Introduction

1. Brief summary of the basic mathematical notions behind TGD

2. Langlands correspondence and TGD

Infinite primes as a basic mathematical building block

1. Construction of infinite primes

2. Questions about infinite primes

3. P=Q hypothesis

How also finite fields could define fundamental number fields in Quantum TGD?

1. P=Q condition

2. Proposal

Do elementary particles correspond to polynomials possessing single ramified prime?

1. Calculation of ramified primes

2. Could D=P correspond to a maximum of D or of maximal ramified prime P_max

3. Spin glass analogy for WCW geometry as a guide line

4. The ultrametric topology of discretized WCW

5. How to study the hypothesis?

Gödel's Undecidability Theorem and TGD

1. What Gödel's theorem could mean in the TGD Universe?