Turing’s Deep Field: Visualizing the Computational Universe

I generated this image in the course of an investigation of the distribution of runtimes of programs in relation to the lengths of mathematical proofs, the results of which are being published in my paper bearing the title “Computer Runtimes and the Length of Proofs with an Algorithmic Probabilistic Application to Optimal Waiting Times in […]

Collections of axioms and information on theories dependency

List of Axioms from Computer Science Department, University of Miami Documentation, Computer Science Department, University of Miami List of axioms collected from Wikipedia. MBase: A Mathematical Knowledge Base. A collection of definitions, theorems and proofs. The Mathematical Atlas. Methamath. Proof symbolic visualizations, University of Texas.

On single and shortest axioms for Boolean logic

Both the philosopher Charles Sanders Peirce in 1880 and the American logician H. M. Sheffer in 1913 realized that the truth-functions of elementary logic could all be defined from a single operation. The Sheffer stroke, also known as the Nand operation, is a logical operator with the following meaning: p Nand q is true if […]