Incompetent pure maths researcher?

[pivoxa15]

Is it true in general that if someone who does not show any talent in maths during school (i.e. performs average in maths competitions and tests) will not succeed in pure maths research if that person chooses to do so? Hence that person is not likely to become a professor if he/she chooses to be a pure maths academic and will mostly be doing teaching duties? Hence for these people, a more applied subject involving maths will be better suited.

I am aware that hard work is most important but in the case of producing top quality pure maths published in repected journals, ability and talent is also an essential ingredient?

 

[vanesch]

If you're not good at something, you shouldn't make it your profession. Most of the time, at some point one will stop you in trying to make it your profession, but some get through. These people are first of all unhappy themselves, and cause quite some harm, especially if they get to jobs with some responsability.

 

[hrc969]

Is it true in general that if someone who does not show any talent in maths during school (i.e. performs average in maths competitions and tests) will not succeed in pure maths research if that person chooses to do so?

NO. Showing talent in math is not about being able to solve tricky math problems.
I have a professor who say's I'm very talented in Math he even wants me to do research with him so that I can take advantage of my talent. He decided this when I took a class from him in my second year as an undergrad (I am in my 3rd year now). However I am probably not good at contests. Last time I checked I wasn't. I took the AMC 12 in HS and didn't pass that test. During my second year I was taking a class with the professor who organizes the putnam at my school and he saw that I was doing well in the class (I was the best student despite there being mostly seniors and a grad student). He put me as 1 of the 3 people on the putnam team just based on my performance in his class. No doubt he saw that I might be talented in Mathematics.
Well guess what I got on the putnam? 0. I couldn't do any of the problems. I attempted a lot of them. I just could not solve any. I didn't train for it as many people do. The professor did not hold any training sessions that year as he did this year. I did not take the putnam this year because I decided I rather learn a lot of math then take a train for and take a test about tricky problems.
Obviously I am not a pure mathematician yet, but so far not being good at math contests and doing horrible on those exams has not done any harm to me.

Now in almost all (probably all) cases the math a pure math researcher has to use and study is very abstract. You can solve all the tricky math problems you want but if you cannot handle thinking abstractly you probably won't be very good at math.
On the other hand a person who is not good at contests and tricky math problems can become a pure math researcher because math is not about tricky math contests problems. Just this past wednesday one of the full professors at my school was telling some of us that he could not solve a putnam problem to save his life. I'm sure he was exaggerating a bit but the point was that he is not good at contests and he was never good at them. He says he's not clever.

Hence that person is not likely to become a professor if he/she chooses to be a pure maths academic and will mostly be doing teaching duties? Hence for these people, a more applied subject involving maths will be better suited.

I'd say it would be a bad idea to go to applied where problem solving skill are more relevant.
The first professor I talk about was great at contests if I remember correctly he got either a gold or silver or something in the international olympiad. Yet he is made to teach the precalculus class. He taught two lecture of it last quarter and is teaching one this quarter. He's a great lecturer and student love him so the administration probably thought it would be a good idea to have him teach those than have some one else who students won't like as much.

I am aware that hard work is most important but in the case of producing top quality pure maths published in repected journals, ability and talent is also an essential ingredient?

If by ability and talent you mean what you said in the i.e. above then no. I think being able to understand abstract mathematics is more essential.

 

[pivoxa15]

If by ability and talent you mean what you said in the i.e. above then no. I think being able to understand abstract mathematics is more essential.

True, after taking some pure maths, I feel that it's all about abstraction. But they will get 'tricky' when the level goes up - othersise most people would have done them and people who are good at maths contests hence tricky problems will be highly advantaged?

 

[pivoxa15]

If you're not good at something, you shouldn't make it your profession.

What happens if you really enjoy it?

Most of the time, at some point one will stop you in trying to make it your profession, but some get through. These people are first of all unhappy themselves, and cause quite some harm, especially if they get to jobs with some responsability.

Lucky there is no harm in pure mathematics, is there?

 

[hrc969]

True, after taking some pure maths, I feel that it's all about abstraction. But they will get 'tricky' when the level goes up - othersise most people would have done them

Some of it is tricky some of it is just hard. For some you have to remember the right things. Some just take a lot of patience. One of my professors told me that there was this thing that S.T. Yau published and my professor asked Yau how he was ever able to get that. Yau's answer was he calculated a certain thing for different manifolds for a period of two years or more. My professor said he did not have the patience to do that. You have to understand that for this you don't know whether your work will lead to anything worthwhile. This particular professor is one who got 3rd place on the putnam one. But all his ability to do tricky problems was irrelevant in that particular case.

