Monthly Archives: June 2013

There are several items of news worth mentioning. Firstly, I have been informed that the current status of the ‘bounded gaps between primes’ effort has now reached H = 6966, which is impressively low for these sieve methods. According to … Continue reading →

The partition numbers (sequence A000041) count the number of distinct ways to partition n identical objects. For example, p(5) = 7, as there are seven distinct ways to partition 5 objects: This visualisation, where partitions are graphs whose connected components are … Continue reading →

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 →