When asked about my subject of research ---something related to homological algebra--- by non-mathematicians, the following conversation usually takes place.
--- It would be too complicated to explain it in detail, but my research is about trying to find connections between objects from different branches of mathematics, so as to explain or perhaps compute one in terms of already known others.
--- What would be the application of this, if any?
--- We don't know it yet, but we are hopeful that these various connections and results lead to a deeper understanding of maths that allows a trickle-down effect to open new doors in reality.
An year ago I've got my PhD in Argentina and right now I'm a postdoc abroad. My country is going through a serious economic and social crisis and I can't help but thinking that any money sent to research on homological algebra is not being destined to much more urgent matters. I'd understand it if the research were about an industry-related subject, but... What I do is probably not going to help my country anytime soon. To conclude:
Why should a third world country invest in abstract mathematical research with no apparent connections to the industry?