PS: Sorry if my retelling of what my professor told me is very vague. I cannot remember exactly what the subject matter was.

and people who are good at maths contests hence tricky problems will be highly advantaged?

It depends, probably if all other (or almost all other) important factors are equal then yes the person who is good at contests will have an advantage. But depending on the problem that might or might not be relevant.

 

[complexPHILOSOPHY]

To me, I think the contest begins after graduate school, when you really have to start producing some interesting results. Whether or not you won the Putnam or whatever the hell it is, isn't going to generate publications for you. I am a retarded undergrad though, so my perception could be potentially displaced.

In that respect, I think it's useless to ponder it.

 

[arunma]

Is it true in general that if someone who does not show any talent in maths during school (i.e. performs average in maths competitions and tests) will not succeed in pure maths research if that person chooses to do so? Hence that person is not likely to become a professor if he/she chooses to be a pure maths academic and will mostly be doing teaching duties? Hence for these people, a more applied subject involving maths will be better suited.

I am aware that hard work is most important but in the case of producing top quality pure maths published in repected journals, ability and talent is also an essential ingredient?

Could you define "school?" Because I consistently failed math up through seventh grade. As a matter of fact I was a year or so behind, until I finally made it into algebra 1 by some strange twist of fate. After that, up through my senior year of college I always got A's and B's in math, and got a degree in math. So if that's the sort of school you're talking about, then I'm living proof that you can do badly in math at school, and turn out to succeed in the field.

Of course, if you're talking about college, then I would say that you probably can't expect to do well in professional mathematics if you don't do fairly well in your math classes. Junior and senior year is when you begin taking courses in advanced topics in math. Of course you'll occasionally run into the class that you just can't do well in (for some people it's rigorous analysis or algebra). But if you're failing advanced calculus, complex analysis, and probability theory, then you may have a problem.

 

[pivoxa15]

Could you define "school?" Because I consistently failed math up through seventh grade. As a matter of fact I was a year or so behind, until I finally made it into algebra 1 by some strange twist of fate. After that, up through my senior year of college I always got A's and B's in math, and got a degree in math. So if that's the sort of school you're talking about, then I'm living proof that you can do badly in math at school, and turn out to succeed in the field.

Of course, if you're talking about college, then I would say that you probably can't expect to do well in professional mathematics if you don't do fairly well in your math classes. Junior and senior year is when you begin taking courses in advanced topics in math. Of course you'll occasionally run into the class that you just can't do well in (for some people it's rigorous analysis or algebra). But if you're failing advanced calculus, complex analysis, and probability theory, then you may have a problem.

I was talking primary and secondary school.

 

[arunma]

I was talking primary and secondary school.

In that case, no I don't think your performance in these early years is all that important. Back in primary and secondary school, I was in the lowest possible math groups. Heck, I even recall a rather unpleasant parent-teacher conference that was convened specifically to discuss my many failures in mathematics. Yet as I said in my earlier post, I somehow got all A's and B's in math from grade eight up through my senior year of college. So I wouldn't really worry about how you did in math back in primary or secondary school. For that matter, I'm not really sure that one's performance in any subject at such an early age points to future success or failure in any particular field.

 

[complexPHILOSOPHY]

I didn't know what the hell $$y=mx+b$$ was last year and now I am working through Hersteins Topics in Algebra, so I really don't think it applies. Just do your best. I know this doesn't necessarily imply you will be a good researcher but I am saying that all you can do is think the best you can.

 

[mr_coffee]

just because you aren't good at something doesn't mean you shouldn't peruse it, if that's what you enjoy.

When I started out programming when I was younger I was terriable, couldn't seem to understand basic arrays for the longest time but one day it just clicked now I'm at the top of my class and IBM is going to be a possible co-op if I land this last interview.

So hard work and determination will help you succeed in anything you really love, just keep at it, there will always be people better than you out there.

 

[JasonRox]

Lucky there is no harm in pure mathematics, is there?

I wouldn't want the Dean or Chair of my department to be an idiot, do you?

