Can Earning a PhD Require More than Just Scoring in the Top 2% of Contests?

[andytoh]

If you can do very well in a math or physics contest (preferably a university level contest), say, scoring in the top 2%, then I would that you are bright enough to be able to earn a PhD. However, what if, say you are good enough to place in the top 25%, but not good enough to place in the top 2%? Do you still have a good chance of coming up with useful original research to earn a PhD some years down the road?

I've been able to place in the top 2% (and top 10 in my city) in the high school math contests I wrote, though I never wrote the Putnam. But I had many high school friends who got A+'s in their high school math courses but could not get a passing mark on a regular high school math contest if their lives depended on it (they just could not use their knowledge in the clever way that the difficult contest problems required). I lost touch with them so I do not know if they ever were able to earn PhD's. But my guess is that they didn't (if they tried at all).

If a university student wrote, say the Putnam math contest, and could not come in, say, the top 10% (and lack of knowledge cannot be blamed due to the nature of the contest), is he good enough at problem solving to be able to solve an open problem years later to earn a PhD? Or should he just forget the whole thing, admit that he is not super-smart, and just settle for a degree?

 

[andytoh]

In my opinion, just because you get an A's or A+'s in your courses, it does not necessarily mean that you are good enough to get a PhD. This is because getting A's means that you studied hard and understood what you learned very well. But it does not necessarily mean that you have the ingenuity to solve very deep problems (which don't appear in your exams). You MUST write a contest and see how well you do with the problems that require great imagination and ingenuity. The contest is the best test to see if you are clever enough to solve open problems later on.

I'm not trying to discourage A+ students. But A+'s alone does not = PhD later. A+'s + successful contests is a better guarantee.

 

[mathguy86]

In my opinion, just because you get an A's or A+'s in your courses, it does not necessarily mean that you are good enough to get a PhD. This is because getting A's means that you studied hard and understood what you learned very well. But it does not necessarily mean that you have the ingenuity to solve very deep problems (which don't appear in your exams). You MUST write a contest and see how well you do with the problems that require great imagination and ingenuity. The contest is the best test to see if you are clever enough to solve open problems later on.

I'm not trying to discourage A+ students. But A+'s alone does not = PhD later. A+'s + successful contests is a better guarantee.

Well the mentality required to do well in math contests is very different than that required to write a PHD thesis. Even the mentality required to do undergraduate research is different enough than that required to do reasearch towards a PHD that some professors advise students not to do undergraduate research.

I don't see how you can even compare a math contest where you know that there are solutions and they are supposed to be accesible with a certain level of knowledge (as long as you have the ingenuity you speak of or have seen a similar problem before) with trying to solve a problem for a PHD thesis where you don't know if what you know is enough to solve the problem no matter how much ingenuity you have. I think this makes a HUGE difference. It takes a lot of patience (usually) in order to solve a problem for a PHD. Contests are about thinking up answers quickly...its totally different.

 

[complexPHILOSOPHY]

We shouldn't even get PhD's. We should just do math contests.

<33 Just kidding homie.

 

[Beeza]

Winning contests has nothing to do with ones' ability to achieve a PhD. Well, possibly in math, but certainly not in physics. If I asked some graduate students that have passed the comp or even professors around my school about this, they would look at me like I had 3 heads.

 

[complexPHILOSOPHY]

Winning contests has nothing to do with ones' ability to achieve a PhD. Well, possibly in math, but certainly not in physics. If I asked some graduate students that have passed the comp or even professors around my school about this, they would look at me like I had 3 heads.

I love mathematics but it's synergy with physics is the most elegant aspect to me and is the PhD that I am pursuing.

I was afraid I was going to have to do some Math contests to earn my PhD! That scared me. :)

<3

 

[George Jones]

Feynman won the Putman.

 

[Moridin]

Do one need to be good at feeding a cat to be able to drive a car successfully?

What makes you think that people are predetermined to be able to obtain a Ph.D just by being in the top 2% of a contest? Even at University level? If you didn't notice, getting a Ph.D demands work and doesn't necessary have anything to do with your problem solving skills. Ever considered that the people who lost spent all of their time studying for something other than this contest?

