Relatively old mathematics that is still relevant: Markov Chains.
It is about predictability of events based on the current state of affairs (and not past state of affairs). Lot’s of AI have been about Markov Chains for a long time: spam filters, text prediction while typing, search engine results, language recognition by letter-pairs, and many more.
A nice video about it is [Wayback/Archive] The Strange Math That Predicts (Almost) Anything – YouTube
Related are many foundations in information technology, of which Markov and Shannon are mentioned in the video:





