The Riemann–Roch theorem

The Riemann–Roch theorem

April 23, 2018 Off By Alex Arnz

A lot of years ago, I was a Teacher. A High School teacher. My subjects were: Physics, Chemistry, Math and, in some point for a short time, Technical Drawing.

It was ever a lot of fun. I have had a very nice relationship with my students, ever based on respect, but very friendly. In the morning class, I was just some years older than the average of them. In the evening class, most of my students, were older than me.

I could not say witch one was better. Morning classes were full of young people that simply didn’t put a lot of effort in learning. Evening classes were full of older students, workers, that want to give a push in their education, to got a little advance in career. Or at least, to have the hope to.

It was the second or third year of my sadly too short experience as Teacher. At the beginning of the School Year, the parents of a young girl, came in, and the first words I listened were: “Don’t give to much effort in your teaching to our daughter, it’s unuseful; she never had understand absolutely nothing in Math. Don’t waste your time”. I was little shocked, and I was not able to counter they advise.

I said to myself: let’s try.

In the first weeks I really understood what the parents told me. Math, for her, was something completely out of her mind. Completely clueless about anything more than easy arithmetic. I can suppose that she had no idea on why we put some letters, in the middle of the numbers, when we made expressions.

I said to myself: i have to.

So, days and weeks after, at least she recognised the letters, the variables, the data, the incognitos. Also in Geometry her results became better and she was able to make the drawings, to set the data and to understand what she had to find. The final search of result was much harder, but I saw effort and not desperation.

Maybe two months later, suddenly she said to me: “It’s funny, it looks easy this way”. Her class test was very neat, complete, without errors. She still had some difficulties to find the right way to get the result, but she didn’t surrender and she ever hit the target.

The day after, the parents came in: “we said to help her with result, to be a little more easy, not to overestimate her and to give votes she doesn’t deserve”. “Don’t worry, I’m valuing her for what she do. No gifts”. “Impossible” replied the father “she is too dumb to understand Math”!

After the test, she asked me: “can you please help me just a little more, maybe after the school time?”. I couldn’t give a negative answer. It was a real heart warming request: she really wanted to get rid of all her problems, with Math.

It was not a long effort. Short time after she became independent and fast to resolve also the hardest problem I assigned her. She never more had problems with Algebra, Geometry and in the years after, also with Calculus.

Some years after, I received a phone call, she wanted invite me on the discussion of her final thesis on the University. Something about the Riemann–Roch theorem.