You need a decent understanding of calculus (mid 1800s level, mulitvariate calculus), a more decent understanding of Linear Algebra (1950s ), information theory (1960s), and probability and statistics. With the last having shifted the most from the past due to more recent respect for bayesian methods. Note the years in parenthesis is not to say that nothing new has been used from those areas, more like if you pick up a book on that topic from that year you would be pretty well covered for the purposes of ML.
Worth having a vague idea of are stuff like PAC learning, topology and computational complexity stuff like Valiant's work on evolvability. If you are doing stuff related to genetic programming then category and type theory have riches to be plundered.
Or if you want to be more hardcore and are looking at very higher dimensional data and reductions on them you might look at algebraic geometry (in particular algebraic varieties) and group theory. So basically the answer to your question is as little or as much math as you want and or depending on the problem and your interests in trying different approaches than the typical toolkits of linear algebra and statistics.