Euclid’s axioms and postulates, intended to be self-evident, are sufficient to prove the many propositions he made in Elements.

## Elements of Geometry: A Brief Guide to the Euclidean Axioms

Euclidean geometry is based on Euclid’s axioms and postulates. What do the Euclidean axioms say, and why are they so important in math?

## Euclid Laid the Foundations of Geometry for Mathematics

## T Cells, Predators and Finances all Walk the Levy Walk

## The Turing Machine versus the Decision Problem of Hilbert

## Algorithm to Solve Arranged Marriages via the Hall Theorem

## Is it Possible for Turing Machines to Solve the Halting Problem?

## The Special Case of Non-Deterministic Turing Machines

Alan Turing (1912-1954) “invented” the Turing machine (TM) as a powerful theoretical model for mathematicians exploring rules-based mathematics. The Non-deterministic Turing machine, or NTM, extends the basic concept by permitting multiple instructions for one state-input combination. The Deterministic Turing Machine A Turing machine has a finite number of states, symbols and instructions. A pattern of symbols are presented on […]

## Examples of Turing Machines: Loops, Halts, and Rewriting

A Turing machine, or TM, is a theoretical model devised by Alan Turing to explore the limits of rule-based math. The model has a finite number of rules, states and symbols, and an infinite tape with cells, each of which can contain a single symbol. The TM can either read the current cell, rewrite it, […]

## The Turing Machine: A Brief Introduction

Alan Turing (1912-1954) “invented” the Turing machine as a theoretical model for exploring the limits of rules-based mathematics. This purely theoretical device became a powerful tool in the minds of mathematicians, and modern computers still follow many of its principles. The Turing machine is even being honored via art at the Intuition and Ingenuity exhibit […]