Shaul Foguel was born to one of the founding families of the City of Tel Aviv[1][2] and his mother Dora Malkin was a direct descendant of Saul Wahl.

He wrote his dissertation under Nelson Dunford on "Studies in Spectral Operators and the Basis Problem".

Shaul Foguel was Professor Emeritus of the Hebrew University of Jerusalem, and a supporter of the Israeli Left.

He ran in the 1969 Knesset elections on the Peace List along with Gadi Yatziv, although it failed to win a seat.

He spent his retirement in New York City, where his two sons, Professor Tuval Foguel of Adelphi University, and Sy Foguel, the CEO of Berkshire Hathaway GUARD Insurance Companies live.