Author Archives: apgoucher

Firstly, the bounded gaps between primes project has made a considerable amount of progress since the value of H = 285278. The latest result has the following parameters: Tables of admissible k-tuples had already been precomputed, so Terence Tao was … Continue reading →

In an earlier post, I briefly mentioned the idea of repeatedly iterating the Aut operator (a function which takes an abstract group as its input and outputs the automorphism group) and observing the behaviour. There have been papers on the transfinite version … Continue reading →

Part IA of the Mathematical Tripos is marked in a rather interesting way. A naïve computation of the maximum score is 1120, although it is (in principle) possible to achieve absolutely any score (it need not even be a real … Continue reading →

One of the more familiar examples of fractal curves is the Koch snowflake. It is a closed curve of infinite length and Hausdorff dimension log(4)/log(3), homeomorphic to the unit circle. It bounds a region which, when combined in two different sizes, … Continue reading →

Given two identical circles lying in parallel planes with a common axis of symmetry, what is the minimal surface that connects them? Initially, one might suppose that it is a cylinder (blue in the diagram below). However, we can quickly … Continue reading →

After Zhang established the result that there are infinitely many pairs of primes separated by at most 70000000, there has been a massively collaborative effort to reduce this bound. The efforts are concentrated on developing methods to strengthen each of three … Continue reading →

In 1966, Norman Johnson completely classified all of the strictly convex polyhedra with regular polygonal faces. It is a remarkable fact, but not too difficult to prove, that there are precisely two infinite families (the prisms and antiprisms), together with a large … Continue reading →