August 21–October 15 – Illinois observes the centennial of the Lincoln–Douglas debates.
September – The University of New Orleans begins classes as the first racially integrated public university in the Southern United States.
September 2- President Eisenhower signed the National Defense Education Act (NDEA), a major piece of legislation passed in response to the Soviet Union's launch of Sputnik the previous fall. It poured federal funding into science, math, and foreign language education.
September 12: Jack Kilby, an engineer at Texas Instruments, successfully demonstrated the first working integrated circuit — a milestone that helped launch the modern electronics and computing industry.
September 15 – Newark Bay rail accident kills 48 people and injures the same number.
September 18 – "Fresno Drop": BankAmericard, the first credit card to be widely offered, is launched in Fresno, California.
September 23 – The Spirit of Detroit statue is dedicated in Detroit, Michigan.
October–December
September 20- Martin Luther King Jr. was stabbed in the chest with a letter opener by Izola Curry, a mentally disturbed woman, while signing books at a department store in Harlem, New York. He survived after emergency surgery — doctors said the blade came dangerously close to his aorta.
September 27- Voters in Little Rock, Arkansas, went to the polls and overwhelmingly voted to close the city's public high schools rather than comply with court-ordered desegregation, following the tumultuous integration crisis at Central High School the previous year. The schools stayed closed for the rest of the school year, an episode often called the "Lost Year."
Other notable happenings
- The country was still in the grip of a recession that had begun in 1957, though it was beginning to ease by that point.
- Space and missile programs were ramping up as part of the Cold War response to Sputnik, setting the stage for NASA's creation the following month (October 1, 1958).
