1. Introduction

  2. Number theoretic compactification and M8-H duality

    1. Basic idea behind M8-M4× CP2 duality

    2. Hyper-octonionic Pauli "matrices"

    3. Are Kähler and spinor structures necessary in M8?

    4. How could one solve associativity/co-associativity conditions?

    5. Quaternionicity at the level of imbedding space quantum numbers

    6. Questions

    7. Summary

  3. Quaternions and TGD

    1. Are Euclidian Regions Of Preferred Extremals Quaternion- Kähler Manifolds?

    2. The Notion of Quaternion Analyticity

    3. Are Preferred Extremals Quaternion-Analytic in Some Sense?

  4. Octo-twistors and twistor space

    1. Two manners to twistorialize imbedding space

    2. Octotwistorialization of M8

    3. Octonionicity, SO(1, 7), G2, and non-associative Malcev group

    4. Octonionic spinors in M8 and real complexified-quaternionic spinors in H?

    5. What the replacement of SO(7, 1) sigma matrices with octonionic sigma matrices could mean?

    6. About the twistorial description of light-likeness in 8-D sense using octonionic spinors

  5. How preferred p-adic primes could be determined?

    1. Earlier attempts

    2. Could preferred primes characterize algebraic extensions of rationals?

    3. A connection with Langlands program?

    4. A connection with infinite primes?

  6. More about physical interpretation of algebraic extensions of rationals

    1. Some basic notions

    2. How new degrees of freedom emerge for ramified primes?

    3. About the physical interpretation of the parameters characterizing algebraic extension of rationals in TGD framework

  7. p-Adicization and adelic physics

    1. Challenges

    2. NTU and the correspondence between real and p-adic physics

    3. NTU at space-time level

    4. NTU and WCW

    5. Breaking of NTU at the level of scattering amplitudes

    6. NTU and the spectrum of Kähler coupling strength

    7. Other applications of NTU

    8. Going to the roots of p-adicity

  8. What could be the role of complexity theory in TGD?

    1. Basic notions of chaos theory

    2. How to assign chaos/complexity theory with TGD?

  9. Why the non-trivial zeros of Riemann zeta should reside at critical line?

    1. What is the origin of the troublesome 1/2 in non-trivial zeros of zeta?

    2. Relation to number theoretical universality and existence of WCW

  10. Why Mersenne primes are so special?

    1. How to achieve stability against state function reductions?

    2. How to realize Mk=2k-1-dimensional Hilbert space physically?

    3. Why Mersenne primes would be so special?

  11. Number Theoretical Feats and TGD Inspired Theory of Consciousness

    1. How Ramanujan did it?

    2. Symplectic QFT, 3, 4, and 5 as Additive Primes, and Arithmetic Consciousness

  12. p-Adicizable discrete variants of classical Lie groups and coset spaces in TGD framework

    1. p-Adic variants of causal diamonds

    2. Construction for SU(2), SU(3), and classical Lie groups

  13. Some layman considerations related to the fundamentals of mathematics

    1. Geometric analog for Gödel's problematics

    2. Number theory from quantum theory

    3. Could quantum set theory make sense?

  14. Abelian class field theory and TGD

    1. Adeles and ideles

    2. Questions about adeles, ideles and quantum TGD