Much has been written about the Turing Test, i.e. Turing's thought experiment
of testing how smart a machine is by checking how "humanly" it behaves.
If one cannot tell that it is a machine, then it is difficult to still treat
it like a "dumb" object. That was the beginning of the discipline of
Turing's most lasting legacy might actually be the Turing Machine, which he
conceived a decade earlier and that is the foundation of computers.
Turing came up with the solution to a problem that Hilbert had originally
posed: does an algorithm exist that would solve all problems that can be
represented symbolically. If everything in the universe can be represented with
symbols by the human brain (which seems to be the case so far) and if
everything in the universe obeys mathematical laws (which seems to be the case
so far), then Hilbert was basically asking: is the human mind omnipotent?
Can the human mind understand everything about the universe?
Turing discovered the "universality" of the human mind: because the human mind
can represent the universe with symbols and can process symbols the human mind
can not only solve any problem (given enough time) but "understand" all of them.
Turing also realized that the answer to Hilbert's question had to be "digital".
The way to universality is digital: there can exist no universal analog machine
because of measurement errors that would pile up (and that instead don't matter
in digital machines).
Of course, Godel's Theorem has a consequence for computing that Turing himself
realized: it is impossible to predict if one problem exists that a Turing
Machine will never finish solving. Turing's own purpose was to show that
the halting problem is undecidable.
And this leaves the gate to metaphysics open...