I think the crucial thing is not so much demonstrating that there might be some use for some not-obviously useful math—I doubt there’s any way to do that usefully in the short run. An accurate answer can’t be known for any but the most obvious cases, and just making up something that sounds vaguely plausible is all too easy, especially if money is riding on the answer.
Instead, I recommend working on understanding the process by which uses are found for pure math, and, if it makes sense, cultivating that process.
Non-functional art quilting
Found while looking for the first link, and included for pretty
I think the crucial thing is not so much demonstrating that there might be some use for some not-obviously useful math—I doubt there’s any way to do that usefully in the short run. An accurate answer can’t be known for any but the most obvious cases, and just making up something that sounds vaguely plausible is all too easy, especially if money is riding on the answer.
Instead, I recommend working on understanding the process by which uses are found for pure math, and, if it makes sense, cultivating that process.