Modern science has really two roots. The first is an empirical or experiential view of the whole of nature, thought to come from Francis Bacon (though it can easily be traced to an earlier Roger Bacon [1214-1294] and others of the scholastics). The second, and more significant, is the “rational” or mathematical view of the same natural world we have already alluded to. Both these sources are evident in the modern “scientific method.” 

This is not a simple deductive or inductive method, but a combination of both. The tension between these two makes it difficult for the modern mind to decide whether modern science is purely factually/empirically or hypothetically/mathematically based.