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Notes -
I think it's still open to debate whether, in the absence of subsidized pure math research, we'd get the same mathematical advancements "never", "much later", "as soon as we need them", or "practically just as soon".
The fact that everybody thinks of (even their own!) pure math as "useless", right up until it turns out to be the foundation for quantum physics or something, is perhaps the best evidence for "never". I got my PhD in Applied Math (unspoken motto: do you want respect, or do you want job offers?), and it feels almost criminal when you hear about a mathematician coming up with an abstract toy only for someone more focused on science and engineering to come along generations later and say, "whoa, that solves my problem; yoink!"
As evidence for "as soon as we need them": the applied mathematicians haven't been just swiping everything; if you don't find something that solves your problem off-the-shelf, you take what you have and you expand it and tweak it and invent more of it until you do, and in the end you're still proving new theorems, just motivated by "this is how I can guarantee when my new algorithm will converge" rather than "theorems are fun!"
As evidence for "much later": the trouble with "do you want job offers" is that some job offers let you publish more than others, and if you're not getting subsidized via something like academic grants or civilian national lab research, it's downhill from there. Math is in part a cooperative team sport, and it doesn't work as well when you want to score in the "free advancement of human knowledge" basket but you're lucky if you get to shoot for "patent" rather than "trade secret" or "national security" instead.
And as evidence for "practically just as soon", I refer back to "theorems are fun!" There are some people who you can shunt off to a job as a patent clerk and it still won't stop them from playing with tensor calculus; if these are the sort who make the critical-path advances then we still get the advances.
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