What Defines a True Mathematician in Pure Mathematics?

[curious mind 111]

I've asked many... what does it mean to major in math (pure). I am a first year sophomore and still undecided about my major.I used to get full marks on math tests n high school, but how can I know if I'm able to be something in math. Anyone can learn how to do math, but few can actually make math...what characterizes a mathematician?
appreciate your help!

 

[GaryFowler]

I majored in math at the University of Alaska during the 1980's. At the time, however, I had no idea that I am autistic. Not being the common social butterfly, I also had no idea of what to expect from such a cirriculum. I did fine as long as I didn't have to prove anything, even though differential equations is considerably more difficult than calculus; we called it "difficult" equations. But as it was, I simply took it a day at a time without knowing what to expect the next day, or in the next class. Then in my senior year, the theory came, and I was completely turned off. They take away the skill that you have, and make you prove what you know, beginning with basic math. If you become a teacher, you have to be able to show students why one is greater than zero. You have to be able to show, on paper, why 1+1=2, and so on and so forth, right on through to the calculus theorems.

If you're on an engineering team that's building bridges, for example, you have to be able to show why the math is valid, and if not, then why not. It simply was not my cup of tea.

 

[Iso]

As a pure math major you'll be focusing on abstract mathematics that isn't done with applications in mind. Your classes will be entirely proof based. Typical courses for a pure mathematician would be real analysis, abstract algebra, topology, number theory and the like. It gets very hard to wrap your brain around some of the concepts and proofs

I believe the biggest factor that separates the best students from the others is simply motivation and hard work. Except for a handful of geniuses, math isn't easy for anyone. It takes long hours of concentrated mental effort to excel in pure math. Math is a lot like a sport where you have to constantly practice and refine your skills if you want to be great at it.

 

[mathwonk]

have you read any of my thread formerly called "who wants to be a mathematician"? it's all about "the love", as they used to say about the nba. i don't want to be negative but you are asking the wrong question. i.e. you are asking how you can tell whether or not you willl be a "success", whereas the real mathematicians just want to know how they can pursue what they love. If you love doing math you will find fulfillment there, regardless of the "success" you find. but don't give up yet. you may have the love and just not have the confidence.

 

[curious mind 111]

thank you all for your replies...mathwonk: yes I do LOVEEEE the abstract of Mathematics and how perfect it can be...I love the logic behind it. Yes I do think it is a matter of confidence, yet justified. a lot of my friends that were math geniuses, didn't score high on the first math course and said that u'll hate math after it. I don't want to hate math...I'll read your thread .

 

[johnnyTransform]

Many pure Math majors I know of who didn't perform "above average" with projects and/or research to show had some trouble finding work right out of school, which is an anecdote to consider. Pure math is incredibly abstract, but is a great basis for just about anything -- applied mathematics, engineering, programming, etc.. As they say, "you can teach the mathematician X, but you can't teach the X mathematics" -- where X is any other profession. You probably won't run into a subject with as much abstraction as pure math unless you end up studying Physics (and maybe not even then). All that being said, if you're all in with mathematics, don't worry about the job bit -- that will fall into place easily if the passion and hard work is there. Good luck!