 

[Tom1992]

i agree:

can't do well in (math) contests = not good enough at problem solving to get a phd (in math)

does well in contests = you might be good enough at problem solving to get a phd

 

[Moridin]

i agree:

can't do well in contests = not good enough at problem solving to get a phd

does well in contests = you might be good enough at problem solving to get a phd

Why? What has winning a contest have to do with being able to obtain a Ph.D?

 

[chuckd1356]

And with the contests, what if people can't work in such a stressful environment? That doesn't mean they aren't going to work hard to get a degree. And getting a degree doesn't necessarily mean you're amazing at something, it just proves that you know what you're doing and you are willing to work hard at it.

 

[Moridin]

And with the contests, what if people can't work in such a stressful environment? That doesn't mean they aren't going to work hard to get a degree. And getting a degree doesn't necessarily mean you're amazing at something, it just proves that you know what you're doing and you are willing to work hard at it.

However, it is not only contests that are stressful. Working on a Ph.D can sometimes be that as well. Also note that if one plans the entry in a contest satisfactory well, then there is no stress most of the times.

 

[mathwonk]

there are all kinds of different math abilities. one recent fields medalist, terry tao, seems like the sort who is good at contests.

others of us are slower and less clever, but a phd allows plenty of time usually.

being good at contests is a strength, and there are other strengths. try to maximize your=s.

 

[Tom1992]

to earn a phd, you have to come up with something original and useful, which means that you must be able to solve an open problem that no one else has been able to before. if you can't solve insightful problems in a contest that involve simple topics that you already know, no matter how good your grades are or hard-working you are, how can you solve an unsolved problem to earn a phd later on?

 

[cristo]

In my opinion, if one does well in a contest, then one would probably be able to complete a PhD, successfully. However, I wouldn't say that the implication that if one does not do well in this contest, that one would not be able to complete a PhD successfully is true. They are two rather different things, and so one who is not able to complete a test in a few hours may be better suited to studying for a PhD, where the problems are solved in a much greater time scale.

 

[mathwonk]

the psychological side mentioned earlier is also more significant than one may think. It takes real guts to commit a lot of time and effort to an attack on a hard problem when one does not know if one is on the right track, or even if the result one hopes to prove is true. A contest problem has already been solved by someone. this knowledge and the consequent lack of doubt, is an enormous advantage.

to be candid however about Phd work, it seems that often the problem is a setup, which the advisor has essentially already solved, or knows how to solve. Not every PhD thesis is particularly startling. One famous advisor, after listening to a lot of criticism of his student's work from the committee is said to have exclaimed, "All right, so its not the best Phd thesis I've ever written!"

 

[TMFKAN64]

How to know if you are Ph.D. Material:
1. Find a brick wall.
2. Start banging your head against it.
3. If after an hour or two, you notice that it is starting to hurt and you think that you would like to stop, a Ph.D. probably is not in your future.

 

[J77]

I see no connection between doing well in contests and doing well in a PhD.

Actually, the whole idea of contests makes me:

 

[Psi-String]

I think the best way to prove whether the prospective is right or wrong, is to investigate how many outstanding scholar have won a contest, such like IPhO, etc.
Though I'm just an ungraduate, so I have no idea about PhD. But for the contest, I know that by heavy training you can won the contest. When I was in high school, some students only study on specific subject, and after lots of training, they do won the medal. But I think wining a contest is quite different from researching. And one who haven't won a contest doesn't imply he isn't clever. My proffesor said that you can learn calculus at 10 or 12 years old, but what you do is just learning many great people's work and use them to solve problem. Research needs creativity, and contest has nothing to do about it.

 

[J77]

Research needs creativity, and contest has nothing to do about it.

That's the crux of it!

You can't write a decent PhD by reading a lot of books!

 

[andytoh]

Research needs creativity, and contest has nothing to do about it.

Contests ARE about creativity. Contest questions are not regular exercises that you find in a textbook (which explains why my old friends who got A's from studying hard with their notes and textbook could not pass the math contests). Contest questions require great ingenuity, imagination, and CREATIVITY to solve. Those who win contests are precisely those who know how to apply their knowledge in a CREATIVE way, not taught in class, to solve the insightful problems found in contests.

Let's take an example contest question from a recent Putnam. Given 4 points on a sphere, find the probability that the center is inside the quadrilateral formed by the 4 points.

The solution is very short, and requires no more knowledge than how to visulize 3D (so a 5 year old can theoretically solve the problem). The solution (go look it up) requires great imagination and creativity to solve--comparable to the imagination and creativity to write a phD thesis.

