Considered with Aristotle and Gottlob Frege to be one of the most significant logicians in history , Gödel made an immense impact upon scientific and philosophical thinking in the 20th century , a time when others such as Bertrand Russell , A. N. Whitehead , and David Hilbert were pioneering the use of logic and set theory to understand the foundations of mathematics .
Many people , such as Bertrand Russell , A. N. Whitehead , and David Hilbert , tried to use logic and set theory at that time .