Is a good GRE score enough for a non-math graduate to be accepted in a decent pure mathematics graduate program? I have a computer engineering degree , and i have studied several mathematics courses like single variable and multiples variables calculus , complex variables , probability , numerical analysis ... etc
I fell in love with mathematics after graduation and employment , and i'm considering doing postgraduate program in mathematics and change my career into mathematics research
Schools around me (where i have established my living) don't have any different study options suitable for my case , all they offer is a regular 4 years undergraduate program followed by graduate studies as in the typical path 
I started to self study mathematics in order to have a high score in mathematics GRE exam so i can apply for a scholarship or find a "paid" graduate program somewhere else .
my question is : 

Can a high score in GRE mathematics exam  be a substitute for a math
  degree ? does it show the required abilities required in decent
  mathematics graduate programs ?

Does that sound like a good plan ? any pointers and suggestions would be appreciated
 A: I don't know if there's some grad program out there that would take you based on GRE scores only, but most places require classes in various subjects like analysis, algebra, topology/geometry with a certain minimum GPA. The problem is there are people out there wanting to go to American grad schools (think: China) who will be motivated to do very well on a standardized test by focusing on just what is in that test. But the GRE doesn't capture that large a range of math background, not to mention the mathematical maturity one gets by doing proofs in various subjects over several years.
My suggestion is to take a few math courses somehow (you probably don't even need that many) and do well in them. Couple that with good GRE scores, and recommendations from your courses, and you should get into a decent grad school. I don't think having been in a different career would hurt that much, as I've seen many nontraditional grad students who do fine. Some of them have entered as old as their late 30's, and I bet even older students would be looked at seriously.
A: Depends on what you mean by a "decent mathematics graduate program", and depends on what you intend to study in graduate school. 
The GRE Mathematics Subject Test focuses highly on "calculus and its applications". The pure topics (abstract algebra, topology, set theory, differential geometry, abstract analysis, etc.) tend to be less emphasised. And the format of the exam (being multiple choice) means questions tend to lean toward computational ones in nature, and less so conceptual ones. (Theoretically a firm grasp of the concrete concepts should allow you to do all the computations; in practice it helps to have good computational abilities since there are lots of questions on that exam.) 
This is to say that (a fact that I think most admission committees will recognize to an extent) while a bad GRE math subject score may raise a red flag, a good GRE math subject score cannot be equated with either having necessary advanced backgrounds or high mathematical maturity. So just having a good GRE score is, in most cases, not sufficient to guarantee you a place in a math graduate studies program. 
However, neither does having an undergraduate mathematics degree. 
How much the GRE score can substitute for an undergraduate degree depends from place to place, but I doubt either is used as the final adjudicator for admission. You also should want to have strong recommendation letters as well as good personal statements. 
In your situation, perhaps the best advice you can get is by writing directly to the directors of graduate studies (and also professors with whom you'd like to work on your degree) to seek their opinion. Since you are in a track less taken, it may benefit your eventual application by calling their attention to this fact. 
A: As other have mentioned, it really depends on what you mean by "decent program."
For top and very good programs, the GRE score is likely to act as a first-round sieve to cut down the number of applicants to be considered. I remember when I was applying, I was told by someone at what was one of the top 5 departments in the US that an application should have a subject test score of at least 880 to be considered (at the time it was scored out of 980; I don't know what they are doing now). However, my impression was that once past that "goal keeper", GRE scores were much less important, and the major emphasis was given to the letters of recommendation and the applicant's past success in mathematics courses (especially advanced ones). A weak math background did not preclude admission, provided it was somehow explained and there was good reason to believe that success in the program was likely, e.g., good letters of recommendation and an explanation of why the student had a weak math background (in fact, my graduate institution had a special program for people with weak mathematical backgrounds but who were otherwise qualified applicants, which gave them an extra year during which they would take upper division undergraduate mathematics courses before being "officially admitted" to the Ph.D. program). 
