Top-notch mathematical physicists at mediocre schools?

[Martin_G]

Greetings,

I am a mathematics masters student applying for a PhD program in mathematics. I have a strong interest in mathematical physics. My credentials would not allow me to go to a top-rated math PhD program, so I'd have to settle for a second- or third-rate program.

My question is this: Can you recommend a mediocre mathematics PhD program that has top-notch professors doing research in mathematical physics? The quintessential example would be John Baez at UC-Riverside, an excellent mathematical physicist at a mediocre school. Can you suggest others?

Thanks.

 

[sokrates]

What are your credentials and why do you identify yourself with a mediocre school if you have strong interests?

I mean if you satisfy the bare minimums for mediocre schools you should be able to apply for decent-to-top schools like the top 25.

Plus you have a masters, so

(1) you'll cost less to the school because you need less classes to graduate, less tuition.
(2) you have taken many more grad level classes as compared to the fresh undergrad that competes with you in the same pool
(3) if you did research , you have experience and you are ready to pursue problems right from start.
(4) you have more quality letters if you got to work with professors and got them to like you.

I could think of many good pluses in any case like this. I wouldn't make the decision myself and apply for a few good school anyway.

 

[counterpoint]

I don't think you should approach it in this way, work hard, do what you love, meditate and live peacefully. the rest will come to you.

i've met some of the greatest minds, from the best "schools", and one thing that we have in common is that regardless of were we are, we do what we love and do it naturally; it's not forced, it's not conditioned. It's not influenced by the media, rankings, all of those things.

Focus on being a better a person, and the rest will come to you. be disciplined too. Good luck.

 

[CharmedQuark]

Quite a few of these "mediocre schools" can actually have great physics/math departments even if the overall reputation of the school isn't that great. Many of these schools get bad raps because they aren't prestigious or aren't "high-ranked" in U.S news. It doesn't mean you shouldn't go there. UC-Riverside is actually a pretty good example of this. There are also other schools that may not be well known at all, but a particular group in the math department may be leaders in their field.

tl;dr go where you think you can succeed, not where others claim success can be found.

 

[twofish-quant]

I am a mathematics masters student applying for a PhD program in mathematics. I have a strong interest in mathematical physics. My credentials would not allow me to go to a top-rated math PhD program, so I'd have to settle for a second- or third-rate program.

Mathematical physics is not my field but if it's anything like astrophysics then...

Ratings are bogus. If you have a great set of professors at a school, then it's a great school. The fact it doesn't have a big name is usually a matter of marketing and politics rather than a matter of quality. One thing that's happened over the last few decades is that there has been a massive overproduction of physics faculty, so pretty much any school that wants to start a physics and mathematics department has no trouble getting top notice faculty.

Also one thing that you'll find is that you may find it surprising how difficult it is to get into a no-name school.

 

[twofish-quant]

I mean if you satisfy the bare minimums for mediocre schools you should be able to apply for decent-to-top schools like the top 25.

One thing that people have to realize is that Ph.D. programs don't work like masters or bachelors programs. Any sort of effort to identify the "top 25 schools in physics" is pretty much bogus.

 

[sokrates]

Well I am in a PhD program, as all my friends are, and I strongly disagree.

There's always rankings, irrespective of people liking it or not, and yes, there's strong correlation between these very rankings and the quality of faculty members at an institution. Obviously, there's no absolute certainty in them, but they definitely have significance. Remember: Top schools are not much better than the rest because we rank them, it's because they are much ahead of the rest, they show up high when a classification is made.

Many PhDs were graduated in the recent years, so what? Are all of these people of the same level? Moreover, Is the reputation of a school only related to faculty? What about culture, resources, money, recognition, impact, students?... "There's many more PhD's out there so there's no such thing as rankings" argument is pretty weak.

But I can imagine why people would like to deny it in order to rationalize their own dissatisfaction. You never hear this from an MIT student, it's always someone whose school is somewhere about the bottom of the list that complains about it.

 

[lurflurf]

sokrates you are confusing. First you say high ranked schools have quality faculty members. Which may be true, but lower ranked schools also have (pehaps fewer) quality faculty. Then you say faculty are not that important. Then you say not all PhDs are equal, which relates to nothing. I believe the point of mentioning the many PhDs was that there are also many good ones, not to assert they were all equal. No one said MIT has nothing to offer, but other places have something to offer as well.

