Aczel's father was the captain of a passenger ship that sailed primarily in the Mediterranean Sea.

When he was ten, Aczel's father taught his son how to steer a ship and navigate.

Aczel taught mathematics at universities in California, Alaska, Massachusetts, Italy, and Greece.

While teaching at Bentley, Aczel wrote several non-technical books on mathematics and science, as well as two textbooks.

Aczel was a 2004 Fellow of the John Simon Guggenheim Memorial Foundation, a visiting scholar in the History of Science at Harvard University (2007), and was awarded a Sloan Foundation grant to research his 2015 book Finding Zero (ISBN 978-1-137-27984-2).