Sheffer was a Polish Jew born in the western Ukraine, who immigrated to the USA in 1892 with his parents and six siblings.
He studied at the Boston Latin School before entering Harvard University, learning logic from Josiah Royce, and completing his undergraduate degree in 1905, his master's in 1907, and his Ph.D. in philosophy in 1908.
Sheffer proved in 1913 that Boolean algebra could be defined using a single primitive binary operation, "not both .
Charles Peirce had also discovered these facts in 1880, but the relevant paper was not published until 1933.
Sheffer's discovery won great praise from Bertrand Russell, who used it extensively to simplify his own logic, in the second edition of his Principia Mathematica.