I understand that there are sometimes deep connections between seemingly unrelated fields of mathematics. However, are there examples of applications of really pure abstract mathematics in the fields of say, symplectic geometry or differential topology (or any other very abstract fields), that have come to impact the lives of a significant number of software engineers?
Most programmers (myself included) spend their days using IDEs building a new API in a CRUD app or implementing a new UI widget in a mobile app. I may be unimaginative but I have a hard time seeing modular forms, fiber bundles, or exact sequences making a breakthrough in my life and impacting my programming.
Most programmers (myself included) spend their days using IDEs building a new API in a CRUD app or implementing a new UI widget in a mobile app. I may be unimaginative but I have a hard time seeing modular forms, fiber bundles, or exact sequences making a breakthrough in my life and impacting my programming.