GÃ del 's work has had a big impact on scientific and philosophical thinking in the 20th century . Many people , such as Bertrand Russell , A. N. Whitehead , and David Hilbert , tried to use logic and set theory at that time . One of the most significant logicians of all time , GÃ del made an immense impact upon scientific and philosophical thinking in the 20th century , a time when many , 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 .