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<p>I agree that having a passion for math and science is no guarantee of success at Caltech. What I mean to say was “admission to Caltech is very difficult”. I was not clear enough, I am not talking about success at Caltech but success in the admission process. I hope that clarifies what I wanted to say. A better wording would be If you cannot show that, admission to Caltech is very difficult.</p>
<p>From what I hear that the admissions committee looks at passion for science and math as an important component of admission requirement. Taking higher level math courses does show interest, but is that sufficient in itself. The OP has not provided any information on other science and math related activities.</p>