 

[Martin_G]

Well, I appreciate all the input, however no one has actually replied to my original question. Ratings are important, like it or not. And getting into a mediocre school is not particularly difficult, as someone suggested. I was simply looking for a school where I could actually get accepted but that also has good mathematical physics faculty to offer. Any input on that question would be appreciated.

 

[twofish-quant]

There's always rankings, irrespective of people liking it or not, and yes, there's strong correlation between these very rankings and the quality of faculty members at an institution.

No there isn't. A lot of it is field specific. If you want to student French literature, then MIT is the wrong school. Personally, I do have an informal ranking of how good/bad astrophysics schools are, but they aren't very close to what the public "branding" is.

So as a general philosophical point, maybe rankings are important, but I've found that the rankings of schools that I have don't come anywhere close to the public rankings.

Many PhDs were graduated in the recent years, so what? Are all of these people of the same level?

Pretty much. If you look at whether you get hired in a school, "general brilliance" doesn't mean very much. What matters is 1) how well you fit into the schools research agenda and 2) how good your political connections are.

Moreover, Is the reputation of a school only related to faculty? What about culture, resources, money, recognition, impact, students?...

In the case of astrophysics, you have the following factors 1) politics. Most physics money comes from the government, and Congress and state legislatures have an interest in making sure that science money gets spread around, and that you don't end up with a few schools getting all of the money. Personally I think this is a good thing 2) geography. Cambridge Mass and metropolitan New York City awful places to put telescopes and plutonium reprocessing centers. So you end up with some really good astronomy schools in Arizona, New Mexico, and Hawaii.

But I can imagine why people would like to deny it in order to rationalize their own dissatisfaction. You never hear this from an MIT student, it's always someone whose school is somewhere about the bottom of the list that complains about it.

WRONG!

I went to MIT. Rankings are totally bogus. One reason MIT is such a great school is that one thing that you learn there is that rankings are totally bogus, and no one at the MIT physics department takes any of them seriously.

I've found that the only advantage of going to a brand name school is so that you can win arguments like this. If I say "I went to MIT. I think rankings are stupid (as to most anyone else that went to MIT)" then people that are really concerned about rankings really have no comeback.

 

[lubuntu]

I went to MIT. Rankings are totally bogus. One reason MIT is such a great school is that one thing that you learn there is that rankings are totally bogus, and no one at the MIT physics department takes any of them seriously.

I've found that the only advantage of going to a brand name school is so that you can win arguments like this. If I say "I went to MIT. I think rankings are stupid (as to most anyone else that went to MIT)" then people that are really concerned about rankings really have no comeback.

Well conversely one might say, "It's easy to think rankings are stupid when you went to MIT."

 

[twofish-quant]

Well, I appreciate all the input, however no one has actually replied to my original question. Ratings are important, like it or not.

I'm jumping up and down telling you that at least in astrophysics, school rankings *ARE* unimportant. What really matters is the reputation of your faculty advisor and dissertation committee and the social networks you form with people in the field. The ranking of your school is not going to help you at all. When people in the field look at me, they see me as the "student of Professor X."

And getting into a mediocre school is not particularly difficult, as someone suggested.

"Highly ranked" and "quality" don't have much to do with each other. Also, if you think of yourself as going to a mediocre school, you are going in with the wrong attitude. A lot of schools with very little brand name are schools that are small, and in small departments a few faculty and Ph.D. students can make a big difference.

You shouldn't think of where ever you end up as a "mediocre school" if for no other reason that it makes you prey to intellectual bullies. You really should go in thinking that this school is going to be great, because you are there.

 

[twofish-quant]

Well conversely one might say, "It's easy to think rankings are stupid when you went to MIT."

Having graduated from there, I think MIT is a great school. One major reason I think it's a great school is that one thing that they teach you is that rankings are bogus.

Also there is nothing that MIT does that can't be duplicated at some small department with committed faculty that no one has ever heard of. You just need a few hungry students and faculty, and maybe a sympathetic congressman and state legislature.

 

[Martin_G]

I have no idea how this thread got so off track. Perhaps I should have worded my question Differently. Like most would-be PhD students, I want to get my PhD from Harvard, MIT, or CalTech. Like most would-be PhD students, I won't get accepted at Harvard, MIT, or CalTech. So, I am looking for math departments to which I have a reasonable chance of getting admitted, and of those I look for those math departments that have top-notch researchers in mathematical physics. (Remember, I am looking for a PhD in math, not physics!) There, I phrased the question without using the word "mediocre", so maybe now we can cool off the discussion about rankings.