 

[pivoxa15]

I wouldn't want the Dean or Chair of my department to be an idiot, do you?

Given that person made it to that position, he/she would have to have shown exceptional results in their field.

My question is more could an 'idiot' produce exceptional results (in the future)? If that person does and for a consistent amount of time then that person will no longer be an idiot and should be legitimate candidates for the senior posistions you describe.

 

[J77]

Lucky there is no harm in pure mathematics, is there?

Defence industry uses a lot of pure mathematicians for, eg. cryptography, communication...

Going back to your OP.

I think you need to show some talent at school but if you have to work extremely hard for those top grades, when someone else is coasting it but not acheiving the absolute top, I think the latter person, with a bit of hard work later in life, will do much better.

 

[arunma]

Given that person made it to that position, he/she would have to have shown exceptional results in their field.

My question is more could an 'idiot' produce exceptional results (in the future)? If that person does and for a consistent amount of time then that person will no longer be an idiot and should be legitimate candidates for the senior posistions you describe.

But one of the problems is that you can't get this far by doing poorly in math courses. If you fail all your math classes, you won't get a Bachelor's, to say nothing of doing graduate work in mathematics. Certainly, there's usually opportunity for improvement in the academic world. For example, if you don't do so hot in your first two years of math, but then do very well in the second two years, then you should be all right. But at some point, you need to show consistent academic success.

Also, the situation you describe isn't all too realistic. People who don't understand basic math (by which I mean first and second year calculus) probably won't understand advanced math either.

 

[JasonRox]

Given that person made it to that position, he/she would have to have shown exceptional results in their field.

My question is more could an 'idiot' produce exceptional results (in the future)? If that person does and for a consistent amount of time then that person will no longer be an idiot and should be legitimate candidates for the senior posistions you describe.

Being the Dean or Chair has nothing to do with results, so what are you talking about?

Yes, there are Deans and Chairs running around that shouldn't be there. A few years with a bad Dean or Chair can ruin a department or program.

 

[pivoxa15]

Being the Dean or Chair has nothing to do with results, so what are you talking about?

Yes, there are Deans and Chairs running around that shouldn't be there. A few years with a bad Dean or Chair can ruin a department or program.

The dean of faculty and chair of disciplines in my university are all professors and any professor would have to have shown exceptional results.

Ironoically perhaps the dean of my university (as a whole) doesn't even have a Phd.

The deans and heads should also have good advisors around them (i.e. other professors) so things may not be that bad.

 

[pivoxa15]

But one of the problems is that you can't get this far by doing poorly in math courses. If you fail all your math classes, you won't get a Bachelor's, to say nothing of doing graduate work in mathematics. Certainly, there's usually opportunity for improvement in the academic world. For example, if you don't do so hot in your first two years of math, but then do very well in the second two years, then you should be all right. But at some point, you need to show consistent academic success.

Also, the situation you describe isn't all too realistic. People who don't understand basic math (by which I mean first and second year calculus) probably won't understand advanced math either.

Good point, at some stage one would have to show some results. What I was trying to get at is that during your primary and junior, midddle secondary school years, you are quite innocent about things so if you do well in maths competitions, it tends to mean you are talented at it. This raw talent will stay with you and will be a big help later on, especially if you work hard later on, competing with somone also working hard but without your talent.

 

[arunma]

Good point, at some stage one would have to show some results. What I was trying to get at is that during your primary and junior, midddle secondary school years, you are quite innocent about things so if you do well in maths competitions, it tends to mean you are talented at it. This raw talent will stay with you and will be a big help later on, especially if you work hard later on, competing with somone also working hard but without your talent.

Oh, you're still talking about these early years. That's an entirely different situation then. To be honest, I'm not so sure that talent shown in math in primary and secondary school will necessarily translate into success in college. For example, I know one person who was so advanced in math that he took calculus 1 in eighth grade. He got into Case Western and majored in engineering. Unfortunately he failed out after a semester. And among people I know who showed early talent in math, this isn't an isolated instance.

I can't really give a recipe for success is university-level mathematics. But it seems to me as though performance in primary and secondary school doesn't matter all that much.

 

[^_^physicist]

Mathematics at the "non-college" level is primiarly laying down basic manipulation methods. You can have a hard time with these; heck, I still make mistakes with these from time to time. The important thing about the "non-college" level is to learn where to find your mistakes.