 

[J77]

You may not find contest questions in books, but they are still questions - you know they have a solution.

When doing a PhD, you don't have a specific path to follow, you don't have a specific goal to attain (aside from writing the thesis).

Ideas/problems develop as you go along - at least that's the way I see it; you don't write a question down at the start and spent 3+ years trying to solve it.

 

[andytoh]

You may not find contest questions in books, but they are still questions - you know they have a solution.

When doing a PhD, you don't have a specific path to follow, you don't have a specific goal to attain (aside from writing the thesis).

Ideas/problems develop as you go along - at least that's the way I see it; you don't write a question down at the start and spent 3+ years trying to solve it.

You are basically saying that writing a PhD thesis requires much more talent than to do well in a contest, and I agree with you. You are thus supporting my point that being able to do well in a contest is a prequisite for being creative enough to write a PhD thesis.

 

[ZapperZ]

You are basically saying that writing a PhD thesis requires much more talent than to do well in a contest, and I agree with you. You are thus supporting my point that being able to do well in a contest is a prequisite for being creative enough to write a PhD thesis.

Er.. saying something is a prerequisite means that it is a "necessary condition". How many people who write PhD thesis have "done well in a contest"?

Zz.

 

[andytoh]

Er.. saying something is a prerequisite means that it is a "necessary condition". How many people who write PhD thesis have "done well in a contest"?

Zz.

I'm sure they would have done well in a contest if they wrote one, but just never bothered to.

 

[complexPHILOSOPHY]

I have no experience with writing a phd thesis or participating in a math contest, so my position is purely of an inquisitive nature. However, isn't the actual architecture of the phd paper, much more intricate and complex than any undergraduate contest problem?

What if a phd student constructed a complex mathematical model, accurately describing some misunderstood physical phenomena and solving not one but a wealth of problems, over the course of 5 years of intense research?

I can not see how one's desire to dedicate their life to a specific problem, which could potentially after the span of five years, emerge as either erroneous, extranneous or just uninteresting can be compared to solving a question in a couple of hours. Also, even if a person is brilliant, if they can not organize their paper into a meaningful way which allows for easy comprehension by their peers, they might never get any attention. There is an art to writing papers and entraping your peers into reading your work.

I assume that when one decides to write a thesis, a strategy must be constructed:

1. Are you going to solve a well-known open problem, a relatively unknown open problem or are you going to discover/construct an open problem?
2. After decided what problem to solve, one must envision possible solutions.
3. After one has selected a few possible types of solutions, one must then decide how to approach the problem in the correct fashion.
4. Once a course of action has been selected, one might explore possible steps, which if correctly resolved, can bridge gaps and help solve the problem.
5. Finally, one must have the character to identify and admit when you are working towards a dead-end and try something new. If one is unable to do this, I would assume that you will not make a good researcher and may work through problems even if it is incorrect.

Again, I have no experience with either but when I think about writing my phd thesis one day, this is how I imagine the process might be. Granted, it is very condensed and probably very incorrect. I am sure it is much more involved, so perhaps you guys can expound upon what I have written.

However, I feel there are unique skills and abilities that are required for research that one can only gain through research experience. While it is probably correct to presuppose the notion that if one is good at contests, then one is more likely to be good at research, however I still think it's a non sequitur to assert it as a necessary pre-requisite.

 

[ZapperZ]

I'm sure they would have done well in a contest if they wrote one, but just never bothered to.

There are two problems with such a response:

1. It can't be tested, so you're making wild speculation, which I think is what this thread really is from the beginning.

2. It still doesn't validate your claim that it is a prerequisite. Try getting away with that in school. "No professor, I haven't taken that class yet to enroll in your course, but I'm sure if I took it, I would have passed."

Zz.

 

[andytoh]

So most of you are saying that if a student gets good grades because he studies hard and can do text-book level questions, but he cannot do higher-order thinking questions, then he still has a good chance of earning a PhD through simple hard-work?

 

[complexPHILOSOPHY]

So most of you are saying that if a student gets good grades because he studies hard and can do text-book level questions, but he cannot do higher-order thinking questions, then he still has a good chance of earning a PhD through simple hard-work?

I don't think that was explicitly stated by very many people, was it? I was under the impression that most of us were in accord with the notion that winning contests and writing up a paper that accurately describes five years of your life's work are incommesurable.

