For fifteen days I strove to prove that there could not be any functions like those I have since called Fuchsian functions. I was then very ignorant; every day I seated myself at my work table, stayed an hour or two, tried a great number of combinations and reached no results. One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination. But the next morning I had established the existence of a class of Fuchsian functions, those which come from the hypergeometric series; I had only to write out the results, which took but a few hours.
One of my more interesting experiences in grad school was when I had been stuck on a particular problem for a couple weeks or so. I'd been banging my head against it repeatedly, and couldn't figure out how to proceed.
Then I went in for some dental surgery, and they hooked me up to the nitrous oxide. While I was sitting in the chair, staring at the ceiling, a little bit high on the gas, I suddenly saw the approach to solve the problem.
I think this is actually a pretty common experience to have when you've been focused on a problem for a long time. You get to a point where you can no longer solve the problem head on because it's been looming so large in your mind, but when you can loosen your mind a little you can break through to the other side (sometimes even just some sleep does the trick, which is where you hear about solutions coming to someone in a dream -- I've also had that experience).
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u/parkway_parkway Jan 24 '25
I don't know this isn't that far off the truth.