# Intersections of Math and Multimedia

The following are some intersections of mathematics, computer science, philosophy and multimedia.

1. Descartes and Analytical Geometry
2. Frege and Russell – the intersection of logic and philosophy of mathematics
3. Turing’s solution of the Halting Problem
4. von Neuman and Game Theory
5. Euler, Graph Theory and the Semantic Web
6. Set theory, Kleene and Regular Expressions

1. Descartes and Analytical Geometry. The appendix to the _Discourse on Method_ on “Analytical Geometry” is important in that it brought algebra and geometry together. Equations could generate shapes and shapes could be converted into equations for solution. This is the foundation of computer graphics – the Cartesian space is the bit map screen.

2. Frege and Russell – the intersection of logic and philosophy of mathematics. Russell’s letter to Frege and the problems it created for the logical foundations of mathematics.

3. Turing’s solution of the Halting Problem. This is where the idea of a simple universal machine (the Turing Machine) is proposed as an idea for dealing with Hilbert’s halting problem.

4. von Neuman and Game Theory. Game theory shows up in the social and economic sciences. Does it have applications to studying computer games and interactivity?

5. Euler, Graph Theory and the Semantic Web. The Semantic Web connects graph theory and ontology. There could be a connection between philosophy (ontology – especially Aristotle) and ways of representing/processing graphs.

6. Set theory, Kleene and Regular Expressions. Regular expressions show up as a mini-language in many programming languages (especially in text processing and web scripting languages.) How did set theory evolve? What did Kleene contribute? How are regular expressions connected to regular languages and set transformations?