Bayan da ya koma Birnin New York ya fara horar da shi a matsayin mai fasaha na rediyo kuma ya zama mai sha'awar ilmin lissafi. Ya sauke karatu daga Jami'ar Columbia tare da digiri na farko a 1949 da digiri na biyu a 1950, dukansu a cikin ilmin lissafi, kuma ya shiga IBM a 1950. A cikin shekaru uku na farko, ya yi aiki a kan Kayan Lissafi na Lantarki na Zaɓuɓɓuka (SSEC); babban aikinsa na farko shi ne rubuta shirin don ƙididdige matsayi na Moon. A 1953 Backus ya ci gaba da harshen Speedcoding, harshen farko mai mahimmanci da aka kirkiro don kwamfutar IBM, don taimakawa wajen bunkasa software don kwamfutar IBM 701. Shirye-shiryen yana da wuya a wannan lokacin, kuma a 1954 Backus ya tara wata tawagar don bunkasa da kuma bayyana Fortran don kwamfutar IBM 704.
Jami'ar Columbia tare da digiri na farko a 1949 da digiri na biyu a 1950, duka a cikin ilmin lissafi