Applying to grad schools, help requested

[Golden Applesauce]

This is my (very rough) draft of my Statement of Purpose for graduate admissions.  I'm applying to a ton of schools for Ph.D. mathematics programs, starting with MIT, UC Berkeley, and Princeton and working my way down.  Any advice or pointers would be greatly appreciated.  (Also, stressing over admissions has been sucking up huge amounts of my time.  I have actual content planned after I'm done with this.)  Important context is that my GPA is only like 3.1~3.2, despite me being really good

   Communication can only occur between peers.  Earlier drafts of this letter tried to write from supplicant/patron paradigm, but they all felt ... fake.  Writing from the position of a lowly applicant begging a favor from an faceless committee does things to a person.  I found myself trying to spin every accomplishment and downplay every fault, engaging in exactly the kind of banal dishonesty that keeps people from engaging each other at anything approaching a meaningful level.  Conversation becomes a guarded dance between public faces.  The people who hide behind those faces eventually shrivel into a mask themselves, having starved themselves of real human contact in favor of playing with the well-groomed homunculi people create to do their socializing for them.
   So: the dialectic of this letter will not be servant/master, supplicant/patron, or even student/professor - but rather of one god to another.  I assume the stance of a flesh-and-blood deity, and invite you to do the same (if only because the view is better from up here.)  I am the undisputed ruler of my surroundings (at least out to my skin, often further), the captain of my destiny, the watcher behind my eyes, the warden of the bar of my teeth.  I wield a thumb in not one but two hands, smile when I want to and laugh when I please.  I wield tools and tell stories, and on occasion I have been sighted traveling at one hundred kilometers per hour, sustained.  And I want to enroll in Berkeley's mathematics Ph.D. program.
   Why?  I'm not a polymath yet.  My strategy is to learn the math first (because a sufficiently clever person can always find the math underlying anything) and specific subject matter second.  The test I've set for myself is to pick up any paper in any subject and see if I tell whether the conclusions are justified or not.  I've found that I need more differential equations and complex analysis to make sense of advanced engineering papers, more statistics to handle correlational studies, more algebraic topology and linear algebra to follow modern physics, and more graph, group, and number theory for theoretical computer science.  Once I've mastered all of those fields of mathematics, I can pick up the subject-specific material on my own at my leisure, but for the intense mathematics program I have planned out for myself I'd greatly benefit from being around knowledgeable professors and enthusiastic students.
   Not that I only want to learn math as a tool for understanding other sciences.  I find math to be the most interesting subject, because math allows you to study things that don't exist.  Math is only bounded by imagination; any internally consistent structure is a valid field of study.  That so many of these structures turn out to be useful in real world applications (games are equivalent to matrices? Who'd have predicted that?) is proof that we live in a really awesome world.  While I'm studying all the aforementioned fields, I want to push the boundaries of mathematics itself.  Modern mathematics has a fixation on the reals and the natural numbers that I think will seem as silly to future mathematicians as the Greek's faith in the rationals does to us.  We talk about metric spaces, but restrict ourselves to real-valued metrics - any poset that is dense around a least element should serve as the range of a distance function.  We define arbitrary rings and groups around things like rotations and knots, things that needn't have any connection to counting numbers at all, and then talk about elements having order 2.  Where did the natural number come from?  I want to see a generalized notion of coefficients and exponents that allows us to simplify expressions like a + a + a without drawing on concepts like "three" if three isn't an element of the group we're adding up elements of.  (This might not be possible, but I'd like to try.)  I'm also interested in the theory of computing.  The computers described by Turing are sufficient to compute any computable number, of which there are countably many - which real numbers aren't computable numbers?  Every model of computing that I know of either turns out to be equivalent to Turing machines or a subset of them - might there be some "weird" models of computing waiting to be discovered?  I suspect that there are, and that investigating them will yield great advances in multiple fields.  Centrifuges perform sorts in constant time, why not computers?  What description of algorithm will allow us to capture this?  I think the answer might have something to do with an unbounded number of processors.
   That's why I want to go to graduate school in mathematics.  What remains is to explain why I should be chosen for one of the very limited number of slots in your doctorate program.  Of those who are applying to your graduate school in mathematics this year, there might be a person or three who is more qualified than I am - but certainly not twenty.  What sets me apart from the crowd of mathematical geniuses who are also applying isn't my towering intellect, creative spark, or exceptional abilities in math - I understand that these are par for the course at Berkeley - but my commitment to radical enthusiasm and curiosity.  I believe that enthusiasm is a choice, and that curiosity is a way of life.  That is what makes me a superior student, and why I think I'd be a valuable addition to your collection of grad students: I will do what it takes to learn, in every subject, because studying interesting material is never a chore, and all material is interesting with the right frame of mind.  That's why my selection of undergraduate courses is so eclectic.  How many other applicants have studied linguistics, quantum physics, organic chemistry, Modern-period philosophy, propaganda, cognitive psychology, and the Ramayana?  My guess is none.
   I have high confidence that I'll make an excellent graduate student, and that whichever school ultimately admits me won't regret it.  It would be to both our advantages if that school was UC Berkeley.  Still, if I've failed to convince you, please don't hesitate to contact me to ask any questions or clarify any points.  I'm always up for an interview.

