It was beginning, tentatively at first and then with increasing seriousness, to think about space.

The Soviet launch of Sputnik in October 1957 transformed that tentative thinking into urgent necessity.

The United States was, suddenly and publicly and undeniably, behind in the development of the rocket technology that would determine who controlled the high ground of orbit.

The response was enormous — the creation of NASA in 1958, the mobilization of engineering talent across the country, the commitment of federal resources to a program that would, within a decade, land American astronauts on the Moon.

The engineering problems involved in getting to space were, at a fundamental level, mathematical problems.