Welcome to MikeTateMath.org
– A New Approach to Mathematics
This is a portal into a unique and evolving framework of mathematical structures, recursive systems, cryptography, and foundational logic. Our goal: build a clear, coherent, and modular map of number, structure, and function—one that helps decode complexity, guide inquiry, and create tools with lasting value.
I. Recursive & Modular Mathematics
Explore a new kind of pattern detection: recursive residue spirals, modular transformations, and harmonic cycles. These Tools expose structural clarity in systems ranging from prime sequences to polynomial roots.
→ Recursive Residue Theorem
→ Totient Harmonic Scaling Function
→ Modular Spiral Curvature Theorem
→ Prime Distribution Models
II. Encryption & Compression Engines
Modern cryptography can be simplified and strengthened through pattern alignment, modular symmetry, and symbolic encoding. Our tools are designed for speed, precision, and adaptability.
→ Codex Transposer
→ Unified Cryptographic Engine
→ Symbolic Compression Toolkit
→ Modular QR Engine (ψ-QR)
III. Geometry, Fields, and Systems
From quaternionic fields to modular vector flows, our research explores high-dimensional structure using stable mathematical anchors. We aim to connect algebraic form with geometric stability.
→ Quaternion Mappings
→ Octonionic Rotation Paths
→ Ricci and Modular Flow Interactions
→ Möbius and Tensor Field Modeling
IV. Structured Tools for Investigation
These tools allow exploration of modular, recursive, and symbolic ideas with immediate feedback and visual support.
→ Name-to-Pattern Decoder
→ Modular Residue Explorer
→ Sigil Generator (Minimal Form Tool)
→ Polynomial Spiral Visualizer
V. Foundational Research Hub
This is the archive for papers, exploratory models, and proof attempts across core mathematical domains: number theory, harmonic analysis, algebraic topology, and cryptography.
→ The Hidden Harmony of Numbers
→ Recursive Encryptions
→ Dirichlet Symbol Toolkit
→ Modular Proof Cluster
→ Codex Convergence Engine
VI. The Project: What We’re Building
This site is part of a broader mathematical initiative:
- Create publicly available tools for advanced mathematical patterning
- Develop harmonic-aligned encryption and compression
- Foster ethical applications of recursive systems
- Help educate and equip independent learners, researchers, and developers
VII. Blog & Notes in Progress
Documenting live findings, model updates, mathematical explorations, and open problems.
→ Prime Sequence Modeling
→ Modular Entropy Reduction
→ New Encryption Protocols
→ Field-Aligned Graph Structures
VIII. Contribute, Collaborate, Share
We’re building something both rigorous and useful—join us.
→ Propose ideas or tools
→ Share insights
→ Support development
→ Collaborate on proofs and testing
From Mike:
This work is the result of focused exploration—an attempt to find clear structure within complexity. Whether you’re here for pure math, applied encryption, or just curiosity, you’re welcome. The tools, concepts, and frameworks here are open for anyone seeking better models for understanding and building.
→ Use the Tools
→ Explore the Framework
→ Join the Effort
🧭 MikeTateMath.org
~Clarity Through Structure
🧭 Voronoi Explorer
🔍 View the underlying structure of space through:
- Voronoi cells: partition space by nearest neighbors
- Delaunay triangles: optimal connection mesh
- Dyck paths: combinatorial flow linkage