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I am just curious about this. Please don't include anything about programming.

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Since this is a site filled with mathematitians, I advise you to post the same question on a more AI-oriented site. They will know better what parts of math they use. However, I imagine that logic must be quite vital, but also that statistics must be important, at least in the machine-learning parts of AI,. –  5xum May 12 at 7:22
    
@5xum Thanks for the advice. I did find a tread discussing this topic There are some pretty good answers on there too: cstheory.stackexchange.com –  Skull-Face May 12 at 8:37

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Artificial intelligence requires extensive use of decision logic. The gateway to this type of logic is Turing machine analysis and recursive/primitive recursive functions. In other words, it really involves the mathematics of the relationship between computability and logic. Additionally, AI requires statistics (used for decision-making and testing probabilities associated with decision-making, i.e., hypothesis testing) and the mathematics required for engineering.

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We have quite a lot of A.I. on university -- probably because I picked specialization called Artificial Intelligence and Software Engineering. Most of methods that were presented used a lot of optimization e.g. for learning neutral networks. Analysis and linear algebra also played crucial roles. We didn't use much beside that but professionals claim that language of A.I. is statistics but we haven't use it extensively.

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So Analysis? That's interesting. Probably Abstract Algebra too? –  Skull-Face May 12 at 8:19

To do computer vision which is a branch of AI you essentially need to understand the unit quaternions, or the related Lie group SO(3). These are mathematical topics par excellence.

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