February 18, 2023•329 words
Yesterday I met with one of my PhD students, who has recently started. I had set the student a preliminary toy problem to solve to help them get up to speed with the relevant topics for their project. I like using this approach for new students as it gives them something tangible to focus on beyond the nebulous literature review and piles of reading. The problem is one that I — along with some members of our group — had solved before, so I knew what the solution should look like.
However, when the student presented their solution to me and the second supervisor, it looked nothing like what I was expecting. It also had certain characteristics that meant that I knew the solution must be incorrect (this is one of the advantages of working on physical problems). Of course, this was not unexpected — as I like to tell my undergraduate students: 99% of maths is learning to identify and correct your mistakes. So, we set about doing what we usually do in such circumstances: working through the solution and performing some sanity checks at key points.
The problem was, none of us could identify the error. We spent almost an hour combing through the solution and the associated code, but were unable to find any material mistakes. This was, to put it lightly, disconcerting. This was a problem that I had solved before. I knew what the solution should be — at least in principle. I had built a physical simulation to check my solution and everything matched up beautifully. The problem was — this wasn’t it.
So, I will be spending the next few days digging through my old notes (hopefully I still have them) and trying to locate my old codes. Wish me luck 🤞
Day nine of one hundred.
This post is part of my #100Days writing challenge, in which I have challenged myself to write for 10-20 minutes for 100 consecutive days.