I'm working on a project in malaria genetics this summer, and I was shocked to find out that the entire analysis toolkit is entirely based on math and statistics (and some non-trivial stuff too, e.g. hidden Markov models to predict CNV). Genotype likelihoods throw an extra wrench into the process, since even basic stuff like predicting allele frequencies requires a maximum likelihood estimator instead of simple counting. This whole area was quite eye-opening, and I'm still amazed that reading billions of base-pairs in DNA sequencing reliably works.

Also gotta shout out to these incredible molecular animations by WEHI: https://www.youtube.com/watch?v=7Hk9jct2ozY