Although, perhaps, my perception is distorted. I am pretty useless, I haven't done any contests and I haven't written a thesis. I fail at life (just messing with you andytoh - you are the homie!).

-cP

 

[Bitter]

Well, let's look at this closely. If a person is trying to obtain a PhD then it can be safely assumed that this person has done fairly well-to excellent in their undergraduate work. Thus, the person was accepted into a PhD program. We can then safely preassume that this person is rather smart or and hard working.

So most of you are saying that if a student gets good grades because he studies hard and can do text-book level questions, but he cannot do higher-order thinking questions,

I find that you won't find many PhD like that. Doing contest questions does not nessary imply you can do higher-order questions. There are better indictors than a contest. For example, at my uni, we solve problems posed by other professors. The answer is not known, so we work to find an original solution and reply to the professor's questions. Once that is completed, we publish our results. If anything, that would, in my opinion, reflect more on a person's ability to complete a PhD than performing well on a test.

 

[andytoh]

Doing contest questions does not nessary imply you can do higher-order questions.

But contest questions ARE higher-order thinking questions.

 

[P3X-018]

I think what people are trying to say, is that just because you can't do well in a contest doesn't imply that you'll never get a PhD.

 

[andytoh]

My point is that I've known people who spent 5+ years trying to earn a PhD, but at the end could not come up with anything good enough. They believed from the start that because they got good grades that they could automatically earn a PhD through more years of work. I think they should have used some other kind of indicator than just their grades. There are 80+ PhD math students in my university and about 8 graduate per year with their PhD's (80/5=16 so about 8 walk out with nothing).

The most accurate indicator, of course, is to go ahead and try to earn your PhD, but the cost is great (wasted years and money) if you don't make it. Instead, perhaps if they should first test themselves with something at a smaller time-scale (e.g. a contest or some small research project like a previous post suggested). This is an idea: before reading the next chapter in your textbook, close your book and YOU try to come up with some theory on your own for the next few days about the subject you are reading. Then compare your findings with what you read in the next chapter. How good were your findings?

 

[complexPHILOSOPHY]

My point is that I've known people who spent 5+ years trying to earn a PhD, but at the end could not come up with anything good enough. They believed from the start that because they got good grades that they could automatically earn a PhD through more years of work. I think they should have used some other kind of indicator than just their grades. There are 80+ PhD math students in my university and about 8 graduate per year with their PhD's (80/5=16 so about 8 walk out with nothing).

The most accurate indicator, of course, is to go ahead and try to earn your PhD, but the cost is great (wasted years and money) if you don't make it. Instead, perhaps if they should first test themselves with something at a smaller time-scale (e.g. a contest or some small research project like a previous post suggested).

What if a brilliant individual 'tests' themselves with something that has no empirical foundation for determining phd success rate, such as a math contest. What if doing poorly discourages them from continuing further and prevents a brilliant person from making a contribution?

What if in the past we decided phd success rates through math contests and people like einstien, fermi or bohr never got their phd's (not suggesting they weren't amazing mathematicians, I was just grabbing random names)?

Perhaps a better indicator (which was already mentioned) is to try your hand at real, open research problems and see how well you can do. I would think working on those as opposed to winning a contest, would be more beneficial. We are all in agreement with you that winning university level contests is a good indicator of one's problem solving abilities but I don't think it is a pre-requisite or even necessary to assume it is even relevant.

I feel that to many people get attached to tests and contests as indicators of specific capacities for intelligence and thinking without considering the lack of empirical support.

You are doing an empirical science so it might be beneficial to begin thinking like an empiricist and stop conjecturing.

You seem like a brilliant guy with a lot of potential so I don't see the hang-up on these contests, which I think you said you perform extremely well in. Or perhaps I am anxious that I might not get a phd because I don't even know how a math contest works.

I won debate, wrestling and lacrosse championships in high school, will that grant me a phd? (Again, andytoh, just messing with you homie! Intonation is lost when translating from text to oral in your head, so I am making sure you get the sarcasm).

 

[SeReNiTy]

I believe there is truth in what Andy is writing about. I have seen many students at my university work very hard, and obtain near perfect GPA's. Unfortunately, upon going to a top end graduate program, a lot have come out empty handed...

Contests like the putnam require real mathematical talent, not just hard work.