I studied mathematics for almost eight years, from undergraduate to PhD. I have a complicated relationship with the subject, which is extraordinarily deep and beautiful, but also requires a type of thinking that can be isolating and impersonal.
Links and resources #
- Fantastic essay by V.I. Arnold in which he describes his visceral hatred for the highly abstract axiomatic approach favoured by French mathematicians in the mid-century and preference for intuition- and example-based exposition of mathematics. There are a lot of fantastic examples in the essay of unusual explanations of common mathematical phenomenae, including the classification of algebraic curves, which he includes as a throwaway line and is explained very eloqently here.
- Continuing the theme of Arnold, this is a brilliant list of 100 mathematics problems that he thinks a decent mathematics student should be able to solve. Not sure how many of them I would be able to solve but definitely something to look at one day. Reminds me a bit of (a much more challenging version of) Coroneos’ 100 integrals from my Extension 2 Mathematics studies in high school.
- Giles Gardam, a friend from my University days and a first-rate mathematician, finding a counterexample to a decades-old conjecture about groups.
- A beautiful series of photographs of different mathematicians’ chalkboards, something I always found very aesthetically pleasing and that I worry is on the way out. Hate whiteboards.
- V.I. Arnold again with a series of 77 problems that he thinks are suitable for children aged 5 to 15. Most of them are fiendishly hard.
- Lo Meduyak, a Hebrew maths blog.
- Terry Tao’s blog.
- A really interesting project manifesto for Timothy Gower’s project on understanding how proving things in mathematics is feasible.
- A great write-up of a first-principle proof by two New Orleans teenagers of Pythagoras which was previously thought not to be possible.
- A nice write-up on approximation theory.
- How to calculate cosine from first principles in C++.