I apologize in the event that you should find this question off topic. Please feel free to delete it if that is the case.
Years ago, I studied undergrad mathematics at university. The understanding passed to us then was that the past centuries have had several phases of "programs", large-scale efforts that defined mathematical research of the time, e.g.
- 18th century: Development of analysis
- 19th century (first half): Foundations of modern algebra (separation of set and structure)
- 19th century (second half) - ca. 1930: Rigorous foundations of mathematics (logics and set theory), further development of analysis
- ca. 1920 - ca. 1970: Formalization of computation, metamathematics
Is there a "big picture" effort going on in mathematics at the moment also? Or is everything happening at the same time? I'd really like to know that, but not being in math myself, I thought I should just ask the pros directly.