 

[twofish-quant]

Like most would-be PhD students, I want to get my PhD from Harvard, MIT, or CalTech. Like most would-be PhD students, I won't get accepted at Harvard, MIT, or CalTech.

And speaking with the voice of experience, I think you are going about Ph.D. admissions the wrong way. You are assuming that Ph.D. admissions work like undergraduate admissions when they don't.

The first thing that you want to do is to figure out what particular bit of mathematical physics you are interested in. They go to the library, do literature searches for the people working in the field that you are interested in, apply to those schools, and then demonstrate in your statement of purpose that you've done your homework. The most important part of your application is the statement of purpose, and if you can articulate why you chose that particularly school and if you are looking at a field that doesn't have too much supply, then your chances of getting in are higher than you think they are.

You'll need to do this sort of research anyway to write your statement of purpose.

 

[DarrenM]

And speaking with the voice of experience, I think you are going about Ph.D. admissions the wrong way. You are assuming that Ph.D. admissions work like undergraduate admissions when they don't.

The first thing that you want to do is to figure out what particular bit of mathematical physics you are interested in. They go to the library, do literature searches for the people working in the field that you are interested in, apply to those schools, and then demonstrate in your statement of purpose that you've done your homework. The most important part of your application is the statement of purpose, and if you can articulate why you chose that particularly school and if you are looking at a field that doesn't have too much supply, then your chances of getting in are higher than you think they are.

You'll need to do this sort of research anyway to write your statement of purpose.

Let me first say that I've found many of your posts very informative and, even when they are not directed at me, I appreciate the courtesy you display.

Now, in reply to the quote above I have a question... please forgive me if it at all strays from the OP's question.

I just started reading the blog of a professor who is in charge of graduate admissions for mathematics at a Top 20 (according to the National Research Council rankings) school. I only mention that to place this in context. He quoted Michael Lugo writing the following:

Your mathematical interests will change during the first year in graduate school, because a lot of subjects “feel” different at the undergraduate level than at the graduate level, and there are some things you just don’t see as an undergraduate at all. (This statement about “feeling” is incredibly difficult to make precise, but two examples are probability and number theory. Probability is usually taught in a “naive” way to undergrads and in a measure-theoretic way to grad students; number theory as taught to undergrads pretty much exclusively concerns itself with reasoning that takes place in the integers, whereas at higher levels it uses Big Fancy Algebraic Machinery. In addition, it may turn out that you think you are interested in X but in reality you had a particularly good teacher of X as an undergrad which colored your perception of that field.)

Now, I think your advice was very good, but I'm not sure how one could implement it while taking Mr. Lugo's statement into consideration. If one applies at a school that has a strong program in X, but quickly discovers that X is not, in fact, the field they wish to pursue, what then? Try to switch programs? How that the same school has good alternatives in other fields?

 

[Martin_G]

"The most important part of your application is the statement of purpose..."

With all due respect, that's not even close to being true. GRE general, GRE subject, grades, letters of reference and research experience all count for more than the statement of purpose.

 

[sokrates]

sokrates you are confusing. First you say high ranked schools have quality faculty members. Which may be true, but lower ranked schools also have (pehaps fewer) quality faculty. Then you say faculty are not that important. Then you say not all PhDs are equal, which relates to nothing. I believe the point of mentioning the many PhDs was that there are also many good ones, not to assert they were all equal. No one said MIT has nothing to offer, but other places have something to offer as well.

Well you managed to confuse yourself. My point was coherent. Let me clarify it:

1) High ranked school have quality faculty.

Correct. BUT this doesn't mean having great faculty is enough for being high ranked, or truly being high quality. It's a necessary condition but not sufficient.

2) Lower ranked schools have fewer but equal quality faculty

Not necessarily. I can usually tell that there's a strong correlation between the quality of the institution, hence the ranking, and the quality (not the quantity) of the faculty.
Of course there are many brilliant people at -not-so-popular institutions, and I have never denied this. We are talking about trends here.

twofish-quant said the rankings were "bogus" which is quite a strong statement; and I objected by saying "They have significance and cannot be altogether ignored", and now you are saying "other places has something to offer as well", well, did anyone say anything on the contrary?

