“In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life.”
-Michael Atiyah

I finally finished my week long class on the ideas behind Galois’ proof of why a quintic cannot be solved using radicals. As if mirroring my inner self the ground is laden with snow today and there is no wind, a quiet calm pervades the city with a piercing whiteness that but absorbs all your thoughts and leaves you cleaner and in peace with your inner self, like a beautiful symphony fading into nothingness.

Galois theory is a beautiful story and representative of a lot of mathematics in general, and historically established the foundations of modern abstract algebra. Perhaps the most beautiful aspect of Galois’ work is the connection it establishes between two seemingly distinct structures of mathematics, groups and fields. Today we know of several such connections, called Galois correspondences, each stunningly remarkable and mysterious, that act as bridges connecting different islands of mathematics and unifying the gigantic landscape. Or perhaps they’re like those oddly shaped mirrors which reveal how two worlds are but distorted versions of each other, none more real than the other.

I was pleasantly surprised by how much my students got interested in the course, and the subject in general. Having taught Calculus etc. for most of my semesters at Hopkins I’d gotten accustomed to math courses being an ordeal, both for students and instructors, so this came as a pleasant surprise.

One thing that went well for me was the length of the course. I think in today’s age, whether good or bad, long courses are bound to fail. Why would you spend so many hours of your life stuck in a classroom when you can learn the same thing by watching youtube videos in the comfort of your room?

The second thing that helped a lot was the subject matter itself, you need to be a really thick individual to not be intrigued by Galois theory. You might not understand it in the end, but that’s a different story. We should stop teaching the standard shitty courses about integrals and derivatives and instead teach the beautiful aspects of mathematics.

The third thing was the format of the course. It was an IBL course which meant that I did not lecture. Not that I’m bad at lecturing, but as a student I NEVER learnt anything from my lectures, for me attending lectures was a way to get some sleep that I find hard to acquire otherwise.

Finally, I like to be professional about teaching. I used to think that I do not care about my students, but I think I do in an abstract way. I care that they learn and enjoy the subject but that’s about the extent of it. During class I am neither extra nice to them nor mean to them, many students can’t digest this but those who do are the ones who end up learning the subject well.

I’ve been experimenting with teaching constantly for almost a year now and it’s been quite an adventure. But now finally I’m done with all my teaching and am free for quite some time. I’m helping to organize the academics for Mathcamp this year but other than that I’m back to full-time research.

To infinity and beyond.

Edit: Oh I forgot to mention, I had really awesome students.