This semester we did something different with the Freshman Seminar course. We did away with the 2nd midterm, and gave the class more time to work on their second paper. The first paper was just practice in writing math. This one was the real deal.
I dedicated three weeks of discussions sessions to these papers, and I emphasized the importance of choosing a topic that was a real challenge. I promised them that choosing something interesting meant that more work would feel like to work at all. I took them on field trips to the math library. Still, I had some concerns on whether or not that was the best use of their time. But then I started grading the papers…
…and they are brilliant. They are so much more than the formulaically correct work of a student motivated only to get an A. They are testaments to the true love for the process of understanding that has been the great joy of my own journey through math. They are brave explorations into abstract ideas. They expose deep connections between complex numbers and Euclidean geometry. They span 15 pages proving the heck out of concepts that, a few months ago, I would never have approved as a topic. They induct correctly (omg). They have taught me things I didn’t know.
I am holding in my hands incontrovertible evidence that the majority of this class have seen the incandescent heart of real, actual mathematics. Mathematics is not rote memorization of formulae without any explanation, but rather the precise and lyrical language needed to communicate the only things in this world that are true, beyond ethics, perspective and opinion. I am so, so proud of them. If my direction had any part in that accomplishment whatsoever, then every moment of this past semester has been worthwhile. My life up until now has been worthwhile.