1. Introduction

    1. The notion of infinite prime

    2. Generalization of ordinary number fields

    3. Infinite primes and physics in TGD Universe

    4. About literature

  2. Infinite primes, integers, and rationals

    1. The first level of hierarchy

    2. Infinite primes form a hierarchy

    3. Construction of infinite primes as a repeated quantization of a super-symmetric arithmetic quantum field theory

    4. Construction in the case of an arbitrary commutative number field

    5. Mapping of infinite primes to polynomials and geometric objects

    6. How to order infinite primes?

    7. What is the cardinality of infinite primes at given level?

    8. How to generalize the concepts of infinite integer, rational and real? /font>

    9. Comparison with the approach of Cantor

  3. Generalizing the notion of infinite prime to the non-commutative context

    1. Quaternionic and octonionic primes and their hyper counterparts

    2. Hyper-octonionic infinite primes

    3. Mapping of the hyper-octonionic infinite primes to polynomials

  4. How to interpret the infinite hierarchy of infinite primes?

    1. Infinite primes and hierarchy of super-symmetric arithmetic quantum field theories

    2. The physical interpretation of infinite integers at the first level of the hierarchy

    3. What is the interpretation of the higher level infinite primes?

    4. Infinite primes and the structure of many-sheeted space-time

    5. How infinite integers could correspond to p-adic effective topologies?

  5. How infinite primes could correspond to quantum states and space-time surfaces?

    1. A brief summary about various moduli spaces and their symmetries

    2. Associativity and commutativity or only their quantum variants?

    3. The correspondence between infinite primes and standard model quantum numbers

    4. How space-time geometry could be coded by infinite primes

    5. How to achieve consistency with p-adic mass formula

    6. Complexification of octonions in zero energy ontology

    7. The relation to number theoretic Brahman=Atman identity

  6. Infinite primes and mathematical consciousness

    1. Infinite primes, cognition and intentionality

    2. The generalization of the notion of ordinary number field

    3. Algebraic Brahman=Atman identity

    4. One element field, quantum measurement theory and its q-variant, and the Galois fields associated with infinite primes

    5. Leaving the world of finite reals and ending up to the ancient Greece

    6. Infinite primes and mystic world view

    7. Infinite primes and evolution

  7. How infinite primes relate to other views about mathematical infinity?

    1. Cantorian view about infinity

    2. The notion of infinity in TGD Universe

    3. What could be the foundations of physical mathematics?

  8. Local zeta functions, Galois groups, and infinite primes

    1. Zeta function and infinite primes

    2. Local zeta functions and Weil conjectures

    3. Local zeta functions and TGD

    4. Galois groups, Jones inclusions, and infinite primes

    5. Prime Hilbert spaces and infinite primes

  9. Does the notion of infinite-P p-adicity make sense?

    1. Does infinite-P p-adicity reduce to q-adicity?

    2. q-Adic topology determined by infinite prime as a local topology of the configuration space

    3. The interpretation of the discrete topology determined by infinite prime

  10. A little crazy speculation about knots and infinite primes

    1. Do knots correspond to the hierarchy of infinite primes?

    2. Further speculations

    3. The idea survives the most obvious killer test

    4. How to realize the representation of the braid hierarchy in many-sheeted space-time?