Is this a good 4-year plan?

[diceydicey]

I am interested in going to a top 10 PhD program, and I am trying to make a plan to ensure I am competitive for those schools. I have a general idea of what I will do over the next 4 years, and I just wanted to know whether this plan is enough to get into HYPSM. Any feedback, advice, recommendations are appreciated.

I am currently a freshman at a t50 institution, domestic male, not URM, expecting a degree in honors mathematics, honors statistics, and computer science (still not decided if I want to follow through on the computer science major, but will get a minor). Currently have a 4.0 GPA, expect 3.8+ GPA by graduation. I would like to go to a pure math PhD program that is strong in analytic and algebraic number theory, combinatorics, algebra, and maybe probability and harmonic analysis.

Coursework:
I have taken/am taking topology, analysis 1, 2, linear algebra 1, 2, abstract algebra, grad intro algebra, grad measure theory/integration, and a reading course in field theory/algebraic number theory.

I expect to finish the commutative algebra 1, 2 sequence, complex analysis, probability 1, 2 sequence, functional analysis, algebraic topology, diff geometry/topology, class field theory, graph theory, and several topics courses. I have space in my schedule for 15-20 grad courses in math/theoretical cs total by the time I graduate.

Research:
I have had a very computational research experience. It was fun, but will likely not be mentioned on apps and did not result in publication. I will have an REU this summer in additive number theory, and I will have a research project during the year in algebraic number theory next year. My mentors for both projects say they expect we should be able to produce publishable results. I expect to do 2 more REU's (if I can get into more) the following summers and continue research in number theory. Also, my faculty mentor here says that my REU project looks very unique and would probably look a lot better than most other programs I applied to. I think I can reasonably publish 3-4 papers at the minimum as a coauthor by the time I graduate.

Exams:
I scored a 19 on the Putnam. This was my first attempt at competition math, and I believe I should have done better. I think that I may be able to get a 30-40 on the 2024 Putnam, and I plan to study consistently this time around. Is a 30-40 something that would help my application for a HYPSM etc school?

I plan to study for the GRE this summer and next summer. What should I be aiming for on the GRE quantitative and GRE subject score? Is a 85 percentile solid for both? 90?

Other Things:
I think I will be an officer of the math club, and I will likely be a tutor. I am pretty sure I will win a few awards related to math from my school. I also have an interesting and compelling story to tell in my personal statements/in interviews about my introduction to mathematics.

I also think I will get a very strong letter of recommendation from my faculty mentor here. I am going to try to get a letter of recommendation from one of the famous faculty at my school in my current areas of interest, and I think I have made a good impression on a couple. I will also try to get a recommendation from an REU mentor.

From the admissions profile threads, it is not clear to me that a profile like this would get accepted to a t10 school. Would I need more focus in my application, better scores, better gpa? Are my areas of interest too competitive? Idk what to think. Is it appropriate to reach out to admissions committees at top universities to ask their opinion since I am not currently in the process of applying, and how would I go about doing this? Thank you so much if you got to this point :)

[Radon-Nikocado]

Someone who got into a T10 from a crappy state school here. You seem more obsessed about rankings and prestige than actual mathematics. Your ego will probably be your downfall... saw it happen plenty of times in my undergrad program.

[diceydicey]

Someone who got into a T10 from a crappy state school here. You seem more obsessed about rankings and prestige than actual mathematics. Your ego will probably be your downfall... saw it happen plenty of times in my undergrad program.

Thank you for the response! I just want to clarify that my first focus is mathematics, and all this is secondary. I am also very happy going to a top 30 school, and I am definitely not only interested in t10 schools cuz that would be foolish. I am just wondering whether a t10 school is within reach. With respect to prestige, I think that is an important factor for me among several. Other factors include that the stipend at top universities is much more livable which is a big concern for me, the post-PhD placements are a good bit better (which I care about because the world is in a precarious place), and the quality of the research experience is better. Also, if my application is stronger overall, there is a higher chance I can stay in my home state, which is important to me for a few personal reasons.

