Loren Booda
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In my 11th grade (1976) functions class, a classmate of mine - Dewey Allen - noticed a pattern with simple derivatives of a curve. Our teacher suggested that I, being his most accomplished student, try to prove the conjecture - and in a month, I did.
The proof helped me get into Yale, and years later I included it on my website (below, the "Booda Theorem"). It took me a few more years (~2005) to get around to giving Dewey credit for finding the pattern.