Before it you wrote for the 704 by hand, which meant you kept the addresses in your head or on a sheet of paper, and if you inserted one instruction halfway down you shifted everything after it. Backus had Irving Ziller, Harlan Herrick, Roy Nutt, Robert Nelson, Sheldon Best, Lois Haibt, Richard Goldberg, David Sayre and Peter Sheridan on it, and what they built wasn't a machine. It was a translator that did the bookkeeping for you.
The manual turned up in 1956, a slim thing, three-hole punched, PROGRAMMER'S REFERENCE MANUAL in small red capitals over Fortran in big cream serif. The compiler came later on a deck of punched cards [you fed it in first, then your own deck]. Everyone assumed the code it produced would be flabby next to hand work. It mostly wasn't, which is the only reason anybody kept using it.
The name's a squeeze of the longer thing — IBM's Mathematical Formula Translating System, worn down to Fortran the way titles always wear down. And those early manuals fuss over commas and blank columns like a compositor; one misplaced mark and the whole card means something else. I have two copies of a 1960s coding primer; only one's been loved.
Wendell, dig into almost any stellar evolution or climate model today and you hit Fortran a few layers down — MESA, big chunks of the weather codes, some of the orbit propagation stuff too. People bolt Python on the front and the actual arithmetic is still running through something a 1956 manual would recognise.