Another overcast morning. I feel as though I must put on the lights to read at 7:16 in the AM. But that is not what I want to talk about. What I really want to talk about is mathematics and my obsession with it this year. (Yes, I am always obsessed with something as you well know by now.)

This is what began all the trouble around 300 BCE.

Euclid’s Fifth Postulate:

That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

Thomas L. Heath translator

Twenty-two hundred years later, Gauss, Bolyai, and Lobachevsky had the audacity to negate the postulate and arrive at the conclusion that its consequences produced a geometry as consistent as Euclid’s although containing propositions strange and contrary to Euclid’s. Several decades later, Betrami and Klein established that if hyperbolic geometry is inconsistent, then so is Euclidean geometry. Today, hyperbolic geometry produces the richer and more useful geometry for mathematics.

The history of this, its impact on philosophy of mathematics, philosophy in general, the connections between mathematics, science, and art, and how mathematics is an art and creative activity is what I have been working on this year.

It is the best year of my life so far.