[greenface1998]

Someone who got into a T10 from a crappy state school here. You seem more obsessed about rankings and prestige than actual mathematics. Your ego will probably be your downfall... saw it happen plenty of times in my undergrad program.

Just for wanting to go to a t10 school?
It’s not like it’s not a relevant consideration for anyone who wants to be a math professor. And you know just as well as I do that there is an extent to which one has to ‘play the game’ of grad school admissions to have a chance at getting into a top school. It’s nice to have an idealized view of the intellectual mathematician doing everything he does purely just out of a love for the field but that is a very naive way to look at things. Fact is ‘politics’ matter .

[activator73]

I would like to go to a pure math PhD program that is strong in analytic and algebraic number theory, combinatorics, algebra, and maybe probability and harmonic analysis.

That is a lot of fields! A broad education during your undergrad is of course necessary, but don't underestimate the importance of discovering what you want to specialize in. This will open you up to more schools, as a school that is T10 in your discipline might not be T10 overall. You probably won't be doing research in all of those fields unless you're Terry Tao

I am guessing that the GREs will be entirely phased out by the time you apply—but if they aren't, you are right that 85-90% is more than enough for the subject. The quantitative section of the general GRE is stupid easy though, so you should be shooting for >95%.

Please do not triple major.

[greenface1998]

I would like to go to a pure math PhD program that is strong in analytic and algebraic number theory, combinatorics, algebra, and maybe probability and harmonic analysis.

That is a lot of fields! A broad education during your undergrad is of course necessary, but don't underestimate the importance of discovering what you want to specialize in. This will open you up to more schools, as a school that is T10 in your discipline might not be T10 overall. You probably won't be doing research in all of those fields unless you're Terry Tao

I am guessing that the GREs will be entirely phased out by the time you apply—but if they aren't, you are right that 85-90% is more than enough for the subject. The quantitative section of the general GRE is stupid easy though, so you should be shooting for >95%.

Please do not triple major.

So if you get a 168/170 on the quant section of the GRE is that gonna be seen as a bad thing? I think for 95%+ you essentially have to get a 169 or 170. The percentiles fall of super quick so 168 is like 92%.

[dolbeault]

I would like to go to a pure math PhD program that is strong in analytic and algebraic number theory, combinatorics, algebra, and maybe probability and harmonic analysis.

That is a lot of fields! A broad education during your undergrad is of course necessary, but don't underestimate the importance of discovering what you want to specialize in. This will open you up to more schools, as a school that is T10 in your discipline might not be T10 overall. You probably won't be doing research in all of those fields unless you're Terry Tao

I am guessing that the GREs will be entirely phased out by the time you apply—but if they aren't, you are right that 85-90% is more than enough for the subject. The quantitative section of the general GRE is stupid easy though, so you should be shooting for >95%.

Please do not triple major.

So if you get a 168/170 on the quant section of the GRE is that gonna be seen as a bad thing? I think for 95%+ you essentially have to get a 169 or 170. The percentiles fall of super quick so 168 is like 92%.

Not sure if anyone would pay it much mind, even a lot of places that require the mGRE couldn't care less about the general so you could likely get by without sending it anywhere. Honestly a low quant score on the general seems like it would automatically make an adcom assume extenuating circumstances, if you major in math basically anywhere accredited then getting a 169 or 170 will be almost automatic. It's intended to test people going into non-math disciplines, not something you need to worry about.

[greenface1998]

idk

That is a lot of fields! A broad education during your undergrad is of course necessary, but don't underestimate the importance of discovering what you want to specialize in. This will open you up to more schools, as a school that is T10 in your discipline might not be T10 overall. You probably won't be doing research in all of those fields unless you're Terry Tao

I am guessing that the GREs will be entirely phased out by the time you apply—but if they aren't, you are right that 85-90% is more than enough for the subject. The quantitative section of the general GRE is stupid easy though, so you should be shooting for >95%.

