The mathematics of the gods and the algorithms of men: a cultural history

Abstraction, existence and reality

Mathematics of the gods

Mathematical and philosophical formulas

Growth and decrease, number and nature

Katà gnómonos phýsin: the nature of the Gnomon

Dýnamis: the capacity to produce

Intermission: spiritual mechanics

Zeno's paradoxes: the explanation of movement

The paradoxes of plurality

The limited and the limitless: incommensurability and algorithms

The reality of numbers: Cantor's fundamental sequences

The reality of numbers: Dedekind's section

Mathematics: a discovery or an invention?

From the continuum to the digital

The growth of numbers

The growth of matrices

The crisis of fundamentals and the growth of complexity: reality and efficiency

Verum et factum

Recursion and invariability.