Adventures in Education: An instant of revelation

In my last post, I discussed how strongly I wanted to understand abstract algebra. Today, I am getting closer.

Mathematics is a play. In this play, there is a character (appropriately named the characteristic) that seemed alien to me. Its definition was quite simple, but the character was mysterious. I knew what it did, but not how it worked or what it was capable of. But then, in an instant, I learned a side of the character previously hidden. As if in soliloquy, it divulged just enough information to give me a taste of it's ambitions and agendas. And then, the rest of the story began to make sense. Those mysterious theorems, those awkward propositions, and those questionable conclusions began to fit together in a cascade of connections. A grand mystery has been resolved, and I can still feel the afterglow of the euphoria in my rosy cheeks and my tingling fingers. It felt like the tipping point in a Sudoku solution, when the identification of a single entry immediately reveals all of the others.

This character reached out and handed me a key. It is not a key that opens the entire subject of abstract algebra, but it is a key to its front foyer. Finally, I could step inside and marvel at the intricate workings of the subject! I expected it to be complicated and detailed and expansive, much like a grand hall with gold leaf designs and high ceilings and fine Victorian architecture. Much to my surprise, it was simple, compact, and clean like a photo in an Ikea catalogue. Where I expected a grand cabinet of tools I found a small cupboard with a few multipurpose theorems. It is incredible that such a great set of perfect ideas can collapse easily into such a small yet robust framework of elegantly simple rules.

Today, I went to class and understood everything the prof said. I didn't find the minor error in his notes. I didn't ask the clever question about a strange definition. I couldn't repeat the lecture back to you. But I understood what he was talking about the entire time. Hallelujah!

Some weeks are good weeks and some weeks are bad weeks. This week is a good week.