According to his commemorative statue, he disliked the city of Ankh-Morpork intensely.
According to The Last Continent, while wearing seven-league boots, a magical hole opened in his left boot. This was one of a number of incidents cited by the senior Faculty as why playing around with rips in space and dimensional holes and so on was a bad idea.
According to The Science of Discworld, he devised the Roundworld thought experiment. All the other wizards at the time said it was impossible, as it would require far too much magic to create and would take months to do, at least for human wizards. Fortunately, when a vast amount of magic needs to be used up very quickly, Hex is able to cast all the spells to create Roundworld in less than a minute, to the disbelief of the Dean.