He stayed at Cambridge, working on
finite groups. Norton was one of the authors of the
ATLAS of Finite Groups. He constructed the
Harada–Norton group and in 1979, together with
John Conway proved there is a connection between the
Monster group and the
j-function in number theory. They dubbed this "
monstrous moonshine", and made some conjectures later proved by
Richard Borcherds. Norton also made several early discoveries in
Conway's Game of Life, and invented the game
Snort. In 1985, Cambridge University did not renew his contract. Norton is the subject of the biography
The Genius in My Basement, written by his Cambridge tenant,
Alexander Masters, which describes his eccentric lifestyle and his life-long obsession with buses. He was also an occasional contributor to
Word Ways: The Journal of Recreational Linguistics. Norton was very interested in transport issues and was a member of Subterranea Britannica. He coordinated the local group of the
Campaign for Better Transport (United Kingdom), and had done so since the organisation was known as Transport 2000, writing most of the newsletter for the local Cambridge group and tirelessly campaigning for efficient, inclusive and environmentally friendly public transport in the region and across the United Kingdom. He collapsed and died in north London, aged 66, of a heart condition on 13 February 2019. ==Selected publications==