Project Tao - Foundations

A structured 6-month initiative to establish mastery of mathematical foundations

“道生一, 一生二, 二生三, 三生萬物.” - 道德經

“The way begets one; one begets two; two begets three; three begets the myriad creatures.” - Tao Te Ching

Project Overview

Project Tao represents my structured 6-month initiative to establish mastery of mathematical foundations, with a particular focus on mathematical logic, set theory, real analysis, complex analysis, and the fundamental limitations of mathematical systems. This journey aims to develop a deeper theoretical understanding of mathematical principles from first principles.

Mathematics serves as the foundational language for understanding complex systems across disciplines. While I possess a computational engineering-focused mathematics background, Project Tao aims to help me:

  1. Comprehend the inherent limitations of mathematical systems through Gödel’s incompleteness theorems
  2. Understand the axiomatic foundations that underpin mathematical structures
  3. Build a firm grounding in set theory and analysis to facilitate advanced study
  4. Develop the ability to trace theorems back to their set-theoretic foundations

Project Structure

The journey is divided into five phases over six months:

  1. Introduction to Mathematical Logic & Big Ideas (Month 1)
  2. Foundations of Set Theory & Formal Logic (Month 2)
  3. Real Analysis Foundations (Months 3-4)
  4. Deeper Dive into Logic & Computability (Month 5)
  5. Complex Analysis (Month 6)

Knowledge Dissemination

Throughout this journey, I’ll be creating:

Weekly Project Tracker

Below is the comprehensive week-by-week tracker for the entire Project Tao journey:

Week Dates Phase Primary Focus Key Deliverables Status
1 Apr 8-14 1 Propositional Logic Infrastructure setup, Initial blog post Planned
2 Apr 15-21 1 First-Order Logic Logic reference guide (draft), First Feynman video Planned
3 Apr 22-28 1 Proof Techniques 2+ formal proofs, Logic exercises Planned
4 Apr 29-May 5 1 Gödel’s Big Ideas Conceptual summary, Monthly seminar Planned
5 May 6-12 2 Axiomatic Set Theory Set theory blog post, First concept map Planned
6 May 13-19 2 ZFC Axioms 5+ set-theoretical proofs, Axiom visualization Planned
7 May 20-26 2 Model Theory Basics Set theory reference guide (draft), Problem creation Planned
8 May 27-Jun 2 2 Number Construction Construction concept map, Monthly seminar Planned
9 Jun 3-9 3 Real Numbers Construction of reals, Blog post on completeness Planned
10 Jun 10-16 3 Sequences & Series Convergence proofs, Sequence visualization Planned
11 Jun 17-23 3 Basic Topology Topological concepts, Open/closed set proofs Planned
12 Jun 24-30 3 Continuity Epsilon-delta proofs, Monthly seminar Planned
13 Jul 1-7 3 Differentiation Derivative from first principles, Multiple proof approaches Planned
14 Jul 8-14 3 Integration Riemann integral construction, Blog post Planned
15 Jul 15-21 3 Fundamental Theorems Analysis-to-set-theory connections, Key theorems Planned
16 Jul 22-28 3 Analysis Applications Mini-project, Monthly seminar Planned
17 Jul 29-Aug 4 4 Formal Systems Gödel numbering, Blog post Planned
18 Aug 5-11 4 Incompleteness First Incompleteness Theorem exposition Planned
19 Aug 12-18 4 Turing Machines Turing machine simulator, Computability exercises Planned
20 Aug 19-25 4 Halting Problem Logic-CS connections, Monthly seminar Planned
21 Aug 26-Sep 1 5 Complex Functions Complex visualization tools, Initial proofs Planned
22 Sep 2-8 5 Analyticity Cauchy-Riemann equations, Blog post Planned
23 Sep 9-15 5 Contour Integration Integration techniques, Multiple proof approaches Planned
24 Sep 16-22 5 Residue Theory Applications to real integrals, Engineering applications Planned
25 Sep 23-29 5 Project Synthesis Final project assessment, Monthly seminar Planned
26 Sep 30-Oct 6 - Project Conclusion Comprehensive documentation, Final blog post Planned

“In mathematics you don’t understand things. You just get used to them.” - John von Neumann