In 1987, Neumann won the Lester R. Ford Award of the Mathematical Association of America for his review of Harold Edwards' book Galois Theory.

[4][5] He was the first Chairman of the United Kingdom Mathematics Trust, from October 1996 to April 2004, succeeded by Bernard Silverman.

[6] Neumann showed in 1997 that Alhazen's problem (reflecting a light ray off a spherical mirror to hit a target) cannot be solved with a straightedge and compass construction.

[8] He was appointed Officer of the Order of the British Empire (OBE) in the 2008 New Year Honours.

[2] Neumann died from COVID-19 on 18 December 2020, ten days before his 80th birthday, during the COVID-19 pandemic in the United Kingdom.