Mukherjee continued publishing scholarly papers on mathematics and physics into his 30s. By 1893, aged 29, Mukherjee had been further elected to the fellowships of the Physical Society of France and the Mathematical Society of Palermo, and was a member of the Royal Irish Academy. He subsequently became a member of the London Mathematical Society, the Paris Mathematical Society and the American Mathematical Society (1900). Although after 1893 he largely abandoned his mathematical pursuits for a legal career, Mukherjee has been recognised as the first modern Indian mathematician to enter the field of mathematical research, and founded the Calcutta Mathematical Society in 1908. Among his mathematical contributions, Mukherjee determined several crucial derivations of Gaspare Mainardi's answer to determining the oblique trajectory of a system of confocal ellipses. He also made lasting contributions in differential geometry, developing analytical methods of simplifying Gaspard Monge's interpretation of his general differential equation for conics.