<p>hi all. sorry about delay -- was busy graduating.</p>
<p>first please stop with this nonsense :). if you looked at the book, you saw that there are numerous seniors much more accomplished and distinguished than i am. you should be asking people like po-ru loh and emily russell how they do what they do.</p>
<p>i've been extremely lucky. in high school i lived a few minutes away from princeton university, which was nice enough to let me take math and physics classes there as a high school student when i exhausted the high school classes. that put me a little ahead at caltech. it is a lot less intimidating to start at caltech if you have written proofs before, etc. so a lot of it was just a head start.</p>
<p>i worked hard on my classes because i was well aware from the start that in the top half of the caltech class, native talent matters much less than effort. even at caltech, where i would say the students are the most academically committed in the country, people just don't take initiative, on average, to know more than they really need to. so by doing that a little -- by reading math books over the summer and doing extra exercises and things like that -- i managed to know a little more and get a little farther. </p>
<p>talking to professors is a big deal. it gives you focus and a feeling of what true research is like and where you should be aiming. good relationships with profs won't get you any success if you don't also excel at your work, but the relationships can make the work a lot more meaningful for you and can make you more motivated. also it does not hurt to be more than just a name on a paper when it comes time to decide about academic honors etc.</p>
<p>i worked pretty hard, but not because i am particularly disciplined. instead, to motivate me, i tried to keep alive my original childish passion for math from high school and my desire to someday do something "important" and intellectually deep and meaningful. it's a lot easier to put in lots of time struggling against an annoying theorem if there is some bigger aim to it than a diploma.</p>
<p>finally, i tended to aim high. evariste galois invented abstract algebra before he turned 21. john milnor solved a big open problem on the total curvature of knots as a freshman at princeton (and got a publication in the most prestigious mathematical journal). these people were extraordinary, but they are made of the same meat and dna as you and me. we can't all accomplish what they did, but we can hope to do a little better than just finishing homework on time. </p>
<p>those are my scattered thoughts.... :)</p>