While Pachter enumerates differences in culture and breakdowns in collaboration, I feel the root cause is individual social attitude. The two cultures differ because their self-selected members differ in personality. What drew me to study math was the department's attitude of anarchy and irreverence. Status didn't matter, funding didn't matter, appearance didn't matter, prerequisites didn't matter, you just needed two people and two pieces of chalk and a blackboard and an afternoon. By contrast biologists I've worked with have been acutely attuned to hierarchy and funding strategy and marketing and credit attribution - social maneuvering that would fall as flat in math departments[1] as "third cohomology group" falls flat on Nature's reviewers.

[1] in my limited experience of two math departments