In mathematics, there may or may not be a "reality" check to preform, so learning how to look for mistakes is an important feature. Additionally, being advanced in "non-college" will give you only two advantages:

1) You will have the freshman and (in some cases) softmore level mathematics courses under your thumb, as you will have had either some work with the material, or you learned how to study mathematics quickly.

2) It gives you extra time to work on understanding the material very well, because time requirements are different.

--------

Speaking for myself, I was quite the apt math student at the primary and secondary levels, hell I was very advanced for my reigion (granted I wasn't taking calculus in 8th grade mind you), and for myself when I entered college my prowess in math stayed with me. As for my friend, who went to a different university, who was in the same math situation as I was in secondary schooling (I would claim he was much better at it than I), isn't doing quite as well; he is still in lower division classes, and to my knowledge still avoids "proof" classes.

 

[mathwonk]

in my experience, being unusually bright and creative is actually less predictive of long term success, than is moderate ability and great persistence.

Of course great ability and great persistence is tops. But ability and weak stamina, is less helpful to success in the long run than moderate ability and strong persistence.

 

[pivoxa15]

in my experience, being unusually bright and creative is actually less predictive of long term success, than is moderate ability and great persistence.

Of course great ability and great persistence is tops. But ability and weak stamina, is less helpful to success in the long run than moderate ability and strong persistence.

Wow that is encouraging. I take it that great ability and great perssitence are the fields medalists and top professors? Are there any field medalists who dosen't have great ability (i.e. did not show talent in primary school or junior high years) but obviously tremendous persistence? Actually the fields medal is only awarded to people under 40 years so there isn't many years for these type of people to persist so a huge disadvantage for peole less talented.

 

[arunma]

in my experience, being unusually bright and creative is actually less predictive of long term success, than is moderate ability and great persistence.

Of course great ability and great persistence is tops. But ability and weak stamina, is less helpful to success in the long run than moderate ability and strong persistence.

Heh, I've figured that out as well. Sure, intelligence helps. But ultimately, I've seen that people who work hard tend to be the most academically successful. The other way I've heard it is: the key to doing well in school is to apply glue to your chair, sit at your desk, and get to work.

 

[J77]

I'm with Poincaré:

It is by logic we prove, it is by intuition that we invent.

Logic, therefore, remains barren unless fertilised by intuition.

without the natural intution (or ability) and that people would do is repeat methods developed by others...

 

[mathwonk]

no I think fields medalists are tops in all measures. remember fields medals are given for work before age 40. so possibly fields medalists fall off afterwards, but they definitey show early promise.

 

[pivoxa15]

I'm with Poincaré: without the natural intution (or ability) and that people would do is repeat methods developed by others...

I've heard of this before but didn't understood it back then. Now after doing more maths and physics, I am starting to understand why he said it. A standard example is in pure maths where people usually have to state what needs to be proven than use logic to prove it. As a student, you are told what to prove but for researchers, one may have to make it up yourself called a conjecture. It would help a great deal if the conjectures are correct because it would mean the proof will exist. For people with bad intuitition, they will create bad conjectures which are wrong in the first place and the time spent looking for the proof is wasted. So there is another way where talent is a big help.

 

[pivoxa15]

no I think fields medalists are tops in all measures. remember fields medals are given for work before age 40. so possibly fields medalists fall off afterwards, but they definitey show early promise.

So the fields is a measure of talent in other words by getting it, be definition you are recognised as a talent in your field and will show results in the future if you continued.

Why don't they have a big award like a Nobel prize for any significant work in maths without age restrictions?

 

[pivoxa15]

Heh, I've figured that out as well. Sure, intelligence helps. But ultimately, I've seen that people who work hard tend to be the most academically successful. The other way I've heard it is: the key to doing well in school is to apply glue to your chair, sit at your desk, and get to work.

True, looking back, I didn't succeed in school because I didn't study hard enough. Although I didn't have the right mindset either or is it because of it.

 

[morphism]

So the fields is a measure of talent in other words by getting it, be definition you are recognised as a talent in your field and will show results in the future if you continued.

Why don't they have a big award like a Nobel prize for any significant work in maths without age restrictions?

They do. It's called the Abel prize.

