Philosophical change (Platonism): Mathematical truth transcends formal proof. We can recognize truth that our systems cannot prove. Reality contains truths beyond our deductive reach. This supports ...

Earlier today I set you the puzzle below, which is based on Gödel’s incompleteness theorem. As I discussed in the original post, this theorem is one of the most famous in maths and states that in any ...

GENEVA, SWITZERLAND - APRIL 19: A detailed view of the blackboard with theoretical physics equations in chalk by Alberto Ramos, Theoretical Physics Fellow and visitor, Antonio Gonzalez-Arroyo from the ...

This project implements a simple logic engine in Kotlin to illustrate Gödel’s First Incompleteness Theorem. It represents first-order Peano Arithmetic (PA), performs Gödel numbering of formulas, and ...

The loss of logical foundations might actually be liberating. What is the greatest mathematical achievement of all time? Judged in terms of the consequences for science and engineering, one might ...