Fight Functors with Fire

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Once during undergrad, my topology professor was trying to prepare the students for an exam. He was an interesting guy. His look and disposition were unusually relaxed, and his clothes looked more like those of a teenager on summer vacation those of a professor. Typical attire included shorts, flip flops, and a t-shirt referencing a cartoon from the 90's. Less than 30 years old, he was by far my youngest instructor. He often told stories of his own mathematical struggles in grad school, which always seemed to end with his adviser yelling at him. No one could fault his enthusiasm; his excitement about topology was too pure for this world. I always enjoyed his lectures.

Needless to say, the students loved him.

To prepare for the upcoming exam, he'd collected some practice problems. Before diving in, he devoted a few precious minutes of lecture time to reading us a quote that he thought perfectly crystallized the way we should learn mathematics.

"Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?" - Paul Halmos

Welcome to Brantley Fights Functors, where I will chronicle some episodes in my fight against anything I try to learn on my own time. This could include neural networks, Galois groups, Pandas for Python, and forgetful functors. I believe in Halmos' strategy; the only way to truly learn these concepts is to step into the ring and fight them for yourself, tooth and nail, until they surrender themselves to your intuition.

Wish me luck.


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