 

[arunma]

Why don't they have a big award like a Nobel prize for any significant work in maths without age restrictions?

It is a bit funny that there are Nobel prizes for so many fields of study, but not mathematics, isn't it? I don't know how accurate this is, but there's a story that Alfred Nobel excluded mathematicians from winning his prize because a mathematican once stole his woman.

 

[Tiger99]

But one of the problems is that you can't get this far by doing poorly in math courses. If you fail all your math classes, you won't get a Bachelor's, to say nothing of doing graduate work in mathematics. Certainly, there's usually opportunity for improvement in the academic world. For example, if you don't do so hot in your first two years of math, but then do very well in the second two years, then you should be all right. But at some point, you need to show consistent academic success.

Also, the situation you describe isn't all too realistic. People who don't understand basic math (by which I mean first and second year calculus) probably won't understand advanced math either.

There's perhaps a big gap between showing mathematical talent and failing mathematics courses. I share the concerns of the OP. I've always worried that perhaps because I didn't show talent at some stage I shouldn't be doing mathematics.

But also, I got fairly good results and I've never actually failed a test. I worry because there's always been people getting better results. I can understand the material, but I never (or atleast very rarely) got 100%. And I didn't even know maths olympiads existed until I started university. Talent is difficult to define. I don't feel like I have much, but getting a maths degree was not a problem. Getting a PhD wasn't a problem. The next step might be. I don't know the answer to the original question.

 

[tgt]

There's perhaps a big gap between showing mathematical talent and failing mathematics courses. I share the concerns of the OP. I've always worried that perhaps because I didn't show talent at some stage I shouldn't be doing mathematics.

But also, I got fairly good results and I've never actually failed a test. I worry because there's always been people getting better results. I can understand the material, but I never (or atleast very rarely) got 100%. And I didn't even know maths olympiads existed until I started university. Talent is difficult to define. I don't feel like I have much, but getting a maths degree was not a problem. Getting a PhD wasn't a problem. The next step might be. I don't know the answer to the original question.

So you have a Phd in maths and is applying for postdoc? Which area of maths?

 

[future_phd]

I find that if you put enough time into anything you can and will get good at it. Different people require different amounts of time, but in general I think that those who aren't doing very good aren't putting in enough time.

If you truly have the passion and motivation to do something, you can do it.

On a side note, I think you will find that pure maths courses are ALOT different than high school maths. ALOT different. :P

 

[khemix]

Is it true in general that if someone who does not show any talent in maths during school (i.e. performs average in maths competitions and tests) will not succeed in pure maths research if that person chooses to do so? Hence that person is not likely to become a professor if he/she chooses to be a pure maths academic and will mostly be doing teaching duties? Hence for these people, a more applied subject involving maths will be better suited.

I am aware that hard work is most important but in the case of producing top quality pure maths published in repected journals, ability and talent is also an essential ingredient?

Given how difficult it is to find a pure math post, I would say some amount of talent is essential these days. Math competitions these days are very biased towards those with preparation. Back in the day, if you stood out, it was a great measure of potential as everyone had equal preperation. These days rich folk or ambitious parents groom children with books and better education, and these are usually the ones entering competitions. Usually (not always) the winners of Putnam are the kids that studied insane amounts of hours for the test, and used a lot of prep books. That I fear is not measuring potential.

It depends also on why you perform poorly on tests. Is it because you study the night before? Or are you genuinely struggling with the material. If its the latter, you should realistically reconsider a math career as struggling in algebra is a very strong predictor of failure in math. At the same time don't let easy courses give you a false sense of security. Take me for instance. I smoked calc in college with flying colors. I mean minimal work and perfect understanding. Then I took a real math course in analysis. Worked harder than my class and pulled a C. 20% of the class got As. Some of the ones I spoke with even did minimal work. To me, that clearly demonstrated I lacked any math talent and that they at least had more potential. Why bother competing? Also, you'll see many people here saying they got As despite not showing any early signs of math potential. You should consider only two things: 1) You cannot confirm if they are telling the truth and 2) That an A in a less prestigious school is not an A at a more prestigious school. My advice is to speak with people who are successful mathematicians like professors and ask them what they think. The only one I know of on these boards is mathwonk.

[none of what i said should be takent as factual information. the information contained is based on personal experiences, anecdotal evidence, and college discussion]