Following an unsuccessful application for the Chair of Mathematics at
Aberystwyth in 1872, he taught at the Training College in
Carmarthen. He finally secured the professorship at Aberystwyth in 1879, and held it until 1919. Along the way his title became Professor of Mathematics and Astronomy. Genese introduced into the United Kingdom the ideas of
Hermann Grassmann (advancing the use of vector analysis). In his 1941 book
The calculus of extensions,
Henry Forder published numerous examples in vector analysis taken from Genese's posthumous notes. (Genese's notes were left to the
Mathematical Association and then given in 1929 to Forder by
E. H. Neville.) Genese was an Invited Speaker of the
ICM in 1904 in
Heidelberg with talk
On some useful theorems in the continued multiplication of a regressive product in real four-point space and in 1908 in Rome with talk
The method of reciprocal polars applied to forces in space. ==Selected publications==