Narrated Ibn Umar (radiyallaahu-anhumaa): The Prophet (ﷺ) said:

”We are an illiterate nation; we neither write, nor give accounts. The month is like this and this, i.e., sometimes of 29 days and sometimes of 30 days.” [Saheeh Al-Bukhaari; Hadeeth No:1913; Vol:3; Muhsin khan]

Imaam Abdul Azeez Bin Baaz (rahimahullaah) said: We depend on the sighting of the moon and not on calculations (i.e. astronomical calculations to affirm Ramadaan and other months).

For further details see: Al-Hulalul Ibreeziyyah Min At-Taleeqaat Al-Baaziyyah Alaa Saheeh Al-Bukhaariy: Vol:2: page:125: footnote:1