Montague Cashmore, a British chemist and druggist, was a member of the (British) Pharmaceutical Society. In 1893, while living in Estcourt, he applied successfully for a licence to practise as a chemist and druggist in the Natal Colony. In 1900 and in 1904 he was listed as practising in Ladysmith, Natal, but in 1903 had already moved to Johannesburg from where he became a member of the South African Association for the Advancement of Science.
On 1 September 1905 Cashmore read two papers at the joint meeting of the British and South African Associations for the Advancement of Science in Johannesburg. The first dealt with an aspect of recreational mathematics, namely "Chess magic squares", that is, magic squares having a constant sum along every chess path. The method of construction was given, followed by an investigation into the number of possible chess magic squares, and an explanation of the theory of their construction. The second, a brief paper "On some new formulae for calculating pi", showed the derivation (from J. Machin's formula of c. 1700) of four series of arc tan terms for finding pi/4. The series converge so rapidly that three terms suffice to give pi correctly to ten places. Both papers were published in Addresses and papers read at the joint meeting of the British and South African Associations for the Advancement of Science, South Africa, 1905 (Vol. 1, pp. 83-90, 91-92).
Cashmore was still listed as practising in Johannesburg in 1907, but had moved to London the previous year. In 1914 he was granted a United States patent for improvements to proportion calculators. He also, rather optimistically, published a monograph entitled Fermat's last theorem; rigid proof by elementary algebra; also dissertation on test for primes and recurring decimals (London, 1916).