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I have completed my Bachelor's degree (3 years) in Mathematics and pursuing MSc(2 years). Currently I am in final year and expect to obtain MSc degree in next May. I am willing to do my PhD (in Mathematics) in USA.

From the information obtained from my seniors and friends, I found that most of the USA institutions ask for GRE and TOEFL score. But are there universities of USA which do not need GRE and/or TOEFL score for admission in Phd in Mathematics?

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    I do not know why you want to avoid those tests, but I do know that those tests are generally just score "good enough" requirements. Furthermore, I'm willing to bet that most of the places you would want to do your PhD in the USA require the GRE; you would be severely limiting your opportunities. You can apply to both types of schools, but only submit the GRE to the schools that require it.
    – Neo
    Jun 13, 2014 at 15:12
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    Shopping questions are not allowed on SE sites, I have therefore removed the parts of your question asking for lists of universities.
    – ff524
    Jun 14, 2014 at 19:40
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    The only time I have heard of a US university waiving the TOEFL requirement is for students who completed their undergraduate studies in the US (I believe there is usually a minimum number of years the candidates had to have been in the US enrolled in the undergraduate program)
    – Aru Ray
    Jun 14, 2014 at 19:44
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    @AruRay I think you need to look at the program-specific requirements. I had no formal education in the USA prior to applying for a PhD program, but the program I picked said "TOEFL is required for international applicants whose native language is not English and who have not studied full-time for one uninterrupted academic year at a university-level institution in which English is the language of instruction and in a country where English is a dominant language." which exempted me.
    – Patricia Shanahan
    Dec 14, 2014 at 10:14
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    I could be wrong, but the last time I helped someone going to the States, the TOEFL requirement was partially because of visa's as well. There was a section in which the sponsoring party (the univ.) had to claim the english skills were good enough to accomplish the purpose of the visa. Through some special situation it was possible to have faculty write-off on saying the person could speak english, but I doubt that would be standard at any university.
    – user-2147482637
    Jun 11, 2015 at 8:06

3 Answers 3

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The truth of the matter is that while you may find many schools that do not require the GRE, virtually every US school is going to require either the TOEFL or a similar test such as the IELTS.

The reason for this is that one of the important criteria for admission to most US graduate programs is the ability to do coursework and interact with fellow graduate students and faculty in their lingua franca, which in the US is English. Consequently, schools need to ensure that the students they accept have a certain level of proficiency in English before they enroll. (A number of grad school admissions officers have mentioned that they blacklisted candidates from certain countries because of problems related to fraud—candidates would hire other people to conduct telephone interviews with universities in the US, and the actual candidate would come with hardly any English whatsoever.)

So, for most schools, you will find it a requirement to be able to speak the dominant language of instruction—and not just in the United States. (For instance, all students at our university must show the ability to speak either German or English, depending on the program to which they apply.)

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    Avoiding the tests is a false economy. If your English skills aren't good enough to pass the test, you're unlikely to do well in an English-language graduate program. I've known a few cases where students' language ability isn't up to scratch, and it never ends well.
    – avid
    Jun 13, 2014 at 22:59
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    The ability to speak English fluently is also tied to funding. Most mathematics PhD students in the US are funded by teaching assistantships. But many universities, especially public universes like mine, require a certain minimal provable level of English proficiency to be allowed in front of any classroom.
    – JeffE
    Jun 13, 2014 at 23:48
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I think you should change your strategy for choosing a doctoral program. That is, determine which programs would provide you with the best training for the work you want to do. It might (probably will) involve these standardized test scores. You run the risk of narrowing your choices by starting with these types of requirements.

Also, you stated that you are "willing to do my PhD." Your decision for doing a PhD should be motivated by your ultimate career trajectory. I think you should clarify this career trajectory (i.e., Why do you want to do a PhD? Because it will prepare me for ...). Then, you should find a PhD program that would be best suited to help you establish this career trajectory. You don't want to get into a PhD program that is inappropriately matched with your trajectory, even though they don't require GRE and TOEFL scores. If you have scores that are not competitive, then it would be a good idea to focus on improving those scores.

Bottom line is you want good training.

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    I wouldn't be surprised if the OP's "I am willing" was intended to mean "I want".
    – Andreas Blass
    Jun 10, 2015 at 23:41
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To answer your question, no: all schools of reasonably well-known merit require a GRE. Shopping for schools that don't is only harmful. I am guessing your mindset is simply wondering if within, say, the top 100 programs there might be exceptions, perhaps because the test is a financial burden, but no, the GRE is the standard for admission. It's not the only important factor, but every school will require it. I've heard it described as a "sanity check" to make sure the student's abilities pass a check relative to what the recommendation letters and transcript advertise.

To flip the coin, imagine a school that doesn't require the GRE. Why not: what's wrong with it? Does it let students in who would have performed terribly, and risk a remedial first year? Does it let students in who are likely to drop out and simply don't fund them? Is it just really lacking merit? I would be extremely leery of such a school.

Regarding the TOEFL, the situation is simple. It would be foolish for a university to not make sure incoming students speak English. Even if you are sure of your ability and don't have the time to study or the money for the test, you should be leery of going to a school where there's a pretty good chance your classmates will include German, French, Japanese and Mexican students who don't actually speak English and went to the only school that admitted them after they failed the TOEFL.

On the other hand it is of course very important that you can pass. It would be miserable to marginally fail but not be able to teach a course effectively (which is how you pay for grad school in part) or collaborate with peers.

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    I don't agree with your second paragraph. As a professional mathematician, I wouldn't have any concerns about a school that didn't require the GRE. My impression is that it is mainly a time saver for the admission committee: it lets them quickly eliminate applicants who are severely underprepared. I mean, have you seen the math subject GRE? It basically checks whether the student can do calculus and linear algebra. Anyone who can't would surely be rejected anyway based on grades and letters; looking at GRE scores just makes that rejection faster.
    – Nate Eldredge
    Oct 2, 2014 at 20:44
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    There is confusion in this post I think - the general GRE and the math subject are different things. And I'm sorry, but the math subject GRE does not just test if students know "calculus and linear algebra" (at least as of two years ago): my test had advanced algebra, real analysis, topology, number theory, and just about every other math topic, often at a graduate level. It is no longer a "time saver" test, at least at the top-10 departments I applied and was admitted to.
    – Danny W.
    Oct 2, 2014 at 22:45
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    In any case, although (for example at Minnesota) we "expect" a GRE Subject Test score, if there isn't one we ... may... look at the rest of the file anyway. So it's simply not true that all "good" (!?!) depts require it. We'd tend to hope for it more from international students... and a sufficient score on TOEFL is non-negotiable, for reasons others have mentioned: certification of approximate capacity to speak and understand English in "recitation/problem-solving" sessions to earn the tuition+stipend.
    – paul garrett
    Jun 10, 2015 at 22:13
  • @JackBauer: I'm definitely talking about the math subject GRE. Note my word "basically". It contains a little abstract algebra, but not much; the bulk is calculus, linear algebra, differential equations. Unless the exam has changed dramatically in the years since I last took it.
    – Nate Eldredge
    Jun 7, 2016 at 5:41
  • @NateEldredge deleted comment sorry for confusion. You said "It basically checks whether the student can do calculus and linear algebra". Are you sure? It seems to have not much on probability theory and differential equations but has abstract algebra. How bulky is bulk?
    – BCLC
    Jun 7, 2016 at 6:31

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