Contrary to Betteridge's law, yes we need polymaths. Asimov wrote a story along these lines. Already there are cases of esoteric knowledge in one field being applicable to another. I recall, though cannot find the reference, of a pure maths technique being applied to quantum physics which only happened by the fortunate meeting of two researchers.
Heck, it already happens entirely inside of a field: probably once a year and at least once a decade, there's a major paper in math or physics that is basically "applying standard technique in subfield A to subfield B".
Indeed, one of my professors in grad school defined a research contribution as adding an edge in a metaphorical bipartite graph to link formerly disparate subfields.
The pure maths technique you are thinking about is the Monster group [1]. Sadly, I don't recall the names of the two researchers involved in the chance meeting.
