Tools of the trade
It's winter break, so here's a short post. I am trying to spend some time doing new non-math things. The other day I was trying to help out with a fence repair. If you have spent time with me, you'd likely think that I would not know how to help someone repair a fence - if you thought that, you are indeed correct. I was not particularly helpful, but while I was embarrassing myself not knowing how to use a hammer, I did gain some insight into the mathematical process, which I wanted to mention here. In low-dimensional topology, as I hope to convey in this blog, it is very beneficial to have a wide range of tricks and tools. This includes knowing topological tools (e.g. the Montesinos trick or Kirby calculus), invariants (e.g. gauge theory, Khovanov homology), but also perspectives and connections from other fields (e.g. viewing torus knots as links of singularities of algebraic curves). However, knowing that hammers exist is not the same as being able ...