His father was Čeněk Čech, a policeman, and his mother was Anna Kleplová.

[1] After attending the gymnasium in Hradec Králové, Čech was admitted to the Philosophy Faculty of Charles University of Prague in 1912.

In 1915 he was drafted into the Austro-Hungarian Army and participated in World War I, after which he completed his undergraduate degree in 1918.

[1] He received his doctoral degree in 1920 at Charles University; his thesis, titled On Curves and Plane Elements of the Third Order, was written under the direction of Karel Petr.

Ivo Babuška, Vlastimil Dlab, Zdeněk Frolík, Věra Trnková, and Petr Vopěnka have been doctoral students of Čech.