Looking forward to working with you,
<>

eta: disregard the letter, it was suck and fail.  I completely rewrote it.

[Persona Facade]

I'll keep modifying this to add anything as needed.
Bold=Original
Italicized=Suggested Changes

Something odd about this wording:

Once I've mastered all of those fields of mathematics, I can pick up the subject-specific material on my own at my leisure, but for the intense mathematics program I have planned out for myself I'd greatly benefit from being around knowledgeable professors and enthusiastic students.

Once I've mastered all of those fields of mathematics, I will be able to pick up the subject-specific material on my own at my leisure. However, due to the intense nature of the mathematics program I have planned out for myself I believe I'd greatly benefit from being around knowledgeable professors and enthusiastic students.

Mine is a bit wordier, but the message is a bit more clear to the reader.

Potential grammatical error:

I assume the stance of a flesh-and-blood deity, and invite you to do the same (if only because the view is better from up here.)

I assume the stance of a flesh-and-blood deity, and invite you to do the same (if only because the view is better from up here).

I am unsure on this rule, however, I have seen my Religion professor harp on someone for this in the past. This professor is very anal retentive about formatting, he is most likely correct.

Awkward Wording:

I have high confidence that I'll make an excellent graduate student, and that whichever school ultimately admits me won't regret it.  It would be to both our advantages if that school was UC Berkeley.  Still, if I've failed to convince you, please don't hesitate to contact me to ask any questions or clarify any points. I'm always up for an interview.

I strongly believe that I'll make an excellent graduate student for whichever school I am ultimately admits me shan't regret it. I believe that it would be advantageous for us both if that school would be UC Berkeley. If I have yet to convince you of my worth please don't hesitate to contact and inquiry me of any doubts you may have, I am more than willing to clarify anything you may wish to ask.

I just plain dislike the underlined part, it seems as if that has been addressed by the prior sentence.

[Kai]

General comment: I think you're overplaying yourself. Maybe this sort of attitude is desired for Mathematics programs, but not for any science I am aware. Programs want to know of your accomplishments, your career goals, and what you personally will bring to their program in very concrete terms. If you don't have a particular professor in mind, best to just shelve it and move on to the next school.

A better way to apply to graduate programs: Find someone you want to work with, who is working on a topic you want to pursue. Email them, humbly speaking interest in their research and their university degree program. Begin a continuing conversation about interests. If they say, I don't have anything available right now but I may in upcoming semesters, keep emailing them, every several months.

Why this works is quite simple. Graduate programs admit students by professor interest. The professors get together in a room and one by one they hold up the applications and quickly discuss each, and if no professor shows any interest, it gets tossed into the rejected pile (or something similar to this). What easily gets the application accepted is a professor saying, "I have been conversing with this student and I want them in the program." This was the way I got into grad school, not at the school I went to undergrad, but at the school with the professor who shared my interests. My undergrad school rejected my application, as did the other school I applied at. That was for a masters degree but it is no different for a PhD program.

[Persona Facade]

This man is fairly arrogant, but he is smart enough to justify it to some extent.
The deadline for this paper is apparently fast approaching, so I just worked with what he has already written.

[Suu]

Why this works is quite simple. Graduate programs admit students by professor interest. The professors get together in a room and one by one they hold up the applications and quickly discuss each, and if no professor shows any interest, it gets tossed into the rejected pile (or something similar to this). What easily gets the application accepted is a professor saying, "I have been conversing with this student and I want them in the program." This was the way I got into grad school, not at the school I went to undergrad, but at the school with the professor who shared my interests. My undergrad school rejected my application, as did the other school I applied at. That was for a masters degree but it is no different for a PhD program.

