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I came here since I know this is the best place to ask a question.

I'm a first year student who changed his major to applied mathematics. In middle school I was a garbage math student, but I realized the importance of math in high school when I was introduced to amazing teachers who truly loved what they did. I put myself in tougher classes and eventually got to AP calculus. There was an error in my idea, I never really got a deep understanding of the stuff I was doing and was struggling since I didn't understand the basics and never really did practice problems.

This year I began to start over from scratch from pre-algebra working to pre-calculus. Even though I have already took Calculus.

I'm in a introduction to research class this semester and we are preforming a meta-analysis of some random topic and then presenting at the end of the semester. I'm really enjoying it, and I will definitely apply for more research as I progress through my undergraduate career. (Urge to Compute)

I know I'll probably never win a field's medal, but I'm really intimidated and humbled by the near perfect SAT math scores and Math Olympiad participants.

It's too late for me to have that, but the best quality I have is sticking with the concepts and problems until I can explain them to my dog. (Basically until I understand it)

I'm really sorry for the long post / soft question, I've just been thinking about this since 11th grade but never asked anyone about it.

Basically I'm just wondering if I'm wasting my time, and if there have been mathematicians that were in a similar situation. (Famous or not.)

Again, sorry for the soft question and thank you for taking the time to read this!

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You might check out the first paragraph in the body of Stepen Smale's wikipedia article--you may find it somewhat encouraging. – Bulberage Mar 5 '14 at 4:37
@Bulberage Wow! What an amazing story. I watched an interview because I was worried that maybe it was just because it was too easy for him, but turns out it was too much classes, not enough effort, and overconfidence! – user133188 Mar 5 '14 at 13:35
Most mathematicians neither win Fields Medals or similarly prestigious prizes nor expect to win such.… – BCLC Jun 5 '15 at 10:07
This does not imply, though, that only the “best” mathematicians should do mathematics; this is the common error of mistaking absolute advantage for comparative advantage. The number of interesting mathematical research areas and problems to work on is vast – far more than can be covered in detail just by the “best” mathematicians, and sometimes the set of tools or ideas that you have will find something that other good mathematicians have overlooked, especially given that even the greatest mathematicians still have weaknesses in some aspects of mathematical research. – BCLC Jun 5 '15 at 10:08
As long as you have education, interest, and a reasonable amount of talent, there will be some part of mathematics where you can make a solid and useful contribution.… – BCLC Jun 5 '15 at 10:08
up vote 8 down vote accepted

Let me tell you that it's not too late to enjoy the field of mathematics. I too went through a circuitous path of getting into mathematics. I was extremely lazy in high school, had mediocre SAT scores and had no idea what a math competition was. I was a business major for undergrad and studied finance. It wasn't until after I graduated that I made friends with a guy that had been a math major in his undergrad. He eventually convinced me to take the honors calculus series at a local community college and promised he'd help tutor me. I was fortunate, my teacher there was a PhD student at a local well known college and took a liking to me and became somewhat of a mentor. I was a little neurotic and became obsessed with math. I ended up quitting a full time job, moving back in with my parents and then taking classes at the local university (you could pay and take classes as a non-matriculated student). I did this for two years, taking only math classes and then eventually applied to their MS program and was accepted. I have since scored in the top 97% percentile of the GRE general math, and published one paper with another in progress. I'm going to take the Math subject exam in the Fall and apply to Phd programs.

So, will I ever be a math wizard... no. But do I love mathematics, yes. I share this with you so that you know, there are people out here that started even later than you and are happy they did.

I'm not sure where you are in your education, but working problems is one of the (if not the) best thing you can do to solidify your foundation. The book that made me want to become a mathematician:

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Thanks for the encouraging words! Last semester there was a point where I was obsessed with math, sneaking in on talks and conferences! I will definitely follow my passions! – user133188 Mar 6 '14 at 4:08

Don't know if this helps but if your aim is to enjoy mathematics, and if you are enjoying it, then that sounds like success to me!! Hang in there, you are not wasting your time.

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Thanks a lot! Sometimes I guess I just overthink too much sometimes! I care too much what other people think. :/ – user133188 Mar 5 '14 at 6:19
You are very right about you advice by the way! – user133188 Mar 5 '14 at 13:47

I can relate to your feeling of being intimidated by other people that seem so far ahead of you, and the sense that you might never be able to catch up. Piling on top of the natural, unprompted feelings of inadequacy, from time to time you will run into professors and/or other students who are into what I've heard called "mathismo"--deliberate effort to prove "I'm smarter than thou". Such things are a fact of life. It helps to put a name on it--"that's just mathismo, I'm going to ignore it"--because you can realize that focusing on this will get you nowhere and in fact will impede your progress.

You don't need to worry about whether you'll be able to prove important theorems or whatever. Not yet. You have only seen a tiny little bit of the field right now. There is so much you can do with math. One thing that sticks out to me, based on your description of yourself, is actuarial work. Great pay and high job satisfaction, and it really fits with your description of yourself as doggedly going through the basics until you understand it really well, etc.

But that's just one possibility. Math is a gigantically varied subject--"set of subjects" would be more appropriate. You are very likely to be able to find a niche that you enjoy. If you like what you are doing so far, I would say that you should keep doing it. Maybe something you end up doing will lead you in another direction eventually. That's not failure, that's just life. If you are really making sure you understand it as you go, you'll be able to use what you learn in math for the rest of your life even if you switch to another major.

My advice is "Onward!". Keep at it, and if it gets to the point where you just aren't enjoying it any more, do something else at that point. There's no point in worrying about the unknowable--you can't know right now what you're going to think about upper level math, because right now you probably haven't really seen anything like it. School unfortunately just doesn't give people a very clear idea of the vast scope and depth of what mathematics has to offer.

If this is what you think you want to do, don't let anything--whether it's an inadequacy in your past or a current deficient comparison to your peers--stop you. At the same time, be honest with yourself in realizing that you can't, at this point, really know where it's going to lead. Mathematics is an awesome universe with tremendous opportunities for exploration. It's a great place to be looking around and taking things in. Enjoy the journey.

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Thanks for taking the time to comment! You're definitely right about not worrying about the future yet. I still have to take the designated "intro to math classes" that are dubbed Calc III, Diff Eq, and Linear Algebra. Along with the first "real" math class, Introduction to Higher Mathematics. I did look into becoming an actuary a while back, definitely not my cup of tea. I did an internship in high school for career exploration. Thank you again for the advice! I'm going to do what I enjoy and not care what people think and just work hard to make my dream come true! – user133188 Mar 5 '14 at 13:45
I noted that @yug's comment (btw, that's the best answer here at present) referenced the book that made him want to become a mathematician. For me, that would be Joseph Gallian's abstract algebra text. – msouth Mar 6 '14 at 17:03

I think I'm in the exact same situation as you. Expect, when I was ~6 I'd love playing with numbers and stuff, just trying to figure out ways to add large numbers and eventually discovering some stuff I later learnt by myself. Come high school, I was total garbage at maths. Absolutely trash tier, until I started taking it seriously and realizing how important it is. From then on, and once I got a good teacher, I started to really like math but I was extremely far behind that it was so unmotivating spending hours everyday to try and do what others got in a couple of minutes, since I was trying to catch up. I am basically in 11th grade now, and I am certainly not as good at maths as I'd hope but I absolutely love doing it. I'm just not good at it, at all. I don't know why.

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What I am doing is basically starting over. I found some materials and I am watching college algebra on youtube and reading a text pdf I got off the internet. I'm also doing puzzles and other logic games, reading philosophy, and anything that will increase critical thinking. – user133188 Apr 2 '14 at 4:32

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