390 on her SAT"). Did I mention that I really hate this type of media coverage? It's also probably the reason that AoPSers get rejected; most AoPSers' academic qualifications are perfectly fine.**

Anyway, the main takeaway I want people to get from this is that the college admissions cycle gets way too much attention in general, but mostly from the students going through the process. There's no particularly good reason to do things "for college" -- while this can be done in a pseudo-sneaky way, students almost always lack the subtlety to pull this off and just end up hurting themselves. Of course there are exceptions -- some students manage to get away with this and get into elite institutions, but even they aren't living the good life: their reputation among their peers summarily tanks, and they once again end up hurting themselves anyway. This isn't to give an unqualified "do what truly motivates you", since college admissions is a very valid concern to have, but in practice it comes pretty darn close.

* For those interested: my SAT score was a 2290 (800 math/760 reading/730 writing), I took four AP tests (Calc BC, Physics C Mechanics, Statistics, Computer Science; 5 on each), 2 SAT subject tests (Math II and Physics; 800s) , and that's the extent of my quantitative data. You'll note that these are not particularly great scores -- sufficiently solid, but nothing to celebrate -- and they're relatively easily attainable by most people who manage to make their way to this blog. So questions like "will a B kill my chances for Stanford?" or "should I add my 17th AP over the summer?" are just answered by a straight up "No"; my academic qualifications were fine, and yours probably will be too.

** I put quite a bit of effort into my MIT essays, both because MIT was by far my first choice of school and because I was applying to MIT early. In comparison, I put practically no effort into my Princeton essays at all (I more or less copied stuff from my MIT essay where applicable and freewrote the remaining prompts), and was summarily rejected (I think the interviews might actually have had a larger effect -- the MIT interviewer was excellent, the Princeton interviewer not so much -- but that's a story for another day). The actual application requires effort -- make sure your essays are as good as they can possibly be. For most of you, that's the deciding point of your entire application.

*** You know who are experts? Admissions officers. Listen to what they say!

This is a compilation of AoPS posts that I feel are useful in some fashion. Some of them are mine, not because I feel they are necessarily the most useful posts around, but because I think they're generally useful nonetheless and they have the benefit of my complete agreement with their author (I also need to make reference to them on occasion, so it's helpful for me to have them in one place). Many others are posts that made a big impression on me throughout my contest career - you'll note that many of these posts are by v_Enhance, who is undoubtedly the leading authority on these matters (even if he protests this point). Others contain useful mathematical information, such as problem sets or articles about particular techniques. Finally, some simply contain oft-requested factual information, such as qualification processes.

I began collecting these posts as a simple matter of convenience: I'm often asked the same questions by many different people, and having posts handy to point them towards saves us all a lot of time - not to mention that many of these posts make the point far better than I could articulate. But when collecting the answers to questions I'm frequently asked, I realized that there is simply far more quality material on this website than people think to ask about. My goal in this compilation is to provide a centralized source of some - but certainly not all, as I could not hope to do justice to all the quality material on this website with a single compilation - of this quality content, and I hope that readers will get the answers to questions they haven't even thought about yet.

Mock tests I wrote or wrote in conjunction with others:

• 2015 Mock ARML
• 2015 Mock AMC
• 2014 Mock MATHCOUNTS (note: largely written for comedic effect; overly difficult)
• 2014 Mock AIME
• 2014 Mock AMC (intentionally difficult)
• 2013 Mock AIME (ASIA TEAM)
• 2012 Mock AIME (note: this, along the below test, is the only one on this list that I was not the main contributor to - which likely explains its high quality)
• 2012 Mock AMC (note: this, along the above test, is the only one on this list that I was not the main contributor to - which likely explains its high quality)
• I wrote a 2012 Mock MATHCOUNTS, but apparently unwisely uploaded it to 4shared (I have no idea where I got that idea from), which evidently does not save uploads for very long. If anyone happens to have a copy, please let me know
• 2011 Mock MATHCOUNTS
• 2010 Mock MATHCOUNTS (roughly Chapter-State level)

Other posts I've made that are useful in some way:

