History
The Limit of Logic and The Rise of The Computer
AI since Aristotle (Part 2)
Turing
Analysis
Cantor’s Diagonal Argument
“Diagonalization seems to show that there is an inexhaustibility phenomenon for definability similar to that for provability” — Franzén…
Philosophy
Platonist Roger Penrose “Sees” Mathematical Truths
What does Roger Penrose mean when he claims to “see” mathematical truths?
Mathematics
Alan Turing in America
Pioneering British computer scientist and mathematician Alan Turing first arrived in America on the 28th of September 1936.
Mathematics
A Computability Proof of Gödel’s First Incompleteness Theorem
A computability proof of Gödel’s incompleteness theorem equally as strong as Gödel’s version, but much easier to deduce
Mathematics
Turing Uncomputability
“As Leibniz suggested, we appear to live in the best of all possible worlds, where the computable functions make life predictable enough to be survivable ...