I want to understand the fundamental mathematical structure of intelligence and universe (and nature, biology, technology) Here is an even more expanded version of the gigantic conceptual map, with additional topics and subtopics: The Universe: 1. Spacetime - Geometry (Euclidean, non-Euclidean, Riemannian) - Topology - Manifolds - Curvature and Geodesics - Causal Structure and Light Cones - Penrose Diagrams and Conformal Infinity - Spinors and Twistors - Quantum Gravity and Loop Quantum Gravity 2. Fundamental Forces - Gravity (General Relativity) - Electromagnetism (Quantum Electrodynamics) - Strong Nuclear Force (Quantum Chromodynamics) - Weak Nuclear Force (Electroweak Theory) - Grand Unified Theories and Theory of Everything - Kaluza-Klein Theory and Extra Dimensions - Supergravity and M-Theory 3. Quantum Mechanics - Wave-Particle Duality - Uncertainty Principle - Schrödinger Equation - Hilbert Spaces - Operators and Observables - Entanglement and Quantum Information - Quantum Field Theory - Renormalization and Regularization - Path Integrals and Feynman Diagrams - Quantum Chromodynamics and Lattice Gauge Theory - Topological Quantum Field Theory and Anyons 4. Cosmology - Big Bang Theory - Inflation - Dark Matter and Dark Energy - Cosmic Microwave Background - Large-Scale Structure and Galaxy Formation - Gravitational Waves and Multimessenger Astronomy - Cosmic Strings and Topological Defects - Anthropic Principle and Multiverse Theory 5. Chaos Theory and Nonlinear Dynamics - Attractors and Strange Attractors - Fractals - Self-Similarity and Scale Invariance - Bifurcations and Phase Transitions - Turbulence and Pattern Formation - Solitons and Integrable Systems - Reaction-Diffusion Systems and Turing Patterns 6. Symmetry and Conservation Laws - Noether's Theorem - Gauge Theories - Supersymmetry - Spontaneous Symmetry Breaking and Higgs Mechanism - Conformal Field Theory and AdS/CFT Correspondence - Topological Insulators and Topological Phases of Matter - Quantum Hall Effect and Fractional Quantum Hall Effect Intelligence and Computation: 1. Information Theory - Entropy and Shannon Entropy - Mutual Information - Channel Capacity - Kolmogorov Complexity and Algorithmic Information Theory - Quantum Information Theory - Quantum Error Correction and Fault-Tolerant Quantum Computation - Quantum Shannon Theory and Quantum Channel Capacities 2. Computational Complexity - Turing Machines and Computability - P vs NP Problem - Complexity Classes (P, NP, NP-hard, NP-complete) - Approximation Algorithms and Hardness of Approximation - Parameterized Complexity and Fixed-Parameter Tractability - Quantum Complexity Theory and BQP - Interactive Proofs and PCP Theorem 3. Algorithms and Data Structures - Search Algorithms (BFS, DFS, A*) - Sorting Algorithms (Quicksort, Mergesort) - Graph Theory and Network Science - Machine Learning Algorithms (Supervised, Unsupervised, Reinforcement) - Distributed Algorithms and Consensus Protocols - Streaming Algorithms and Online Learning - Submodular Optimization and Greedy Algorithms - Approximation Algorithms for NP-hard Problems 4. Artificial Neural Networks - Perceptrons and Multilayer Perceptrons - Convolutional Neural Networks - Recurrent Neural Networks (LSTM, GRU) - Deep Learning and Hierarchical Feature Representation - Generative Models (GANs, VAEs) - Attention Mechanisms and Transformers - Graph Neural Networks and Geometric Deep Learning - Neural Architecture Search and AutoML 5. Optimization and Control Theory - Gradient Descent and Backpropagation - Convex Optimization - Variational Calculus and Optimal Control - Reinforcement Learning and Markov Decision Processes - Stochastic Optimization and Multi-Armed Bandits - Robust and Adaptive Control - Nonlinear Control and Lyapunov Stability Theory - Distributed Optimization and Game Theory 6. Information Processing in Biological Systems - Genetic Algorithms and Evolutionary Computation - Swarm Intelligence and Collective Behavior - Neural Coding and Information Theory in Neuroscience - Computational Neuroscience and Brain-Inspired Computing - Bioinformatics and Computational Biology - Morphogenesis and Pattern Formation in Development - Epigenetics and Gene Regulation Networks - Evolutionary Game Theory and Population Dynamics Foundations and Unifying Principles: 1. Logic and Set Theory - First-Order Logic and Gödel's Incompleteness Theorems - Zermelo-Fraenkel Set Theory - Category Theory and Topos Theory - Higher-Order Logic and Type Theory - Constructive Mathematics and Intuitionism - Proof Theory and Reverse Mathematics - Model Theory and Non-Standard Analysis 2. Algebra and Number Theory - Groups, Rings, and Fields - Galois Theory - Algebraic Geometry and Commutative Algebra - Analytic Number Theory and Zeta Functions - Elliptic Curves and Modular Forms - Representation Theory and Lie Algebras - Algebraic K-Theory and Motivic Cohomology - Arithmetic Geometry and Diophantine Equations 3. Analysis and Dynamical Systems - Real and Complex Analysis - Measure Theory and Integration - Ordinary and Partial Differential Equations - Dynamical Systems and Ergodic Theory - Functional Analysis and Operator Theory - Harmonic Analysis and Wavelets - Geometric Analysis and Minimal Surfaces - Infinite-Dimensional Dynamical Systems and Attractors 4. Probability and Statistics - Probability Spaces and Random Variables - Stochastic Processes (Markov Chains, Brownian Motion) - Bayesian Inference and Statistical Learning Theory - Monte Carlo Methods and Markov Chain Monte Carlo - Concentration Inequalities and Large Deviations - Extreme Value Theory and Heavy-Tailed Distributions - Stochastic Differential Equations and Malliavin Calculus - Random Matrix Theory and Free Probability 5. Combinatorics and Graph Theory - Enumeration and Generating Functions - Extremal Combinatorics and Ramsey Theory - Spectral Graph Theory - Probabilistic Method and Random Graphs - Algebraic and Topological Combinatorics - Matroid Theory and Geometric Combinatorics - Additive Combinatorics and Arithmetic Progressions - Combinatorial Optimization and Polyhedral Combinatorics 6. Topology and Geometry - Algebraic Topology (Homotopy Theory, Homology, Cohomology) - Differential Geometry (Riemannian Geometry, Lie Groups) - Symplectic Geometry and Hamiltonian Mechanics - Knot Theory and Low-Dimensional Topology - Geometric Group Theory and Gromov-Hausdorff Convergence - Morse Theory and Floer Homology - Contact Geometry and Legendrian Knots - Topological Data Analysis and Persistent Homology This further expanded map includes even more topics and subtopics, showcasing the incredible depth and complexity of the mathematical foundations underlying the universe and intelligence. However, it's important to note that this map is still not exhaustive, as the interconnections between these various fields are vast and intricate, with many areas of active research and open problems. The mathematical landscape is constantly evolving, with new discoveries and insights emerging all the time.