• How do I prepare for AIME?. An AIME-level "study guide" that basically intends to be an "AIME syllabus". First draft; hopefully will get around to version 2 at some point.
• Response to: "Test day tips?". Quick link to number sense/computation tests, which I used throughout middle and high-school competitions to "wake up" on the mornings of.
• Response to: "Power round solutions". BCA's solutions to the 2014 PUMaC Power Round, for which official solutions are not available.
• "QEDMonthly Issue 2". The second edition of the (now defunct) QEDMonthly magazine, which I authored along with a few friends. I simply didn't have the time or inclination to continue with this project, but the existing material is still solid (and perhaps someday I'll revive the concept).
• "Learn how to learn". Probably my most useful posts; describes how to efficiently practice (the focus is on MATHCOUNTS due to that being the question asked, but the post applies in a more general way).
• "QEDMonthly Issue 1". The first edition of the (now defunct) QEDMonthly magazine, which I authored along with a few friends. I simply didn't have the time or inclination to continue with this project, but the existing material is still solid (and perhaps someday I'll revive the concept).
• Response to: "CD strategies". Advice on performing well at MATHCOUNTS countdown.
• MATHCOUNTS Tips. A few general tips for MATHCOUNTS, many of which scale to other competitions as well.

Other posts I'm saving for ease of reference, in order to reply to FAQs more quickly (these are more meta-oriented posts than posts that are useful for competitions):

• Response to: "AMC Rant". Response to statements of the type "math competitions are useless", "math competitions have nothing to do with real math", "math competitors only know stupid tricks", etc.
• Response to: "What is your typical school day like?". Response to questions of the type "why do people homeschool", "why are you homeschooled", "doesn't homeschooling hurt socialization", etc.
• Response to: "Telling a high school teacher that he cannot teach math". Description of my single year in high school, and advice on dealing with suboptimal educational situations.
• Response to: "Alternate American competitions". (Intentionally) snarky response to people who are so concerned with finding optimal practicing methods that they don't actually do any practice, or those who complain incessantly about a disliked contest format. Inspired by the classic pair of posts by the master. Remarkably adaptable to a variety of situations.

Mock competitions by other users (not necessarily in chronological order; I just added high-quality ones as I came across them). Note that this is a very small sampling of mock tests out there; I chose the ones that I was impressed by:

• 2015 Mock AIME I. Written by Binomial-Theorem and djmathman, well known for creating very high quality contests.
• Mock MATHCOUNTS competition. Written by Th3Numb3rThr33, Benq, donot, AKAL3, and RadioActive. I'd definitely call this closer to state than chapter, but this is one of the few remarkably high quality mock MATHCOUNTS tests.
• Crowd-sourced mock MATHCOUNTS. Written by the community at large. This isn't included here so much because of the final result, which I will freely admit I'm not entirely thrilled with (most mock MATHCOUNTS tests tend to be way overboard on difficulty, and this one falls victim to the same issue), but for the rather novel concept: crowd-sourcing a mock competition. This seems like an idea that, with proper development, has a lot of potential.
• Mock AMC 10 2014-2015. Written by AlcumusGuy. The difficulty curve is a little wonky here, though less so than is usually for a mock test, but the problems are of quite high quality. Slightly harder than an AMC 10; could conceivably be rebranded as an AMC 12.
• Triple Mock AIME. Written by mcdonalds106_7, Iggy Iguana, and fractals. These are way more difficult than you should expect from the actual AIME, which makes it good preparation for those already looking at 10+ scores. If you're not there yet, though, there are more difficulty-appropriate ones you should look at first.
• Northeastern WOOTers Mock AIME I and II. First one written by codyj, djmathman, and yugrey, second written by ABCDE and codyj; both organized by ahaanomegas.
• MWMT. Operated by MSTang. This has been of excellent quality in the past, and a new "season" is about to start. Definitely well-worth checking out.
• (Not a post, but useful anyway) In the same vein, CleverMath is a relative newcomer to the math scene, but it seems like an excellent resource that's well worth getting used to doing. Unfortunately you'll have to start off in the lowest division, so there'll be a few weeks of cleaning up some easier problems, but the weekly set of fairly high-quality problems is worth it.

Useful general posts from other users (again, not necessarily in chronological order):

• Response to: "Silly mistakes" (by v_Enhance). A great look at how a top mathlete handles a contest, and addresses the question of avoiding silly mistakes in the process.
• How do I prepare for the AMCs? (by AkshajK). Not the greatest article ever (especially in terms of formatting and ordering of content), but still an excellent one-stop resource if you're not sure what to do next.
• Stop looking for the "right" training (by v_Enhance). The above post is a good collection of resources, but don't forget the main point of this post: what you do is far less important than how you're doing it.
• Response to: "USA(J)MO index" (by MSTang). A useful flowchart of the USA(J)MO qualification rules. This post, along with the below one, should answer most of the qualification questions around AMC season.
• Response to: "MOP Qualification" (by Wolstenholme). A quick explanation of how the MOP cutoff rules work. This post, along with the above one, should answer most of the qualification questions around AMC season.
• Response to: "Favorite Problem(s)?" (by v_Enhance). An excellent explanation of what makes a good problem a good problem (though of course there is room for subjectivity). Especially excellent reading for aspiring problem-writers.