Please do not triple major.

So if you get a 168/170 on the quant section of the GRE is that gonna be seen as a bad thing? I think for 95%+ you essentially have to get a 169 or 170. The percentiles fall of super quick so 168 is like 92%.

Not sure if anyone would pay it much mind, even a lot of places that require the mGRE couldn't care less about the general so you could likely get by without sending it anywhere. Honestly a low quant score on the general seems like it would automatically make an adcom assume extenuating circumstances, if you major in math basically anywhere accredited then getting a 169 or 170 will be almost automatic. It's intended to test people going into non-math disciplines, not something you need to worry about.

IMO getting a 169 or 170 on the quant section is more a test of your ability to do fast easy math under pressure without any silly errors, which is not a given even if you're good at doing real mathematics.

[diceydicey]

I would like to go to a pure math PhD program that is strong in analytic and algebraic number theory, combinatorics, algebra, and maybe probability and harmonic analysis.

That is a lot of fields! A broad education during your undergrad is of course necessary, but don't underestimate the importance of discovering what you want to specialize in. This will open you up to more schools, as a school that is T10 in your discipline might not be T10 overall. You probably won't be doing research in all of those fields unless you're Terry Tao

I am guessing that the GREs will be entirely phased out by the time you apply—but if they aren't, you are right that 85-90% is more than enough for the subject. The quantitative section of the general GRE is stupid easy though, so you should be shooting for >95%.

Please do not triple major.

Thanks for the response! Yeah the stats major is only there cuz I can do it in only a couple of courses on top of a math major, but I probably won't follow through with it. I also am somewhat sure that I will do number theory, not sure which flavor, since that is currently most interesting to me and what I have two projects on this year, but I also feel like I want the program I go to to be strong in the other areas in case I decide to change my research interests. Also since algebra, additive combinatorics, harmonic analysis for example are connected with number theory and I'd probably want to be able to pick up some basic techniques and gain a working knowledge of some those fields during grad school. Thx for the clarification about the gre scores.

[Grothendieck69]

I am interested in going to a top 10 PhD program, and I am trying to make a plan to ensure I am competitive for those schools. I have a general idea of what I will do over the next 4 years, and I just wanted to know whether this plan is enough to get into HYPSM. Any feedback, advice, recommendations are appreciated.

I am currently a freshman at a t50 institution, domestic male, not URM, expecting a degree in honors mathematics, honors statistics, and computer science (still not decided if I want to follow through on the computer science major, but will get a minor). Currently have a 4.0 GPA, expect 3.8+ GPA by graduation. I would like to go to a pure math PhD program that is strong in analytic and algebraic number theory, combinatorics, algebra, and maybe probability and harmonic analysis.

Coursework:
I have taken/am taking topology, analysis 1, 2, linear algebra 1, 2, abstract algebra, grad intro algebra, grad measure theory/integration, and a reading course in field theory/algebraic number theory.

I expect to finish the commutative algebra 1, 2 sequence, complex analysis, probability 1, 2 sequence, functional analysis, algebraic topology, diff geometry/topology, class field theory, graph theory, and several topics courses. I have space in my schedule for 15-20 grad courses in math/theoretical cs total by the time I graduate.

Research:
I have had a very computational research experience. It was fun, but will likely not be mentioned on apps and did not result in publication. I will have an REU this summer in additive number theory, and I will have a research project during the year in algebraic number theory next year. My mentors for both projects say they expect we should be able to produce publishable results. I expect to do 2 more REU's (if I can get into more) the following summers and continue research in number theory. Also, my faculty mentor here says that my REU project looks very unique and would probably look a lot better than most other programs I applied to. I think I can reasonably publish 3-4 papers at the minimum as a coauthor by the time I graduate.

Exams:
I scored a 19 on the Putnam. This was my first attempt at competition math, and I believe I should have done better. I think that I may be able to get a 30-40 on the 2024 Putnam, and I plan to study consistently this time around. Is a 30-40 something that would help my application for a HYPSM etc school?

