There is no argument that fundamental research (including, but not limited to pure mathematics) is a high-risk investment with a small chance of a large pay-off

There is no argument that fundamental research (including, but not limited to pure mathematics) is a high-risk investment with a small chance of a large pay-off. But, like most good, high-risk investments the potential pay-offs can be massive and, importantly, not always well-understood in advance. Would we have GPS without relativity which in turn depends on non-Euclidean geometry, initially considered a curiosity? What about public key encryption, built upon number theory, proudly described as "useless" by the pure mathematician G.W. Hardy? There are so many examples like these. Be careful of committing the fallacy in assuming that because a clear line of ideas can be traced back from the present day that finding that line was as easy as recounting it. Out of interest, what is your position of the spending on sport, the arts, and other cultural endeavours?