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In 1844 he was awarded the First Gold Medal of the Royal Society.
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In 1849, the scientist became the first professor of mathematics at King's College in Cork (Ireland).
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Married Mary Everest, niece of a professor at King's College in 1854
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Since 1854 Buhl has been studying logic and algebra
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In 1857 he was admitted to the Royal Society of London.
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In 1857 he took up a law position at Oxford and Dublin Universities.