This research paper concerns the work of the austrian-american mathematician Kurt  Gödel and its consequences. With Douglas Hofstadter's book Gödel, Escher, Bach: An Eternal Golden Braid as a guide, the Incompleteness Theorem  is introduced along with its connection to Alan Turing's work concerning artificial intelligence, resulting in some conclusions about the nature of intelligence.

Kurt  Gödel proved that it is impossible to construct a formal (mathematical) system which can be deemed consistent and complete. Alan Turing reproduced  Gödel's results within the context of computing machinery and posed the question “Can machines think?”  Gödel's conclusions are of particular importance to the development of the Turing's conjecture that artificial intelligence is feasible.

Douglas Hofstadter devotes his work on the quest of the nature of intelligence and consciousness. He agrees with Turing's position, something that requires the interpretation of the human brain as a machine. The views he presents put aside the “dipole” of machine and human and suggest a juxtaposition between formal reasoning and intelligence. A distinction of qualities, independent of the context they concern (machine, human).

The relation of these qualities leads to some comments concerning the role of methodology and intuitionism  in a production process, such as design. The technical content of the research paper is used essentially to underline a well known debate about design and to stress the importance of understandingcreative reason