Begle's early academic work was in the field of topology, which is where he earned his Ph.D. at Princeton, studying under Solomon Lefschetz in 1940.

Instead, Begle's introductory mathematics texts actually address freshman mathematicians, a revolutionary concept in teaching math.

In the wake of Sputnik in 1958, Begle gained the directorship of the School Mathematics Study Group, a post he would hold for 15 years.

Under his leadership, the SMSG published numerous reports and studies, culminating in its series of books detailing the teaching revolution known as The New Math.

At the time of his death in 1978, Begle was working on a compilation of the results of his 15-year tenure as the director of the SMSG and a culmination of his lifetime of experience in mathematics education.