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hugo/content/posts/2018-09-20-mathematics-teaching.md

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+---
+lastmod: "2021-09-12T22:47:44.0000000+01:00"
+author: patrick
+categories:
+- hacker-news
+comments: true
+date: "2019-09-20T00:00:00Z"
+title: The stages of mathematics teaching (a note from Hacker News)
+summary: "A quick note from Hacker News about the various stages of learning and teaching in mathematics."
+---
+
+In response to [a linkpost](https://news.ycombinator.com/item?id=18034714) to [an article about the disputed nature of a proof of the ABC conjecture](https://www.quantamagazine.org/titans-of-mathematics-clash-over-epic-proof-of-abc-conjecture-20180920/), [user barbecue_sauce](https://news.ycombinator.com/user?id=barbecue_sauce) [commented with surprise](https://news.ycombinator.com/item?id=18035656):
+
+> You have an MSc in mathematics but don't consider yourself an expert?
+
+[I replied](https://news.ycombinator.com/item?id=18035956):
+
+> 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.