Meaningful Math Proofs and “Math is not Calculation”

Mathematicians are generally thought to be very good at calculation, and they sometimes are, but this is not because math is about calculation, just as astronomy is not about telescopes and computer science is not about computers (paraphrasing Edsger Dijkstra). But if it is not preeminently about calculation, then what is mathematics about? The common […]

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.

“The ways of paradox”: Quine on Berry’s paradox.

“Ten has a one-syllable name. Seventy-seven has a five-syllable name. The seventh power of seven hundred seventy-seven has a name that, if we were to work it out, might run to 100 syllables or so; but this number can also be specified more briefly in other terms. I have just specified it in 15 syllables. […]

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 […]

Kurt Godel: The writings. Université de Lille III

Kurt Godel workshop for studying his legacy and writings. Lille, France, May 19-21, 2006 My thoughts, ideas, references, comments and informal notes: – The wheel machine, a machine for real computation which I am proposing -as a thought experiment- in a forthcoming paper  on the Church-Turing thesis -Yes, one more paper on the CT thesis!- […]

Experimental Metamathematics

Metamathematics is to mathematics what metaphysics is to philosophy. It is about stepping outside the discipline and attempting to grasp it as a single entity/ object of study; it is an investigation into the foundations of mathematics. (For an elucidation of  Foundations of Mathematics see http://www.math.psu.edu/simpson/hierarchy.html) Some mathematicians have begun to practice  a quasi-empirical brand of mathematics and insist on results for which there […]