The I, Mathematician section of my website is my writings on being a Mathematician. The articles here will contain more personal opinion than in the Counting on my Fingers section and will be more about my approach to Mathematics. Some of the articles in the Counting on my Fingers section should be in this section. To avoid dead links, I'm not going to change their URLs but I'll list them here as well.

Part of being a Mathematician is doing Mathematics, and part of doing Mathematics is being a Mathematician, so there will inevitably be a significant intersection between these two parts of my website. Putting an article here is my way of signalling that it is more about my approach and less about the objective Mathematics.

I'll see how it evolves.

1. Story of a Proof.

   Many years ago I stumbled on a neat result about determinants of matrices formed from Pascal's triangle. It was a few years after that when I finally proved it, in part because I didn't originally need a proof. This article attempts to explain how I went from something I'd observed to something I'd proved.

2. Refuge – a poem.

   There was a poetry competition at my school, and staff are allowed to enter (not to the actual competition, mind). The title was "refuge". Took me a bit of time to figure out an angle.

3. An Average Opinion.

   Statistics is a crucial part of mathematics in school because of its relevance to everyday life. Like so many areas of mathematics various aspects of it provoke differences of opinion. However, unlike so many areas of mathematics, the immediate relevance of statistics means that some of these differences actually matter.

4. From Clocks to Categories

   Back in 2020, I gave an online talk called From Clocks to Categories as part of the Talk Math With Your Friends virtual colloquium. The intent was to illustrate how Category Theory can be seen even in so-called "school mathematics".

   This is a write-up of some of that talk, focussing on the categories that I see arising naturally within school mathematics.

1 Older Articles

These are articles that I wrote before creating this section but which would now be classified as more about my approach to Mathematics than the Mathematics itself.

1. Euler's Identity.

   Euler's equation consistently tops the list of "most beautiful equation". I think that this is ill-deserved. This is my explanation as to why.

2. The Right Angle.

   This is my contribution over the semi-annual debate as to which angle deserves a symbol of its own. There can only be One True Right Angle.

3. Counting Fermat

   The author of the Math with Bad Drawings posted an interesting article about a combinatorial interpretation of Fermat's Last Theorem. It got me thinking. This is the result of those thoughts.

4. My Favourite Proof of Pythagoras' Theorem.

   There are many, many proofs of Pythagoras' Theorem and amongst them I've found one that I particularly like. It has ingredients that closely relate to what Pythagoras' Theorem is really about (how lengths behave in Euclidean Space), and extends to a proof of the cosine rule.

5. Similarity and Area

   This is a summary of my thinking about Pythagoras' Theorem and how it relates (or not) to the concept of area. It also details my attempts to find an area-based proof of the Intersecting Chords Theorem.

6. On the Nature of Proof (Original Version).

   I originally wrote this way back in 2011 for a course where students were required to prove results rigorously. I used it as the basis for this answer on Mathematics.SE, and so am reposting it here.

7. A Tale of Two Puzzles.

   There's something about mathematical puzzles that I find not quite to my liking. Two puzzles that recently came my way gave me the opportunity to try to figure out why that is.