This.

I would recommend getting a hold of advisors/dept heads at schools you really want to go to, as well as your backup schools, and establishing a relationship. Find out what they would recommend your course of action would be. As advisors, it's part of their job to help you get into the school, especially if you're very proactive, and can offer the department something they want. Some of those schools, like MIT, are extremely competitive, and you will be up against brilliance not just from Mass or the USA, but the world as a whole (I'm convinced nobody American actually GOES to MIT, the student body is so diverse that when I'm over in that area, I hear an amazing plethora of languages). But it's a fucking GORGEOUS campus, and if you're ready for a challenge, go in full-throttle. Even if it means flying into Boston to talk to someone in person.

If Brown and Harvard are on that list, you can kill them all in one stone as well....Plus you can meet us New England spags. See? It's win/win to get some interviews up here.

[leln]

Do you have any real life experience that's relevant to the program? If so, your statement of purpose is a good place to trot it out. I don't know much about math and science programs, but in the Humanities a lot of places will look at you and say "okay, you've completed an undergraduate degree. Like everybody else applying. Huzzah. Have you ever worked in the field?" Tell them what you've done, what you can do, how a degree will help you do more and what you plan to do once you have it. Also, you want to sound confident without being arrogant, so be careful with your conditional statements. Don't say "if I get into your program, I will..." Try "your program will enable me to do x, y and z, and this is why I deserve to be part of it." Maybe you feel your statement needs to prove you're qualified, but try not to sound unsure of your own ability. Good luck!

[Golden Applesauce]

Thanks, all.

After sleeping on it for a bit, I realized that I really wrote the first two paragraphs for my benefit, and that they don't help the letter much.  Will probably cut those out.

Kai / Suu - I didn't realize that you were allowed to do that.  Seriously.  The top tier colleges have their deadlines really soon, so I don't know if it will have time to work, but I will try that.

[rong]

speaking as a former mathematics grad student -

if your goal really is to become a polymath, graduate school is a step in the wrong direction. 

based on your justification:

My strategy is to learn the math first (because a sufficiently clever person can always find the math underlying anything) and specific subject matter second.

you really want to study logic.  there's a PhD program in the netherlands, i believe.

1st year graduate studies in math are "Advanced [classes you already took]"
2nd year graduate studies in math are - specialize in something.

if you really want to get accepted, the biggest advantage you will have over other applicants is a)the ability to speak english and b)willingness to teach incoming freshmen.

[Golden Applesauce]

What's the university?  I'd love to go to grad school in the Netherlands, but I was under the impression that not knowing Dutch or German was a disadvantage.

[rong]

i don't know the university in the netherlands - i'm not sure if the program still exists.  some internet searching should let you know either way - or perhaps 000 may know of something.

after re-reading my post, i realize i may have mislead you into thinking that speaking english will get you into the forementioned program in the netherlands - i meant that speaking english would increase your likelihood of acceptance into a math program in the states.  sorry about any confusion.

[Triple Zero]

What's the university?  I'd love to go to grad school in the Netherlands, but I was under the impression that not knowing Dutch or German was a disadvantage.

That's not a problem, especially in the exact sciences, most textbooks are English, and even a lot of classes (especially in the higher years) are taught in English, and often by foreign professors (which is not always a plus for their comprehensibility when they try to speak English, but yeah).

Foreign PHD positions are screwed over sideways when it comes to pay, though. But then, most seem to survive just fine. It's mostly really unfair when you compare it to Dutch PHDs (not that that is a very well paid job either).

Which university, I have no idea. The one I went to has a maths and logics faculty, I dunno what positions they  have, check their website: http://www.rug.nl (there's a link or little flag somewhere so you can view the English version of the pages).

[Rumckle]

What's the university?  I'd love to go to grad school in the Netherlands, but I was under the impression that not knowing Dutch or German was a disadvantage.

A friend of mine is doing her masters in the Netherlands at the moment, and she didn't really speak any Dutch before she went over there.

[Triple Zero]

People generally think it's real awesome if you take an interest and take a course in Dutch while you're there, but you can easily get by with just English just about anywhere.

[Suu]

Plus once you're immersed in the language you'll learn it a lot faster.

[Triple Zero]

You'll need to get the Dutch to stop speaking English to you first, though.