Where high-school mathematics was analogous to learning to form letters with a pencil, undergraduate BSc mathematics is analogous to learning to form words and short sentences.

By the end of your BSc in the analogy, you can look at a sentence and recognise at least what sort of genre it might be part of, and you can write down many of the most common words as well as a number of rehearsed useful sentences.

An MSc is like reading some examples of long sentences and short paragraphs, and being shown some long paragraphs or even chapters of books (which you have no hope of understanding, but you try, and the experience is salutary). If you're lucky, you did a research project in which you perhaps rewrote a certain very specific short paragraph in your own words.

The job of a research mathematician is analogously then to read and write books.

> If you're lucky, you did a research project in which you perhaps rewrote a certain very specific short paragraph in your own words.

Well stated. this pretty accurately characterises my experience of undergraduate studies & an honours year in mathematics

This is beautiful. Thank you.

I've also got an MSc in mathematics, I and feel that that was barely enough time to just start scratching the surface.

Trust me, an MS in math doesn't even get you to the fun part. :)

Haha not at all. My MSc project was about splitting graphs into other types of graphs and some generalizations of graphs into hypergraphs. I don't even consider myself an expert on graphs, let alone number theory.

Mathematics is this beautiful and terrifying field where, much like swimming in the Ocean, the further into it you get, the deeper and infinitely more vast it becomes. Now consider that most people can only really swim in one direction at once and this Ocean goes off in all directions.