Black and White

This painting requires slight context. It is about an idea- 'Self reference' that revolutionized the field of mathematics in the last century in several ways.

What do I mean by self reference?

"This statement is false"

By referring to its own self, the statement gave rise to a paradox.

The great mathematician, Godel, found self referential structures in mathematics that exposed the inherent incompleteness of any strong enough logical system. By this, I mean that any logical system that is powerful enough to describe numbers is inherently incomplete in the sense that there are truths that cannot be reached through the system, and would hence have to be assumed as new axioms of the logical system. So, from a systemic science, mathematics reduces to faith.

But having faith in mathematics is not problematic as it works consistently. Does it? Can we prove the consistency of mathematics? No, and as Godel further found out, for the same reason. The illusive and mysterious self reference!

I have written a very short summary of Godel's incompleteness theorems in this blogpost.