I'm writing this fresh from giving a talk at Poole Grammar School about the maths of Alice in Wonderland and didn't get a real chance there to talk about one of the ninjas behind it.
János Bolyai is my favourite kind of mathematician: the glorious failure. He came really close to being the discoverer of non-Euclidean geometry, but sadly missed out by most possible metrics.
He was born in what is now Cluj, Romania - then Kolozsvár, in the Hapsburg Empire. Cluj is much easier to say, and Bolyai was a genius from an early age: he knew about the sine function at the age of four, something the Mathematical Ninja is still trying to drum into 18-year-old A-level students.
Bolyai's dad was good mates with Carl Friedrich Gauss, and wrote to him saying "hey, Charlie, my kid's a genius, can he come and live with you and you can be his tutor?" Gauss declined this kind offer. Overall, Gauss was a bit of a jerk towards Bolyai, as you'll see from the next, most famous Bolyai-related anecdote.
Bolyai, like his father before him, and 2,000 years' worth of other maths students before HIM, had spent quite a lot of time trying to prove Euclid's fifth postulate - the parallel postulate - from the other four. Bolyai, though, was one of the first to say "'ang on a second... if you assume something different, it still sort of works." It's hard to say how radical an idea this was: Euclid had been accepted as true since about 300BC, so for this pipsqueak to come along and say "it ain't necessarily so" was a bit out of the ordinary. However, his dad - a good mathematician in his own right - couldn't see anything wrong with it, and sent it off to his bessie, C.F. Gauss.
His bessie told his friends "this Bolyai kid, he's the next big thing." However, he didn't tell Bolyai senior that. He told Bolyai senior, "this stuff isn't bad, but I figured it out yonks ago, just didn't think it was worth publishing," an early equivalent of someone posting "Old" under a youtube video, and just as vile behaviour.
It sent Bolyai into a spiral of depression, sadly - he didn't get around to publishing his work, in an appendix to his dad's textbook, for several more years; in the meantime, Lobachevsky had come, probably independently, to similar conclusions.
Hence Tom Lehrer's brilliantly scurrilous song, Lobachevsky: In Dnepropopetsk, my name is curse / when he finds out: I publish first!