Useful math posts from other users (again, not necessarily chronological):

• Olympiad Combinatorics book (by Pascal96). This is very much a work in progress (and unfortunately appears to have been largely abandoned), but the existing content is excellent and this is a resource not enough people are aware of.
• Not a post, but everything on v_Enhance's website is incredible material for olympiad-level preparation, as well as understanding how advanced mathletes think about and approach problems in general. His blog also contains a lot of mini-articles (though many are quite advanced) that are worth reading even if you don't 100% understand what's going on.
• Barycentric coordinates in Olympiad geometry (by Mewto55555 and v_Enhance). This is on the above website, but is significant enough to mention twice. You can thank this post for the sharp uptake of geometry difficulty, as well as the cult following it's attracted. Almost mandatory reading at these for olympiad-level participants.
• Cyclotomic Polynomials in Olympiad Number Theory (by dinoboy). Another great Olympiad-level article with a lot of applications, including several connections that are definitely not immediately obvious.
• Olympiad number theory through challenging problems (by Binomial-Theorem). An excellent introduction into the basics of Olympiad number theory. Unfortunately this is slightly dated now as Olympiad number theory seems to have largely died off, but this is still excellent reading for you AIME/JMO-level people.
• One hundred geometry problems - bridging the olympiad gap (by djmathman). In today's contest climate, one of the major downsides to geometry is that it's geometry. Another, albeit far less important, issue is that there exist few resources for "mid-level" geometry. This article helps bridge that gap through a well-selected set of problems.
• Response to: "AIME level geometry book" (by v_Enhance). A quick syllabus of AIME-level geometry, to complement the above problem set.
• AIME level practice problem set (by djmathman). A nice collection of 40 problems (10 per subject) from AIME-level competitions not named AIME. Definitely worth doing when you "run out" of AIME problems and/or want a different flavor.

Please don't take offense if you think you made a particularly useful post that didn't appear here; more than likely, I'm simply not familiar with the post and didn't think to include it here. If you know of (or authored) a post that you think deserves to be in this compilation, let me know and I'll consider adding it in. Also, if any of the factual information above (authorship etc.) is in error, let me know and I'll correct it ASAP.

As the more astute among you will notice, this is my new blog. The reason for this is quite simple: after the site migration, I discovered that post-specific permissions were no longer possible, and I left my old blog private as a result.

I'm not entirely sure what I hope to use this blog for, as its creation very nearly coincides with the end of my high school career. As some of you know, I'll be headed to MIT in an amount of time that can effectively be described as "momentarily", so perhaps I'll stick to my original intentions of talking about that a lot. Mostly, however, I don't feel like I'm quite ready to leave the world of competitive mathematics just yet, and this blog provides a connection - however indirect and tenuous - to that culture. Really this will probably just be a place to toss out some stream-of-consciousness stuff when I feel somewhat emotional or unusually productive.

Of course, my connection to math competitions is one that will never really be broken. It's impossible to simply distance oneself from something that they've been pursuing for over a decade, and it's simply impractical to try. Regardless of what happens from here, my time within the realm of AoPS will forever shape my future. Nor will I become detached from this site in the future; my role is simply shifting from enthusiastic participant to wizened old TA. I should digress here for a moment: the last few months working with AoPS have been some of the most rewarding of my mathematics career. I get to see - and directly interact with - hundreds of kids who, quite literally, are the future of mathematics. In a class I'm TAing now, the instructor mentioned that he remembered me from a class he taught here around 8-9 years ago . It's extremely humbling and gratifying to realize that, somewhere down the road, I may very well recognize names from classes I helped assist.

Along those lines, I was fortunate to briefly speak with some of the top middle schoolers at ARML this weekend. Of course, they were more concerned with insisting they were fat and seeing who could wrap their hands around their legs, but the scene took me back - if only for a brief moment - to my glory days of MATHCOUNTS et al, when my primary concerns were less about major life decisions and more about who was fatter (sidebar: why is "fat" such a universal term in the math competition sphere?). I left (or, more accurately, they ran off to "Chipotle") without a very good idea of what exactly room 604 meant, but their sheer enthusiasm reminded me of what I'm leaving behind.

