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Incompetent pure maths researcher?

  • Thread starter pivoxa15
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  • #26
mathwonk
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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.
 
  • #27
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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.
 
  • #28
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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?
 
  • #29
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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.
 
  • #30
morphism
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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.
 
  • #31
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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.
 
  • #32
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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.
 
  • #33
tgt
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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?
 
  • #34
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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
 
  • #35
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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]
 
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  • #36
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I failed algebra twice in high school and am now pursuing a mathematics degree. Go figure.

Actually the reason was because I didn't know I could achieve stellar mathematical understanding with my visual-spatial intelligence -- my high school teachers always called me stupid and never had any patience with the fact that I'd sketch abstract landscapes instead of solving polynomial equations.
 
  • #37
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Talent is upfront. Show me what you've done and why it is unique and or important. If you can't produce interesting mathematics, past history and precociousness means nothing. You're judged by what you do.
 

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