Taxonomy?!
Before the term "machine learning" was coined, it was "Statistical learning"; machine learning became prominent in the "learning systems" component of AI. Most machine learning techniques are - speaking in numerical analysis/methods terms - interpolations and extrapolations with a rarely known, yet too often imposed/assumed/accepted/shoved-down-the-throat pdf (probability distiribution function) or "the mighty pdf".
The author says" "Wherever you set the bar, I guarantee that you will find that the system you are calling AI is heavily dependent on machine learning, which only works if we have data mining, which relies heavily on statistics, which is fundamentally founded on maths."
Here is a counterexample from the times when the data was not so aplenty. Medical diagnosis systems of the 1970's or 1980's were rule-based, no machine learning - and they were AI, which began to have an impact as soon as computers were used according to the "definition" from the Association for the Advancement of Artifical Intelligence http://www.aaai.org/
There is no need to attempt to define AI so many times over. It is hard to give a definition of AI that would be accepted by everyone - so AAAI provides the standard - agree or not, let's use that one. Yes, there are people who think "AI is a small corner of machine learning" - but only after mastering, for example, the book by Hastie. Tibshirani, and Friedman "The Elements of Statistical Learning"
http://statweb.stanford.edu/~tibs/ElemStatLearn/printings/ESLII_print10.pdf should we speak about where machine learnig fits in regard to AI, math, life, Earth, Galaxy, etc
Fukoku Mutual Life Insurance has an AI system - because they likely use a statistical learnign/machine learning to exploit the data. If rules are provided for any possible scenario, it is TurboTax for insurance - and it is AI (TurboTax is an expert system). Imagine life w/o TurboTax, with everyone's tax done by a knwoledgeable person. Now we talk millions of jobs lost to AI! Since before the term AI was omnipresent.