Another conversation I had this weekend was, basically, me nodding a lot while I was treated to a primer on investment banking. It's not a field I have much interest in, but that same enthusiasm that I experienced in the fatness debates made it impossible not to be interested. At the same time, it reminded me of how different things had become: instead of trying to sneak a pizza around and talking about AMCs, here we were - quite literally - talking about our careers. Growing up is terrifying.

Anyway, enough of me complaining about biological processes - on to ARML. As the final math competition of my life (Putnam exists, but to be totally honest I'm not that enthusiastic about it), I really cared about the results and put a serious effort into preparation. This seemed to be rather unusual among my friend circle, who were probably correct in focusing on more important matters, but I wanted to go out - for lack of a better term - with a bang. Unfortunately, we failed in my main goal of reaching the top 10 - a feat we've accomplished just once in recent memory - largely due to lackluster performances on the team and individual rounds. This was largely due to a completely failed strategy on the former of those two, in which our stronger members focused exclusively on the later questions, and failed to produce a positive number of points. In particular, 2 of our 4 strongest spent the entire round failing to solve #10, and I blew both #8 and #9 (apparently doesn't actually have two solutions despite the discriminant being 0, and I never really got close on #9). Somehow we ended up failing both #6 and #7 as well, despite many checks, and ended up with a truly... well, pathetic 5/10.

Power went much better; I personally did all of #6 and #7. However, we didn't end up getting most of #8, and we discovered afterwards that we had fakesolved #5. This left us with a 37, which wasn't too bad but well below what we needed to make up the team round. Individuals were rather demoralizing from the start, as we had just 19/30 on the first pair and little improvement from there. It almost seemed like we were making a comeback on the relay round (!!!) with our 21/25 on the first portion, but we were quickly returned to our ground state with just 3/25 on the next one (in which I didn't believe could actually be an answer to an ARML relay, didn't check my computation carefully, and realized just before the 6-minute mark that it was in fact ). This echoed #6 on the individual round, in which I didn't really believe that could be right because it was a pretty random number, but I wrote it anyway with ~15 seconds left (which I also did on #9 due to thinking were the side lengths in that order and not catching that until ~15 seconds left). Also, highly amusingly, one of our #2s passed back the sum of the side lengths of a rectangle instead of the perimeter (a common mistake on that relay), thus accidentally halving the answer. Fortunately for us, yugrey accidentally calculated the area of a triangle as , thus effectively doubling the passed answer. Give those men some medals.

Somehow we managed to finish as high as 14th, but it was quite a disappointing result nonetheless. On the bright side, I made it to tiebreakers for the first time - something that I had figured was so improbable that I didn't bother setting it as a personal goal. I also didn't realize they called my name for a while due to applause from other members obfuscating the sound, so that was mildly awkward as well. Even more awkward, however, was my brief conversation with nsun48, in which I legitimately thought he was ksun48 until sitting down for the problem. Oops. Anyway, as soon as I read the problem I figured that ARML was trying to be tricky and would be negative, which basically solved the problem as the entire point was remember that could be negative. However, I misremembered as (which is another perfect power - - so I get them confused), and then paniced when I realized might be the answer, but then I realized is definitely not 243 and correctly submitted at something like 1:55.

Evidently that was fast enough to break into the top 20, though not fast enough to match Wolstenholme's 16 seconds, which was an extremely satisfying end to a very long (this was my 9th ARML) math career. I actually don't think we've had a top individual in recent memory (at least not within the last 10 years), despite having many tiebreaker participants, so - finally - those endless hours of speed-training FTW paid off

And so, for me at least, the end of an era has arrived. My final year was certainly a rousing success by most measures (top individual performances at PUMaC [which included 2nd place team], ARML, top ~50 USAMO, etc.), so my swan song was - quite fortunately - a successful one. At the same time, however, the close of this chapter leaves a large gaping void in my life, one not dissimilar to loss. I, for one, am quite interested in seeing what shows up to fill it.

In other news, I recently came out of pseudo-retirement in chess, having an incredible result at the Philadelphia Open to pick up a ton of rating points (and an unofficial IM norm in the process, just short of a GM one). A couple more solid performances later, and now I'm sporting an absurdly high 2456 rating. Certainly this is not something I had expected by any stretch of the imagination - it wasn't that long ago that I was floating over and under 2400 - but now it seems that I might be obligated to pursue a quest to GM once more. Two tournaments at the end of this month (and the beginning of next), the DC international and the World Open, will provide excellent barometers for me to see if I'm the beneficiary of an auspiciously-timed fluke, or if there's something deeper lurking. Could it really be that I'm not the worst IM in the world?