 

[twofish-quant]

"The most important part of your application is the statement of purpose..."

With all due respect, that's not even close to being true. GRE general, GRE subject, grades, letters of reference and research experience all count for more than the statement of purpose.

The order that I'd put things in are

1) research experience
2) letters of reference
3) statement of purpose
4) what courses you've taken
5) GRE subject
6) grades - provided they are decent
7) GRE general

The reason I think that statements of purpose is the most important part of the application is:

1) if you have a bad statement of purpose then 1) and 2) on that list won't matter. People on admissions committees don't have mental telepathy, and if you don't tell them why what you did is important then people won't know. So if you have a bad statement of purpose then your research experience and letters of reference aren't going to matter because the admissions committee won't take them into account.

and

2) that most people that apply to graduate school have decent research experience and letters of reference, but the statement of purpose is often so badly written that writing a good one gives the application a huge, huge boost. There is a "standard cliche" statement of purpose that most grad school applicants write, and if you are on the admission committee and you've flipped through fifty statement of purposes that are all cliche, and you come on one that is decent, that gets popped to the top of the list.

The reason grad school applicants write such horrendously bad statement of purposes, is that I think most of them don't realize how important it really is. The basic issue here is that applications to Ph.D. programs are simply not the same as applications to undergraduate colleges.

 

[sokrates]

"The most important part of your application is the statement of purpose..."

With all due respect, that's not even close to being true. GRE general, GRE subject, grades, letters of reference and research experience all count for more than the statement of purpose.

I most emphatically agree. I have participated in the real-time process of seeing how applicants are pooled and evaluated and I could tell you: It's THE last item in the list.
that could get you in. I am not saying it's totally ignored, but saying that it's the most" important part is gravely misleading and inaccurate.

 

[twofish-quant]

BUT this doesn't mean having great faculty is enough for being high ranked, or truly being high quality. It's a necessary condition but not sufficient.

It depends on what you define as quality. Physics professors at MIT are all great researchers, but as graduate student advisors, some of them totally stink. Remember, that people get Nobel prizes for great research and not for great graduate student advising. One thing that you have to realize is that for several years, your advisor will be the closest thing to God there is, and your life will suck if God is a total jerk, and there are some very famous, brilliant researchers at MIT that are total jerks as human beings.

two-fish-quanta said the rankings were "bogus" which is quite clear; and I objected by saying " they have significance and cannot be ignored", so I don't know what you are objecting to.

It depends on which rankings you are talking about. If you ask someone in a particular field, which university would you study at if you had to do it all over again, *that* would matter. However, I've never seen those rankings published, and the schools which have faculty that I think very highly of don't match anything published that I've seen.

 

[twofish-quant]

It's THE last item in the list.
that could get you in. I am not saying it's totally ignored, but saying that it's the most" important part is gravely misleading and inaccurate.

I've also seen the process, and I've seen something quite different.

 

[sokrates]

No there isn't. A lot of it is field specific. If you want to student French literature, then MIT is the wrong school. Personally, I do have an informal ranking of how good/bad astrophysics schools are, but they aren't very close to what the public "branding" is. So as a general philosophical point, maybe rankings are important, but I've found that the rankings of schools that I have don't come anywhere close to the public rankings. In the case of astrophysics, you have the following factors 1) politics. Most physics money comes from the government, and Congress and state legislatures have an interest in making sure that science money gets spread around, and that you don't end up with a few schools getting all of the money. Personally I think this is a good thing 2) geography. Cambridge Mass and metropolitan New York City awful places to put telescopes and plutonium reprocessing centers. So you end up with some really good astronomy schools in Arizona, New Mexico, and Hawaii.
I went to MIT. Rankings are totally bogus. One reason MIT is such a great school is that one thing that you learn there is that rankings are totally bogus, and no one at the MIT physics department takes any of them seriously.
I've found that the only advantage of going to a brand name school is so that you can win arguments like this. If I say "I went to MIT. I think rankings are stupid (as to most anyone else that went to MIT)" then people that are really concerned about rankings really have no comeback.

You may not like the reality of it, it may be (and probably it is) silly and useless. But the simple fact that people (mostly students who are applying and general public) take it seriously is enough to "win the argument".

