I'll answer briefly now, with maybe more detail later. Do you mean science and humanities in universities and education, or attitudes across society in general?

Roughly speaking, the cracks started to form in mid to late 19th century, and the fissure was almost complete in the early 20th century. In an extremely famous lecture in 1959 that is always cited in the context of this question, C.P. Snow noted how wide the cultural gap had become.