Smaller programs may have their hands forced by their University's Graduate Division, though in almost all cases they are likely to be able to request exceptions. 
Generally speaking, a weak math background needs to be explicitly and clearly explained in the application materials. This can be as simple as "I didn't realize how much I liked math until after graduation; since then I've done this, this, and this..." The letters of recommendation carry more weight, but only if they are from people who are in a position to speak knowledgeably about your ability to succeed in a mathematics graduate program: that is, (i) people who have gone through a graduate program in mathematics; and (ii) who are in a position to be familiar with your mathematical abilities as well as any personal qualities that will help you overcome any deficiencies in your background. I can't tell you how many times I've read applications by people with weak mathematical backgrounds who offer no explanation of why they are now applying to a math program, and whose letters of recommendation come from either professors in other Departments or their bosses at their current (completely non-mathematical/non-academic) jobs. Such applications always get rejected, often "with prejudice" (I am unhappy to be asked to waste my time reading through it, and will not give this applicant the benefit of the doubt if the applicant applies again, which some do).
While most departments are more than happy to accept someone who is likely to succeed, whatever their background prior, budgetary realities mean that they are unlikely to take a gamble on an unknown (also, they may be penalized later by their administration, since drop-outs count against the Department). 
In short: a good GRE score is certainly a good idea, and probably necessary, but by itself it cannot and will not substitute for a thin background. Address the background directly and clearly, and try to secure at least one recommendation letter from someone who meets the two qualities I described above. Contact the Department's Graduate Coordinator (or whoever is in charge of graduate admissions; it may simply be a committee in the Department) and ask about admissions, explaining your situation, ahead of time, to know what you will need to address explicitly in that application.
A: "is a high score in GRE mathematics exam can be a substitute for a math degree ?" 
Answer: No.
I have a Bachelor's degree in Applied Mathematics and Informatics from a university in Russia and a Ph.D. in Mathematics from the Pennsylvania State University.
When I was accepted into the Ph.D. program they waived the GRE requirement, because I had other things to do and it was too inconvenient for me to take it. At least in the case of Penn State, the GRE is a department requirement, not a university requirement. In my impression, though, the GRE math subject test is quite simple, and even if you get 100%, this doesn't really mean much. 
At Penn State virtually all math Ph.D. students have a teaching assistantship. This is normal for math departments across the country. Think about it: a lot of undergraduates take math courses.
My advice is, try to find some place where you can go to talks or seminars and listen to the people who actually are doing mathematical research. Ideally try to find someone, perhaps a professor, who can give you some problems to think about. Mathematical research is about trying to solve problems that nobody knows how to solve yet (no, not the stuff from the textbooks). 
Read some good books, but get advice, which books are good. I don't want to recommend anything because I don't really know you. However, do not read those 300-page books used in university classes. A normal book should have propositions, lemmas, theorems. 
Once again, do not focus on getting into a good program. Focus on studying and doing mathematics. Also, you may consider getting into theoretical computer science, such as algorithms and data structures. Do you know what is a suffix tree? What is dynamic programming? What is Hungarian algorithm? How jpeg encoding works? What is Huffman coding or LZW? How RSA cryptography works? How Google search works, at least on a primitive level?
A: To some extent, a high subject GRE score will serve as a substitute. Prospective schools will also look at other data, such as your grades in math and cs courses as an undergrad (they better be close to perfect), your letters of rec (this could be an issue for you), and your personal statement.
My suggestion is to list explicitly which books you studied on your own in your personal statement, to give the graduate school an idea of where you are. Another, obvious, remark is that you should be applying to a wide range of schools.
Last, but not least, you should try to make some personal contacts at nearby universities.
A: actually it depends.. my advice would be, search for mathematical programs you like in different universities and talk with the graduate study director. they would be perfect people to give you good advice based on that grad schools criteria. hope that helps. and my story is exact same like you. am from computer engineering and computer science background but desperately in love with mathematics. wish you best of luck friend
