DISCLAIMER: This is not a step-by-step or comprehensive or even possibly completely accurate guide on how to get into the camps you want. I don't know your situation. I'm some random person the internet spewing out advice with questionable amounts of experience backing up my statements. Take everything you read here with some decently large helpings of salt.

With that out of the way, let's begin.

SUMaC applications opened a few weeks ago, along with Ross, PROMYS, MathILY, and Mathcamp, which opened just yesterday. HCSSiM opens soon, along with SPARC. For those not applying to "math camps", there's also SSP, BU RISE, RMP, and many more that have either opened or are opening very, very soon.

I got a lot of these questions last year after I got into Ross, and I also got more after I got into PRIMES, and then more after I got into SPARC, so I thought I would just go ahead and compile some of my thoughts on
The short answer, and I think most of you expected this, is that "it's complicated" and "there's no one way of getting into a camp". People have a lot of different experiences/qualifications/entire lives than you, and the people who wind up going to one of the camps I listed above tend to be really different from each other - after all, you don't see 80 clones of myself at Ross, nor do you see 50 clones of me in PRIMES. What one person says helped them get in is not something you should take for gospel - rather, something you should take into light consideration. Not just that, but also, a lot of these camps select for a lot of different things, even if only subtly. In very similar flavor to Stop Looking For the "Right" Training, Stop Looking for the "Right" Way to Apply. There isn't really a good formula of doing this.

So yes, I'm encouraging you to stop asking for this kind of advice. While you definitely gain some amount via this kind of interrogation, you're asking one specific person who's gotten in to something who is (very likely) not extremely qualified to speak to "what did X like about me", most of the time. So take their advice with some handfuls of salt, and just understand that it's not going to be extremely useful. I myself tend to be very wary of giving out this kind of advice to people because I know for a fact that I don't have a good answer to "what did X like about me" - I can only guess, and sometimes my guesses are wrong, and that tends to be pretty bad for whoever I just gave advice to. So, instead of giving you advice, I'll provide you some lenses.

I think while there's no particular "hard" technique to get into camps, there are some "soft" techniques to do so, borrowing off of Evan's Hard and Soft terminology he uses to describe math problems. I think some of the best "soft" techniques you can gain are interesting lenses by which to look at an application and to look at your own application. I will provide some and update this whenever I think of a new one to add.

• The admissions officer is likely going to be looking at quite a few applications.Harder Lens
  How do I avoid being "just another application" that looks "just like any other" that'll be forgotten as soon as it was read?
  Even Harder Lens
  Other people will be thinking the same thing, so how do I make myself not seem like a tryhard who is doing this just to stand out?
  Note
  I feel like if we graphed a bunch of applications on a chart and somehow quantified "goodness", that a lot of people fall onto the exact same y-level - a little extra something something (doesn't even have to be big) really stands out at that point. See quote below
• What kinds of things does this camp seem to like? What does their general clientele look like? Harder Lens
  How do I fit my application to reveal qualities the camp likes about myself?
  Note
  I like asking past participants for some advice because it gives me a feel for what kind of people get in, rather than what kinds of things they did to get in
• What does the camp hope to gain from my response to the short answer essays? Harder Lens
  Short answer essays can more be thought of as a detailed snapshot of some part of yourself, similar to a closeup photo of some part of your body.
• What does the camp hope to gain from this specific question they're asking me? Why are they asking this? Harder Lens
  There's a reason why the camp is asking you this - figure out a plausible reason and work with that.
• What does the camp hope to gain from my response to this problem set? Do they really actually just want to see me solve hard problems? Harder Lens
  Some camps don't care about how many you solve, but rather how you think and how you articulate how you think.
• How do I feel like the admissions committee will feel after reading this part?
• How do I feel like I will be summarized during conferencing of the admissions committee?
• I am going to be on the campus for a long time. Harder Lens
  Let's try to make it clear I'm not just a math one-trick and a really boring person to hang out with.
• I should put in my best ability to get in. Harder Lens
  I always submitted day-of-deadline because I was always sleeping on ideas for essays, problems, and just thinking through my application
• "A little thing like that don't cost nothing, and it's just the little things that makes a man to be looked up to and liked." ~ Mark Twain

As an example of why I think "hard" techniques fail, consider my experience from about two years ago.

I often hear the advice "PROMYS likes to see extensions to problems." When I first applied to PROMYS, I did exactly that - extensions of every problem - taking the 3D case or deriving a general formula or something like that. But now, after reading them again, I feel all of them were forced and uncreative and put there for sake of being there, to check off boxes on a list, so that somehow I would get in easier. And I knew a plethora of other people who would follow this same advice, and a plethora of those people, who, like me, got (expectedly) rejected that year.

I would like to attribute this advice to some person who, in the past, did extensions of the problems and got in and gave that advice to other people, not realizing that this would trap people into a slightly not-as-faithful interpretation of their advice. Rather, I think this advice was a consequence of the soft technique of "The admissions officer is likely going to be looking at quite a few applications", repeated over and over by applicant after applicant without truly thinking about "why am I actually making these extensions?" or "what do I hope the admissions committee sees from my extensions? My ability to build off of ideas? Am I really successfully conveying that here? Am I just ticking boxes" and the like.

If hard technique H worked for P person, there's a chance that it wouldn't work for Q person. Or there's a chance that hard technique H is simply a representation of soft technique S, done specifically in the case of P person. Imagine soft techniques as a template, and hard techniques as the instantiation that worked for someone.

I went into the PRIMES application strongly with the mindset of "The admissions officer is likely going to be looking at quite a few applications" - so I spent way more time than I needed to fine-tuning my .sty file, fine-tuning my writing, rewriting solutions upwards of a dozen times (I wish I was kidding), making things as clear as possible, and then trying to extend problem G1b of the application as far as I could take it, spending way more effort into it than I think any other applicant did. I stand out. But it wasn't forced - it wasn't "done to be done", not "I have to do this, so I'll just extend G1b and make my solutions look pretty" - it was, rather, "I'm good at this, so let me make it abundantly clear I'm good at this, and let me allow my solutions to be my medium to convey this."

I could go on to tell people that "you should extend a problem completely" or "you should write up your solutions really nicely" or something of that sort when people ask me for advice. I don't. Because I don't think what I did would work for others - not because I'm "special", but rather that feelings and exact ideas are stupidly difficult to convey easily through words without misconstruing the original interpretation/faithfulness - what I did is hard to describe. And also, I don't think people should try to mold themselves into looking like me to get in - I'm me, you're you - make the difference clear. I don't tell people any hard techniques for it because I think my hard techniques manifest themselves naturally via considering these soft techniques for yourself.

This is only a short snippet of some of the thoughts that should be running through your mind. I've only attached some of my most prominent ones that came to mind first, but you should just take careful deliberation and constantly question things like "Is this actually something I should be putting on this application/putting here?" You should be thinking about your application while you are making it. Don't be a robot and try to just "follow a formula" - think about what you're doing. Take these soft techniques in mind.

Good luck, little soldier.

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I'd love to hear what you have to say about this - comment! - I by no means claim to be an authority on this, so I'd like to disagreement with this.