I plan to study for the GRE this summer and next summer. What should I be aiming for on the GRE quantitative and GRE subject score? Is a 85 percentile solid for both? 90?

Other Things:
I think I will be an officer of the math club, and I will likely be a tutor. I am pretty sure I will win a few awards related to math from my school. I also have an interesting and compelling story to tell in my personal statements/in interviews about my introduction to mathematics.

I also think I will get a very strong letter of recommendation from my faculty mentor here. I am going to try to get a letter of recommendation from one of the famous faculty at my school in my current areas of interest, and I think I have made a good impression on a couple. I will also try to get a recommendation from an REU mentor.

From the admissions profile threads, it is not clear to me that a profile like this would get accepted to a t10 school. Would I need more focus in my application, better scores, better gpa? Are my areas of interest too competitive? Idk what to think. Is it appropriate to reach out to admissions committees at top universities to ask their opinion since I am not currently in the process of applying, and how would I go about doing this? Thank you so much if you got to this point

One advice which I can suggest is try making good set of notes or reports(latex definitely) for the papers you read in your areas of interests and also for advanced/exotic courses and put it on some website or something. Definitely try reading the foundational and celebrated papers if you are going into more theoretical fields like number theory. This usually helps a lot especially in fields like algebraic number theory where publishing research is too long of a shot for undergrads. Of course definitely try to have good connections with potential recommenders and do projects under them. You will need to trim down your interests a lot which will happen I believe automatically once you start going deeper into stuffs. Best of Luck.

[fear_of_sheep]

I will say that by far the most important thing is letters of recommendation. At least, this is what I was told, and to be frank the only notable part of my application was my letters and I did pretty well (you can see my profile). So, I'd really recommend taking as many classes as possible with that big name faculty mentor you mentioned to try and build a good relationship. If they don't teach often, ask if you could do an independent study with them on some paper or topic.

[greenface1998]

I will say that by far the most important thing is letters of recommendation. At least, this is what I was told, and to be frank the only notable part of my application was my letters and I did pretty well (you can see my profile). So, I'd really recommend taking as many classes as possible with that big name faculty mentor you mentioned to try and build a good relationship. If they don't teach often, ask if you could do an independent study with them on some paper or topic.

My advisor told me his rec for me was 3.5 pages long and he said as just gonna straight up tell the admissions committee to let me in and he’d be my PhD advisor and fund me. Still disnt work for rejected everywhere w a 3.97/4 ‍

[diceydicey]

I will say that by far the most important thing is letters of recommendation. At least, this is what I was told, and to be frank the only notable part of my application was my letters and I did pretty well (you can see my profile). So, I'd really recommend taking as many classes as possible with that big name faculty mentor you mentioned to try and build a good relationship. If they don't teach often, ask if you could do an independent study with them on some paper or topic.

I am not really sure if my notion of what it means for a faculty member to be famous is right, so I just wanted to ask. Is being an AMS fellow enough? Is there a certain threshold of citations, say 2000? Is being a distinguished professor in mathematics enough?

I have one faculty member in mind who is an AMS fellow. He has made significant contributions to the Langlands program, and teaches the algebraic number theory and class field theory courses at my school, so I was thinking about going to him to do a reading course in analytic number theory. According to my faculty mentor, he is considered the best living mathematician from his country or origin. I think this would make him famous in number theory circles? He also has 5000+ citations.

Also there is another distinguished professor who is also a very strong number theorist, and he was the department head and held a title at a good English university before coming to the US a few yrs ago. He has 3000+ citations. Would this be enough to be considered famous?

[fear_of_sheep]

I will say that by far the most important thing is letters of recommendation. At least, this is what I was told, and to be frank the only notable part of my application was my letters and I did pretty well (you can see my profile). So, I'd really recommend taking as many classes as possible with that big name faculty mentor you mentioned to try and build a good relationship. If they don't teach often, ask if you could do an independent study with them on some paper or topic.

