I'm not an amateur astronomer. Given all the hobbies I haven't time to do right that might not be surprising, although my long fascination with space (the first books I remember reading were about astronomy and astronauts) suggests I might have anyway.
Still I imagine anyone who knows it finds the discovery of Neptune about the coolest mathematics thing ever. John Couch Adams studies anomalies in the movement of Uranus and projects a new planet beyond it; while the Royal Observatory sits on the request to look, Urbain Jean Joseph Le Verrier makes a similar projection, sends it to Johann Gottfried Galle, who finds Neptune in one hour. (Maybe more amazing, Adams didn't resent Le Verrier.) No wonder astronomers went crazy seeking anomalies in Neptune's and Uranus's orbits and convincing themselves they'd seen Vulcan inside Mercury's orbit.
I can't say I studied mathematics and physics just because of the romance of the discovery of Pluto, and that Pluto moved inside Neptune's orbit while I was young and impressionable, but Pluto certainly helped. I always wanted to do something that cool.
Trivia: The Percival Lowell observatory took pictures of Pluto on 19 March and 7 April 1915, while Lowell was preparing his memoir A Trans-Neptunian Planet. Source: The Explorers of Mars Hill: A Centennial History of Lowell Observatory, 1894-1994, William Lowell Putnam.
Currently Reading: I, The Machine, Paul W Fairman. Lee Penway is a relentlessly average shlub in a hedonistic world where every whim is satisfied by nigh-omniscient giver The Machine. In a unique development, he falls in with a bunch of rebellious sorts (the women wear nothing; the men wear only spray-on jock straps) and learns The Machine is covering up severely dysfunctional behavior. Now he wonders helplessly how The Machine's robots keep finding and shredding his new fleshy friends while he holds telepathic conversations with a taunting Machine. Meanwhile he heads for a shocking discovery all sentient readers and some advanced forms of moss spot a hundred pages before.
You know you're in for a good ride when on paragraph six it's mentioned Lee keeps such good care of his body ``he still had, at thirty, his original sex organs.'' Still, it's got -- for 1968 -- a nifty bit of miniaturization, as the brain-wave patterns of all the residents of what becomes of the United States fit in one box four feet long.