It is as simple as that. And believe me, it is not up to the physics faculty to really decide whether rankings are important or not -- you would be shocked to hear the amount of money these schools are spending to get their rankings right. It is a very important advertisement for the school to keep attracting the best students, and it usually is a concern to rank high. Every school proudly announces their ranking (if they do well) every year or discreetly ignore it they don't.

MIT could be an extreme example, it already ends up among the top schools anyway, and it's natural for the faculty to dislike the idea. But physics (or astrophysics) faculty are really not the people to ask. They are not the people who prepare months of reports and statistics for submission to ranking companies.

 

[sokrates]

I've also seen the process, and I've seen something quite different.

Just be honest and tell me this: A physics undergrad with a 3.0/4.0 average, some exposure to research but nothing concrete, 700M/500V GRE General, 700 Subject, with decent letters, but with a GREAT, FANTASTIC statement of purpose.

Would he make it to MIT?

Come on, he wouldn't even pass the "screening"!

 

[eof]

I am at a top math program and one of the profs told me that he doesn't even read the SOPs. He does read the letters of recommendation though.

 

[twofish-quant]

Come on, he wouldn't even pass the "screening"!

If he has some exposure to research not nothing concrete, he isn't going to come up with a great statement of purpose.

The problem is that if he has some really good exposure to research, but he doesn't mention it in the SOP, then no one is going to know about it.

Also whether you get into MIT physics or not depends a lot on what division of the physics department you apply to.

 

[sokrates]

If he has some exposure to research not nothing concrete, he isn't going to come up with a great statement of purpose.

So now you are saying a great SOP is not enough, it must be accompanied with "great research".

Well, see, it all comes as a package. Great research means great background, great GPA, great test scores and great letters (in which case SOP becomes redundant).

Isolating everything else and leaving SOP, as you admit, doesn't amount to anything.Edit:

Also whether you get into MIT physics or not depends a lot on what division of the physics department you apply to.

You can pick any division you like for my dream applicant! Just be sure to choose the most indulgent one.

 

[twofish-quant]

You may not like the reality of it, it may be (and probably it is) silly and useless. But the simple fact that people (mostly students who are applying and general public) take it seriously is enough to "win the argument".

Students that are applying and the general public are not sitting on the admissions committees.

And believe me, it is not up to the physics faculty to really decide whether rankings are important or not -- you would be shocked to hear the amount of money these schools are spending to get their rankings right.

Like everything else it's all about money. The reason that undergraduate and some graduate programs (like MBA's) care about rankings is that if you have high rankings, then you can charge more money for tuition.

But physics departments pay stipends for their graduate students and are funded by grants, mainly from the government but also from private industry. The main way that physics departments make $$$ is to have a research program that they can use to apply for grant money, which means that their main focus is how you are going to fit into the departments research program.

It is a very important advertisement for the school to keep attracting the best students, and it usually is a concern to rank high. Every school proudly announces their ranking (if they do well) every year or discreetly ignore it they don't.

And it's important for undergrad and some MBA programs where money comes from tuition. Useless for physics (and I would presume math) because it doesn't. School rankings are useless in physics. What really, really matters is the reputation of the individual professors. Also social networks matters a lot.

MIT could be an extreme example, it already ends up among the top schools anyway, and it's natural for the faculty to dislike the idea. But physics (or astrophysics) faculty are really not the people to ask.

They are since they are the one's on the admissions and hiring committees.

Well who are

 

[twofish-quant]

So now you are saying a great SOP is not enough, it must be accompanied with "great research".

I'm saying that a great SOP is one that tells what sort of research experience you have, and how it is relevant to the research program of the university.

Great research means great background, great GPA, great test scores and great letters (in which case SOP becomes redundant).

It doesn't because if you have a lousy SOP, then you are going to be at a huge disadvantage.

GPA doesn't matter a huge amount. If you have a really bad lousy GPA, then it will hurt you, but there is so much variability between schools that it's hard to figure out what it means. Subject test scores matter, but general GRE scores usually don't.

 

[twofish-quant]

Come on, he wouldn't even pass the "screening"!

A lot of my information comes from this talk that the head of the admissions committee gave about what MIT is looking for, when I was an undergraduate, and it's been reinforced by what I've observed since then.

And someone that I do know that got into MIT grad school had truly dreadful undergraduate scores and grades because he was moonlighting as a Boston cabbie to feed his extended family. He got a job as a lab assistant, and got in on the basis of recommendations and (I would assume) a good statement of purpose.

