It's true that people fall behind in math, but the bright side is that since knowledge isn't a physical structure, you can always go back and strengthen the fou

It's true that people fall behind in math, but the bright side is that since knowledge isn't a physical structure, you can always go back and strengthen the foundations later. Plenty of theories have been useful before mathematical foundations could be built for them. Newton and Leibniz developed calculus long before it could be given proper axiomatic foundations. If a theory turns out to be unsupportable, science abandons it and moves on, scavenging any useful ideas. Maybe knowledge is more like a web than a building that strictly has to be built from the bottom up.