The majority of the world's mathematicians came through the normal school-university system. However, there are those who, for various reasons, could get no formal degree despite having brains Plato would have been proud of. Most of these died unknown, like Evariste Galois the hot-headed French revolutionary. A few were discovered, but not after much suffering and years of obscurity. Typical examples: the intuitive Indian Srinavasa Ramanujan and the rigorous German Karl Weierstrass.
And George Boole.
He was born in 1815 (the year Napoleon met his Waterloo) to a cobbler. Boole Senior was not an unimportant man in the city and was "able to do everything well except his own business of managing the shop". He was a kind man who recognised his son's talent and, most importantly, encouraged it actively. But his financial troubles meant George could not go Cambridge.
The next alternative was for George to become a priest, but it soon became clear to him that he'd have to support his parents and would therefore have to do something else. So he became a teacher and had set up his own school by the time he was 20.
He kept reading in his spare time. The fact that he had something to read was due to his bookseller friend. Still, reading Newton's Principia on your own is no joke, especially with no-one within a 100km radius to talk to about it. He'd sometimes rack his brains for months over something that a good teacher could have explained in minutes.
We can ask ourselves many questions. Why was he reading such stuff at all? He was just a teacher doing his job, and had enough adminstrative problems to handle as well. Was he hoping somehow, to make a name for himself, or did he just enjoy the subject? What would he do when he reached a tough point in Principia? Turn the page? Sleep on it? Spend a week stuck at the same place?
At least he was not living in such abject poverty as Weierstrass, the rural teacher who went on to become the greatest mathematician in Europe. For he (Weierstrass) could not even afford the postage required for correspondence with other mathematicians and was only 'discovered' in his forties!
Things went right when Boole was 24 when he published his first paper and was received as a mathematician of note. He could have received a belated entry into Cambridge as a mature student but did not as he wanted to support his parents.
So he continued at his humble teaching job. The entire community held him in esteem, and this was probably worth more to him than anything else. He won the prestigious Royal Medal when he was 29 and published his "Analysis of Logic" three years later.
Then another turning point. He was 34 when the new post of Professor of Maths at Queen's College came into being. "Apply for it!" pushed his mathie friends. "Why would they want me", he countered, "I have no degree - how can I teach a degree?" But they got him to apply. And the Appointing committee, in one of those rare occassions where sense took precedence over rules, accepted his application.
It would not be fair to say that his dreams had come true, for he had probably never dreamed of such a post. But he wasn't questioning it and happily moved to do Cork (the location of Queens' College) to take up his vocation of maths full-time, while at the same time being able to fully support his aged parents. Now he could wander around a vast library and ,of course, ask questions on Newton's Principia. He had plenty of time for research, and to write his 1854 book "Laws of thought".
He also had time to get married, which he did when he was 40. He had five daughters, three of whom certainly inherited the brilliance gene. One was known for her work on the three-dimensional sections of four-dimensional objects! (Can someone please do a biography of them?)
Sadly, he died before they became teenagers.
For George Boole was an excellent teacher (hell, he'd had the practice!), devoted to his equally devoted students. Nothing would stop him teaching them. So one not-so-fine day he got caught in a storm and arrived at the college totally bedraggled. But he waved aside all pleas to dry himself out by a nice cosy fireplace and went on to lecture in wet clothes.
He caught pneumonia and quit the earth before he had reached his half-century.
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