## How Modal Logic Proved Gödel was Right, and God Exists

Does God exist? Modern software and math have verified Gödel’s proofs of a being that expresses all positive properties.

## Free Will, Determinism and Turing’s Halting Problem

MIT’s Seth Lloyd says a test for free will versus determinism must predict decisions accurately every time. How does the Turing Machine factor into this?

## The Lottery Paradox Versus the Math of Probability

We know one ticket must win, but are sure it couldn’t be our ticket. If the same principle applies to each ticket, there can be no winner: That’s the Lottery Paradox.

## How to Convert the Base of an Exponent with Logarithms

Why would anyone want to convert an exponential expression from one base to another? Why would logarithms help? Mike DeHaan breaks down the math for you.

## Introducing the Binomial Coefficient for Positive Integers

How many ways can we select ‘k’ outcomes from ‘n’ possible outcomes, without concern for order/sequence? The binomial coefficient holds the answer.

## Introducing the Factorial: the Exclamation Mark of Math

What is a factorial, and how is the exclamation point used in mathematics? Learn more about gamma functions and more.

## A Brief Guide to the Euclidean Postulates Found in Euclid’s Elements

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

Euclid’s geometry is still the cornerstone of today’s math theory, why are his axioms, theories, and postulates so important?

## The Turing Machine versus the Decision Problem of Hilbert

David Hilbert raised the “Decision Problem,” or Entscheidungsproblem, in 1928. Turing Machines cannot solve Halting Problems, one specific type of decision problem.