Could you give an example?
Statistics itself is a hypothesis driven methodology, so I fail to see how the application of statistics is not science. I also don't see how using technology to run experiments is not science, nor do I see how using advanced mathematics to make predictions about experimental results is not science.
Almost all "science" now is an example. From evolution to global warming to cigarettes causing cancer are examples.
Mathematics doesn't work because humans invented something so remarkable.. It works because all of reality obeys simple logic and the rules of nature. It matters very much why it words because language obeys no laws at all. Even grammar evolves over time. If you say "smoking" causes "cancer" then it is necessary to define "smoking" and "cancer" and to find the mechanism by which it operates which is obviously different for each individual and each instance of "smoking".
All we can really say is that there is a significant correlation between smoking and cancer and individuals are exposing themselves to this correlation by smoking tobacco.
But applying them in some instances is far less meaningful because terms are more open to interpretation.
"Technology" used for experimentation is only natural. I'm merely saying that a new rocket with new improvements is not science. More accurate measurement is not science. New things to measure is not science (in every instance).
We want to see improvements in the economy and technology as "science" but the reality is cosmology is struck in the 1920's and the other sciences are either based on assumption or taxonomies that haven't withstood knowledge shown by technological advances in most cases. We have a science that is more and more becoming bogged down in semantics, beliefs, and 19th century assumptions.
Here we are and we simply ignore age old beliefs that are falling by the wayside and underlie almost all of science.
That isn't the science I am familiar with. Hypotheses are hotly contested until there is enough evidence to support them.
Real theory is based on experiment. But we are still using outmoded and obsolete perspectives to build models and extrapolate new "knowledge".