> She said she never had any trouble initiating contact with authority figures when she had some business to discuss. “We’re all just people,” she says.
A professor of mine once told me about when he was in school he studied a book written by a famous expert in the field and found a bunch of errors. So he wrote back to the author with the error and, after some back and forth correspondence, the author offered him a job after graduation. So that was how he first got his foot in the door in the field.
I've found the same. If you contact an authority with serious questions about the subject they are an authority on, they will generally respond in a positive way. Keep in mind, this is very different than kids asking a math PhD for help with algebra homework - algebra is not their specialty and there is no reason to contact them specifically about such things.
I have also had similar experience cold-emailing domain authorities. I spent days writing 10s of words, double checking my facts, doing my homework and have gotten a response everytime. They are excited that someone is reading their work, thinking about it and then having the gumption to contact them. I think it is actually quite rare.
I contacted a guy about a paper he'd written on image de-blurring. Just some high level questions because the paper was behind a paywall. He asked for my snail-mail address and sent a full color printout of the paper in a large envelope! I still have it.