I am not really sure if my notion of what it means for a faculty member to be famous is right, so I just wanted to ask. Is being an AMS fellow enough? Is there a certain threshold of citations, say 2000? Is being a distinguished professor in mathematics enough?

I have one faculty member in mind who is an AMS fellow. He has made significant contributions to the Langlands program, and teaches the algebraic number theory and class field theory courses at my school, so I was thinking about going to him to do a reading course in analytic number theory. According to my faculty mentor, he is considered the best living mathematician from his country or origin. I think this would make him famous in number theory circles? He also has 5000+ citations.

Also there is another distinguished professor who is also a very strong number theorist, and he was the department head and held a title at a good English university before coming to the US a few yrs ago. He has 3000+ citations. Would this be enough to be considered famous?

In number theory, 3000 and 5000 citations are definitely famous. I'm not sure if I have a hard number to give; I think the main thing is how likely some random number theorist is to have heard of your letter writers, times how strongly the recommend you.

[diceydicey]

I will say that by far the most important thing is letters of recommendation. At least, this is what I was told, and to be frank the only notable part of my application was my letters and I did pretty well (you can see my profile). So, I'd really recommend taking as many classes as possible with that big name faculty mentor you mentioned to try and build a good relationship. If they don't teach often, ask if you could do an independent study with them on some paper or topic.

I am not really sure if my notion of what it means for a faculty member to be famous is right, so I just wanted to ask. Is being an AMS fellow enough? Is there a certain threshold of citations, say 2000? Is being a distinguished professor in mathematics enough?

I have one faculty member in mind who is an AMS fellow. He has made significant contributions to the Langlands program, and teaches the algebraic number theory and class field theory courses at my school, so I was thinking about going to him to do a reading course in analytic number theory. According to my faculty mentor, he is considered the best living mathematician from his country or origin. I think this would make him famous in number theory circles? He also has 5000+ citations.

Also there is another distinguished professor who is also a very strong number theorist, and he was the department head and held a title at a good English university before coming to the US a few yrs ago. He has 3000+ citations. Would this be enough to be considered famous?

In number theory, 3000 and 5000 citations are definitely famous. I'm not sure if I have a hard number to give; I think the main thing is how likely some random number theorist is to have heard of your letter writers, times how strongly the recommend you.

Ok good that was what I was expecting. I think I will be doing some additive and analytic number theory this summer, so I may do a reading course with one of the profs in additive number theory since that is his main area of expertise. Maybe I'll look at some important papers or something. Hopefully, I can build some rapport with this prof. From what I've heard, he's an excellent teacher and hopefully, I'll also get to take a couple of classes with him. Thanks for the response!

[diceydicey]

I did some soul-searching in the past few days and realized that I no longer want to do a CS major. I think I will do a minor since I would like to pick up some CS skills. I think this will free me up to do so much more in math. Now it feels manageable to take 3 grad classes a semester and a reading course without that burden. I think it is now very reasonable to take 18 more math courses (3 a sem) + some number of reading courses. I am planning on writing detailed notes with more free time. Thank you for convincing me not to continue with it.

I was interested in what some of you thought about selecting grad courses. I am pretty set on doing number theory, so I am thinking that I will take a topics course on number theory every sem, or something closely related in algebra, combinatorics, or analysis. I also think I want to finish up some of the more core grad classes. I was thinking about finishing the commutative algebra sequence next year. I also think I will take complex analysis and a reading course with one of the famous faculty in number theory at my school in analytic number theory or additive number theory. I got to ask Terrence Tao (holy shit) something to this effect and he said to get very good at one thing before you try to branch out, and that's what I think I will try to do with number theory, and I will maybe branch out in grad school or even later.

I was also thinking about taking probability theory next year, but I am not sure whether to finish the sequence because I am not sure how much would be helpful to know in number theory and additive combinatorics.

Are there any courses I should consider taking if they are offered at my school?

Thanks!