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June 5th, 2010, 08:48 PM   #1
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Career in Pure Mathematics

Hello everyone, I have some questions about a career in pure Mathematics as a researcher and professor at a university. What does it take to become a good mathematician researcher and professor? I am just in 10th grade and have just started about a week ago to love mathematics, the thing is I took two IQ exams and got 113 and 123. Does this mean I am not good enough for such a career ? I am willing to give my best effort on math practicing all day if I need to. Please can you tell me your expert opinion on my problem.
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June 6th, 2010, 01:10 AM   #2
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Re: Career in Pure Mathematics

There's this terribly mistaken and pervasive belief that to make it in math you need to "be really smart", and even, with students who are good at it growing up, that all it takes is being smart. There's also a mistaken belief that problem solving skills can't be taught.

Well. It's all lies, and don't listen to it. An above average IQ is plenty for math; Succeeding in math requires a lot of dedication, passion almost to the point of obsession (4am? Let's check out the math forums!), creative problem solving (yes, despite what you've likely seen so far, math is incredibly creative), and a strong dose of humility (There will be smarter people wherever you end up; there will be better mathematicians wherever you end up. And even if not-- math is sneakier than you are, and it's always an uphill battle).

As far as being a good professor-- teaching is a very difficult thing, but the ability to communicate well, say the same thing in multiple ways, and the ability to catch on when other people are confused, are 3 very useful tools. One good way to practice is, after learning something that's particularly difficult or abstract, try writing "lecture notes" for a 10-15 minute talk you could give someone (if someone said "show me the math you just learned"). Try to make them as clear (but concise!) as possible. This will help you to learn how to tie everything together in a clear manner, and will also help you to get a better grasp of the difficult concept.

Tastes can change a lot in the 6 years between 10th grade and graduating college, but if you want to try to get a better feel for the sort of math that's done at higher levels, look into an introduction to discrete mathematics, or a low level set theory book like Sets, Functions and Logic.

Also, I cannot emphasise enough how much easier your life will be in college if you work hard to get a really deep understanding of the algebra/trigonometry/precalc classes you're taking now.
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June 7th, 2010, 09:10 PM   #3
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Re: Career in Pure Mathematics

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Originally Posted by cknapp
There's this terribly mistaken and pervasive belief that to make it in math you need to "be really smart", and even, with students who are good at it growing up, that all it takes is being smart. There's also a mistaken belief that problem solving skills can't be taught.
I hate to take the common line, but I do think that doing math (on a research level) does take a high level of intelligence, more than just above average. (Sometimes I wonder if I would be cut out for it, if I chose to go in that direction.) But I do agree that it's not nearly enough - you need to work at it.
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June 7th, 2010, 11:58 PM   #4
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Re: Career in Pure Mathematics

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Originally Posted by CRGreathouse
I hate to take the common line, but I do think that doing math (on a research level) does take a high level of intelligence, more than just above average. (Sometimes I wonder if I would be cut out for it, if I chose to go in that direction.) But I do agree that it's not nearly enough - you need to work at it.
It does require a certain amount of intelligence, and perhaps "above average" is slightly naive of me, but everything I've seen shows that intelligence is overrated in math, and that problem-solving skills can be learned. More than intelligence, I think it requires a certain type of thought process; and the ability to ask the right types of questions. Again, "the right questions" are something that you learn over time. (Hey, there was a short exchange at a U of C algebraic topology seminar about a month ago, "What's the geometric realization of that?" -- "Oh, I wouldn't do that.")

Last edited by skipjack; July 30th, 2014 at 10:52 AM.
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June 23rd, 2014, 07:05 AM   #5
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Just work hard mate, you can achieve if you don't give up and ignore the naysayers or you'll start to doubt yourself. Good luck
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April 7th, 2016, 10:45 PM   #6
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Well for one thing that should be considered is the cost, so that depends on which country you are in.

In a lot of countries you will need to get to the point of receiving a phd before you can be even remotely considered for research positions, which are far less than the opportunities one would be presented if they had of chosen a degree that is in economic demand such as engineering and would complete it in half the time for the math phd.

If you are only of average intelligence then it will be even more difficult for you, how ever you will succeed as long as you are able to solve problems quickly in the exam time allowed.

Creativity is important in high level mathematics, and the reality is that once you get to that stage and you understand abstract concepts like the assignment of finite values to divergent series, and this is beyond the comprehension of the simpletons in a lot of math departments that have ignored that kind of ambiguity since they were taught a few suggested evaluations of the Grandis series by the university gardener.

And so that's where ill have to wrap this up and give you a decent amount of honesty, you really should consider giving up. I wish I did. I'm 32 and still living with my mother unfortunately I'm too obsessed to give up now, but in heinsight my life would be infinitely better without mathematics, people no longer know what that is anymore there is nothing to be capitalised upon in pure mathematics.
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April 7th, 2016, 11:47 PM   #7
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Originally Posted by Adam Ledger View Post
And so that's where ill have to wrap this up and give you a decent amount of honesty, you really should consider giving up. I wish I did. I'm 32 and still living with my mother unfortunately I'm too obsessed to give up now, but in heinsight my life would be infinitely better without mathematics, people no longer know what that is anymore there is nothing to be capitalised upon in pure mathematics.
I believe that life is all about balance, and to advise someone to 'give up' based on the fact that math has consumed your life due to your lack of a balanced lifestyle is a rather obscure piece of advice in my opinion...

Then again, this thread is over 5 years old, who knows what OP is up to now.
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May 27th, 2016, 01:16 AM   #8
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I support all the hard working suggestions but I think it's important to understand to find the people that have dedicated as much as they have and to build on their work.

Also realize that when you learn something you need to port it to your "native language".

People think in a certain way and they have a language that facilitates that.

Find your native language and find a way to bridge concepts to that language.

It can be based on physical intuition, a particular organization of concepts, things that you are good at (and understand well) and a variety of other things.

Mathematics is a language and one of the reasons many find it difficult is because they haven't bridged the concepts to something that gels with their intuition. Once the connection gets made it's a lot easier.

Don't look at mathematics in terms of symbols - it's a collection of well organized well connected ideas that have many forms and you will find that there are many ways to get this intuition - and some work better than others for certain kinds of people.

If you are curious, work really hard, and understand to look beyond the symbols (as well as to look at the symbols to put in context) it will no doubt be difficult but it will be a lot easier and you should have more success.
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May 31st, 2016, 05:16 AM   #9
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hello,
what is advance mathematics and research mathematics
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May 31st, 2016, 11:28 AM   #10
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f--- the internet seriously
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Last edited by skipjack; May 31st, 2016 at 12:04 PM.
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