Computability theory provides a bridge between "pure'' and "applied'' mathematics.
Considered as a chapter of modern mathematics it throws new light at certain of its
central problems (such as Kontsevich-Zagier periods conjecture), but also provides
quite unusual structural/categorical features which deserve further study.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/6477