Machine learning has its roots principally in mathematics so if I wanted to be not only an expert but an innovator in this area would I have to be a computer scientist or would I need to be a mathematician? I ask this, because I have found that most of the Turing Award winners are mathematicians. Therefore seems logical to think that the great advances in computer science including machine learning are produced by mathematicians not by computer scientists. Can anyone clarify this for me?
If you are good at math, it certainly helps. But you don't need to be a mathematician to make great contributions in computer science. Some important problems in computer science are of algorithmic nature and do not require deep mathematics. For example, in data mining, some very popular data mining algorithms explained in every data mining books such as K-Means, DBScan, Apriori do not have a very complicated math foundation. Another example is some great data structures such as a KD-tree for spatial point indexing do not require complicated mathematics. But of course, the more you learn, the better it is. Especially, math helps to express ideas more formally.