He was one of the "American postulate theorists" (according to Michael Scanlan, the expression is due to John Corcoran), American mathematicians active early in the 20th century (including E. H. Moore and Oswald Veblen) who proposed axiom sets for a variety of mathematical systems.

His 1902 axiomatization of the real numbers has been characterized as "one of the first successes of abstract mathematics" and as having "filled the last gap in the foundations of Euclidean geometry".

His 1917 book The Continuum and Other Types of Serial Order was in its day "...a widely read introduction to Cantorian set theory" (Scanlan 1999).

Yet Huntington and the other American postulate theorists played no role in the rise of axiomatic set theory then taking place in continental Europe.

In 1919, Huntington was the third President of the Mathematical Association of America, which he helped found as a charter member and its first vice-president.