This might be useful in relatively young fields (e.g. information theory) , or ones where the topic itself thwarts any serious tower-building (e.g. archaeology), but in general I think this is likely to be misleading. Important problems often require substantial background to recognize as important, or even as problems.
A list of applications of sophisticated math to physics which is aimed at laymen is going to end up looking a lot like a list of applications of sophisticated math to astrophysics, even though condensed matter is an order of magnitude larger, and larger for sensible reasons. Understanding topological insulators (which could plausibly lead to, among other things, practical quantum computers) is more important than understanding fast radio bursts (which are almost certainly not alien transmissions). But a “fast radio burst” is literally just a burst of radio waves that appeared and disappeared really fast. A neutron star is a star made of neutrons. An exoplanet is a planet that’s exo. A topological insulator is … an insulator that’s topological? Well, A: no, not really, and B: now explain what topological means.
Once people can ask well-posed questions, providing further motivation is easy. It’s getting them to that point that’s hard.
This might be useful in relatively young fields (e.g. information theory) , or ones where the topic itself thwarts any serious tower-building (e.g. archaeology), but in general I think this is likely to be misleading. Important problems often require substantial background to recognize as important, or even as problems.
A list of applications of sophisticated math to physics which is aimed at laymen is going to end up looking a lot like a list of applications of sophisticated math to astrophysics, even though condensed matter is an order of magnitude larger, and larger for sensible reasons. Understanding topological insulators (which could plausibly lead to, among other things, practical quantum computers) is more important than understanding fast radio bursts (which are almost certainly not alien transmissions). But a “fast radio burst” is literally just a burst of radio waves that appeared and disappeared really fast. A neutron star is a star made of neutrons. An exoplanet is a planet that’s exo. A topological insulator is … an insulator that’s topological? Well, A: no, not really, and B: now explain what topological means.
Once people can ask well-posed questions, providing further motivation is easy. It’s getting them to that point that’s hard.