Author Archives: Oscar Cunningham

Consider this $9\times 9\times 9$ grid, in which some cubes have been shaded. It can be represented in two dimensions by viewing it from one side and using numbers from $1$ to $9$ to give the location of each cube … Continue reading →

The most recent of Matt Parker’s Maths Puzzles was the unique distancing problem: For which $n\in\mathbb N$ is it possible to place $n$ counters on an $n\times n$ square grid so that there’s a different distance between each pair of … Continue reading →

There are various ways that we can multiply vectors. We can multiply a vector by a scalar to get another vector: $w=\lambda v$. We can multiply a vector by a linear map to get another vector: $w=\alpha v$. We can … Continue reading →

In the last post, I talked about Monads on Monoids. We defined these by turning each monoid into a category (its delooping), and then looking at monads on this category. This data could then be reexpressed in terms of the … Continue reading →

This post is inspired by a couple of posts on math.stackexchange.com asking what a ‘monad on a monoid’ is. In category theory there are a couple of especially simple kinds of category. For any partial order we can put a … Continue reading →