**The Limits of Mathematics**

Let's take a mathematical system built on a set of axioms. Number Theory would be a good example.

The system allows up to write statements, and we have 2 types..

A statement is true if no counter example exists.

A statement is provable if it can be deduced by a series of logical steps from the axioms.

Godel showed there can be true statements that are not provable statements.

So, the axioms are not "strong enough" to generate all true statements.

In Number Theory perhaps Goldbach's Conjecture is one such statement. But it's so simple. How could it hold such complexity?

So here we have the limits of mathematics. Or at least the limits of mathematics as it exists today. To move forward we need to rethink axiomatic systems and move to a more generalized approach.

Content written and posted by Ken Abbott abbottsystems@gmail.com