About us

Hello! Welcome to my blog! 

What is on this blog

Anything that we (I or my guest contributors) deem nice mathematics! This includes (but isn't limited to) proofs of theorems that we find particularly nice (so-called "Book Proofs"), useful tricks, and overviews of areas where it is difficult to find a coherent account of the theory, why and how it arose, and where it is going. The last one is the sort of thing which one can learn much more easily by word of mouth than from reading hundreds and hundreds of pages of textbooks, which we feel deserves to be written down. It will also contain our attempts at pedagogy and exposition, especially when we write up accounts of things we are trying to learn. Our lofty ambition, which we will undoubtedly fall far short of, is to have a collection of all the mathematics we find nice (and we will do our best to justify why it's nice). 

This blog will often assume things that are 'standard'. While this is not strictly well-defined, the guiding principle is that anything covered in the Cambridge Mathematical Tripos, the syllabus of which is available online, is standard. Where we assume further material, we will (hopefully) signpost and point to where one might read up on the assumed knowledge.

Who is this blog for and how to use it

As you might be able to tell from the previous paragraphs, this blog is meant for people who are interested in mathematics beyond high school level. Some familiarity with basic concepts in abstract algebra, analysis, topology, geometry, and high school mathematics in general is required to appreciate the blog. We hope to cover a broad range of topics corresponding to our various tastes, which means that not everything here will be for everyone. We encourage you to click around and explore. Hopefully the tags are useful. As we try to provide alternate proofs of results, we hope that a good undergraduate student will be able to find material to supplement their course, and more mathematically mature audience members will be able to get a flavour of different fields from the material we present.

What's not on this blog

For olympiad/high school maths, we recommend this blog.

We will not comment on what constitutes good research practice, nor what constitutes 'good mathematics' in general (we mostly care about the aesthetics here, but that isn't the only thing that should be considered). On such matters, we defer to more senior mathematicians such as Terence Tao and Timothy Gowers, who have written extensively about these on their respective blogs (those blogs serve as inspiration for this one).

That's all we have to say about the general structure of the blog. Have fun exploring!