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<p>I very much agree with you. I knew early on that mathematics was sort of my thing, but only in college did I really begin to love it in a special way, and participate in anything organized (like seminars). My only math activity, though, was reading math in my spare time. This is hardly meaningless, and actually let me make especially good use of some of my college years, because I somewhat knew what I was doing early. In other words, the main reason I was convinced I was passionate was that I read and fiddled for fun. </p>
<p>Maybe you’re sort of like this. I am not a Caltech student, and don’t know how Caltech would have viewed my own commitment to the subject I like, but something tells me that having organized activities helps. However, I wouldn’t try to force organized activities – that usually flops, and you waste time that you could’ve been doing something more meaningful with.</p>