 

[sokrates]

It doesn't because if you have a lousy SOP, then you are going to be at a huge disadvantage.

No you wouldn't because nobody would even read your lousy SOP, if you had an otherwise great application.

Because you can't easily rank people based on how bad they want to be a physicist, or what they "hope to accomplish" in the future.

On the other hand you can easily make a list of 15 applicants based on papers, scores, and letters. This is very obvious. Committees don't have all the time in the world to sympathize with the applicant's wishes and purposes.

 

[twofish-quant]

Because you can't easily rank people based on how bad they want to be a physicist, or what they "hope to accomplish" in the future.

So that's why you shouldn't put any of that crap in your statement of purpose. The reason that a great statement of purpose will help you a lot is because most people write truly awful ones. What you want in a good SOP is to state 1) the research program that you have and 2) how your experience and goals will concretely fit the research program of the school that you are applying to. Why *ARE* you applying to MIT?

Cut the "I really want to be a physicist" nonsense.

Committees don't have all the time in the world to sympathize with the applicant's wishes and purposes.

So again, don't put any of that "cliche" "I'm passionate about being a physicist" crap in your SOP. Putting that sort of nonsense in is why most of them are dreadful. If you have ten people with crap SOP's that say the same thing, then of course you are going to be ranked on something else, but if you have a *good* SOP, that can trump an awful lot.

The most important criteria that will help you get into graduate school is the quality of any undergraduate research that you've had, the quality of your recommendation letters, and the quality of your coursework. The problem here is that most graduate applications do not have the space for you to talk about your research and your recommenders, and *that's* what you need to put in your SOP. If you don't explain what you did in your undergraduate research and why in you SOP, the committee is not going to be able to guess it from the rest of your application.

 

[sokrates]

Going back to the original question posed by OP:

Writing a good SOP is probably important as it's an element of the application process, PROVIDED that you have all the other ESSENTIALS.

I think the OP has figured out himself that his credentials are not very competitive and is asking for advice.

My advice is, as I said before, don't underrate yourself because you have an M.S degree, and if you did research these are big pluses. But don't overrate yourself either by devising the best SOP possible, hoping that it'll take care of the job for you.

From my personal experience (a brief look into the inner workings of an admission committee of a competitive school and years of experience as a student) a SOP is decisive ONLY when it compares otherwise equal applicants, with close tests, gpas, letters and publications.

Faculty research as twofish-quant suggests is VERY important, not that I think it'll improve your chances of getting in, but were you admitted, it will make your life easier and prevent a lot of headache.

I had to change my advisor two years into my PhD and I learned this the hard way.

Edit: and remember to talk to people...Don't rate your application yourself. There's nothing wrong with e-mailing graduate program heads, or individual faculty about advice on whether to apply or not. More often than not, they provide valuable feedback on how to proceed. If you are unsure about the school you are applying, you should certainly contact someone from that school before you decide to apply.

Good luck!

 

[Martin_G]

"A lot of my information comes from this talk that the head of the admissions committee gave about what MIT is looking for..."

That explains your unrealistic over-emphasis on the SoP. Admissions committee members are as truthful as politicians when they talk to the public. They all sound the same ("we are looking for the whole package" type of bunk) and they're all giving misleading information on how things get done. Remember: more applications mean more money in application fees and lower acceptance rates, which count a lot in rankings. So, their interest lies in encouraging more applications, no matter how improbable it is that the applicant will be accepted.

 

[twofish-quant]

From my personal experience (a brief look into the inner workings of an admission committee of a competitive school and years of experience as a student) a SOP is decisive ONLY when it compares otherwise equal applicants, with close tests, gpas, letters and publications.

My experience is that the most important thing in getting into graduate school is a track record of good undergraduate research and coursework. The reason that SOP becomes important is that it's the only part of the application where you have a chance to talk about any undergraduate research and coursework that you've done. If you have good recommendation letters the committee will know about the research from the letter, but the trouble is that you cannot count on the professor to mention the research that you did.

If you have demonstrated undergraduate research, that trumps tests and gpas. If you have a lower GPA, but your courses are in differential topology and general relativity, this needs to be pointed out in the SOP. They *might* figure it out from the transcript, but the SOP let's you put that fact front and center.

The reason I think that the SOP is so important is because it's the only real chance that you have to explain yourself, and most applicants waste it.