1. Title
2. Level 1
3. Level 2
4. Level 3
5. Level 4
6. Level 5
7. Frogs (depths of structure)
7.1. Father: Francis Bacon
7.2. Supporters:
7.2.1. Rutherford
7.2.2. Marie Curie
7.2.3. Darwin
7.2.4. Faraday
7.3. John von Neumann
7.3.1. Rings of operations
7.3.1.1. Describe quantum dynamics
7.3.2. Computers
7.3.2.1. Prediction of control of weathers
7.3.2.1.1. Fail due to weak chaos
7.3.3. Set theory
7.3.3.1. Kurt Gödel
7.3.3.1.1. Mathematics is inexhaustible
7.4. String theory students
7.5. Abram Besicovitch
7.5.1. solved the Kakeya problem
7.5.1.1. Connection with general theorems about structure of sets of points in a plane
7.5.1.2. Typical frog problem:
7.5.1.2.1. Concrete problem without much connection with rest of mathematics
7.5.2. Architectural style with hierarchical plan
8. Birds (generality of concepts)
8.1. Father: René Descartes
8.2. Supporters:
8.2.1. Pascal
8.2.2. Laplace
8.2.3. Poincaré
8.2.4. Newton
8.3. Franc Yang
8.3.1. Theory of non-abelian gauge fields
8.3.1.1. Framework for the standard model of particle physics
8.3.1.1.1. Simmetry dictates interaction
8.4. Hermann Weyl
8.4.1. expert in Number theory and Quantum theory of radiation
8.4.1.1. Gauge fields invention
8.4.2. Goal: comprehend the physical universe by a direct of creative math imagination
8.5. String theory creators
8.6. Yuri Manin
8.6.1. Mathematics as metaphor
8.6.1.1. Similarity in structure between number theory and physics
8.6.2. Advances in math come from programs
8.6.3. The Empty City Archetypes
8.6.3.1. Based on Archetypes theory
8.6.3.2. Collective unconscious description
8.6.3.3. Collective consciousness as solution for escaping the unconscious
9. Mixture
9.1. Solution for mathematical issues
9.1.1. Complex numbers
9.1.2. Precise linearity of quantum mechanics
9.1.3. Existence of quasi crystals
9.1.4. Similarity between quasi crystals and zeros of the Riemann Zeta function