How do I keep up with math prodigies, become a mathematician and what are good books to read?

Pre-College Issues Home Schooling and College
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<p>Hello, I am a high school sophomore (grade 10) in Canada and I am 16 years old (you could probably guess that). I want to become a mathematician and I am very interested in mathematics. However, I feel like the work I am putting into math is not comparable to match the talent of the math prodigies or hard working students with decent talent. I can try to buckle up and work on math but I can go up to max 3 hours a day. I come home at 4 from school and sleep at around 12. How do I increase my work load effectively and how can I match up with those math prodigies? </p>

<p>I feel like I wasted a lot of years when I was little not being exposed to mathematics at all. I started Kumon for math in grade 6 (I was 12 I think) and started pre-algebra (not the prodigy-level math you expect as you can see :D) and that's when I first learned math outside of school. I hear stories about 5~10 year old kids who started calculus already and that makes me feel very bad. I finished single variable calculus (Calculus I and II) when I was 14 so that made me feel bad that I was up to 9 years behind the smart kids. My IQ isn't very high either. It's around 130, no where near brilliant. I watched the entire MIT OCW for both single variable and multivariable calculus and I studied them through Schaum's Outlines so I am done the videos and the textbooks (as well as working out the problems in these texts) and I am finishing off Linear Algebra (of course, MIT Linear Algebra videos and Schaum's as well). I am okay with my progress but there are big problems for me because I cannot do math contests for the life of me. I get decent in Canadian Waterloo contests (I was top 100 for Fryer I took this year out of 20000+ but this is not a hard contest. And I got my name on their websites a couple of times before that: once for top 1~2 % which were multiple choice contests and others for top ~5% which were contests where you explain your solutions but not nearly as good as Fryer. Fryer, I think for me, was just noob's luck) but in actually hard contests like COMC (which a lot of smart dudes think is actually easy) I bomb them so hard it's not even funny. I finished Kumon and I am trying to study Analysis (Real & Complex), Differential Equations (Ordinary and hopefully Partial before I go off to a university; I want to go to U of Toronto and not a U.S. school because not only will they not accept me, the tuition is too much), Abstract Algebra (using the Harvard thingy) and hopefully get exposed to a little bit of Topology and Differential Geometry. (I studied probability and statistics already). I am also interested in physics (I suck at it though because my physics mark does not compare to my math mark. I am in pre-I.B program and we are doing grade 11 math in grade 10 for the actual I.B. years to go by easier and I got 100% for both grade 10 math and grade 11 math so far: don't jinx it please while I got 91% for physics). I am barely an average 90% student though because I suck at English and History. </p>

<p>The topic I'm most interested in however, is the foundations of mathematics (like set theory) and the history of mathematics. So practically the purpose of this long text/post was to find ways to buckle down and study a long period while matching the progress of actual math prodigies (or as much as I can because I lack their mathematical talent that is given to them as well as their hard work) and to see if you guys can suggest any great books (both casual books or textbooks) on mathematics (any topic, but foundations/history of mathematics especially) and suggest any online videos/lectures on any of the topics mentioned above (YouTube is preferred due to it being my favorite video engine). Thanks for reading my rant and give me some feedback on my work ethic (I can't say it with a straight face because I can only study 3 hours max) and my progress. I am following the "How to become a pure mathematician" guideline. You can google it easily. Thank you and have a nice day. </p>

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<p>Have you tried this site: <a href=“http://www.artofproblemsolving.com/”>http://www.artofproblemsolving.com/&lt;/a&gt; ?</p>

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<p>@fluffy2017 Thank you. I didn’t know they solutions as well as the problems archived. I’ll try some problems right now :)</p>

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<p>I’d suggest Khan Academy, really great curriculum and it’s wonderful for cramming. Also, just a note: there’s no age limit for success. There are novelists that didn’t start writing until they were already half-way through their lives; Descartes didn’t really take up philosophy until the end of his life, point is this: as long as you’re busting your hump to achieve something, it doesn’t matter when you do it.</p>

<p>Also – and this is just my personal observation, correct me if I’m wrong – but you seem to be struggling with the idea that other students have this ‘it factor’ that you feel you lack. Which could not be farther from the truth, you know what ‘prodigies’ have that you don’t? An ego-- that, and they already put their time in. You’re putting yours’ in now.</p>

<p>I can tell you personally, that the way schools and society at large tracks ‘genius’ is not an accurate reflection of potential. When I was very young – about third grade – I was told within the space of a year that I, one, was going to be put into a reading class for students with special needs and that my literacy was so below grade level that I’d need to be held back and, two, near the end of the year that I tested into my school’s gifted and talented program. Both of those decisions made by the school were framed as absolute evaluations of my self-worth; one said that I was special needs and the other said that I was ‘gifted’. Both were inaccurate, any student in my school, if subject to the same circumstances I was, would have tested ‘special needs’ and then, subsequently ‘gifted’.</p>

<p>But, to sum it up: No one is inherently better than you and don’t think that they are, because if one thing will sink you, it’s doing something that you don’t believe you can do. As hokey as this sounds, believing that you can do something affects your ability to do it.</p>

<p>EDIT : Just realized how old this post was-- after I posted a long-winded response to it. My suavity knows no bounds, it seems.</p>