write a gigantic list of as many sciences as possible in categories Here is a comprehensive list of sciences organized into major categories: ### Physical Sciences **Physics** - Astrophysics - Atomic physics - Biophysics - Chemical physics - Classical mechanics - Condensed matter physics - Cryophysics - Electromagnetism - Geophysics - Nuclear physics - Optics - Particle physics - Plasma physics - Quantum mechanics - Relativity - Thermodynamics **Chemistry** - Analytical chemistry - Biochemistry - Inorganic chemistry - Organic chemistry - Physical chemistry - Quantum chemistry - Stereochemistry - Electrochemistry - Photochemistry - Polymer chemistry - Radiochemistry **Earth Sciences** - Climatology - Ecology - Geology - Hydrology - Meteorology - Mineralogy - Oceanography - Paleontology - Petrology - Seismology - Volcanology **Astronomy** - Astrometry - Cosmology - Planetary science - Radio astronomy - Stellar astronomy ### Life Sciences **Biology** - Anatomy - Biochemistry - Bioinformatics - Biomechanics - Biophysics - Biotechnology - Botany - Cell biology - Chronobiology - Cryobiology - Developmental biology - Ecology - Embryology - Entomology - Epigenetics - Ethology - Evolutionary biology - Genetics - Genomics - Histology - Immunology - Marine biology - Microbiology - Molecular biology - Morphology - Mycology - Neurobiology - Paleobiology - Parasitology - Pathology - Pharmacology - Physiology - Proteomics - Systematics - Toxicology - Virology - Zoology ## Formal Sciences **Mathematics** - Algebra - Analysis - Applied mathematics - Arithmetic - Calculus - Combinatorics - Cryptography - Geometry - Graph theory - Number theory - Probability - Statistics - Topology **Computer Science** - Algorithms - Artificial intelligence - Computer architecture - Computer graphics - Computer networks - Cryptography - Data structures - Database systems - Information theory - Machine learning - Operating systems - Programming languages - Software engineering **Logic** - Mathematical logic - Philosophical logic - Computational logic ## Applied Sciences **Engineering** - Aerospace engineering - Bioengineering - Chemical engineering - Civil engineering - Computer engineering - Electrical engineering - Environmental engineering - Industrial engineering - Materials science and engineering - Mechanical engineering - Nuclear engineering - Software engineering **Medical Sciences** - Anatomy - Anesthesiology - Cardiology - Dermatology - Endocrinology - Epidemiology - Gastroenterology - Genetics - Geriatrics - Gynecology - Hematology - Immunology - Neurology - Oncology - Ophthalmology - Orthopedics - Pathology - Pediatrics - Pharmacology - Psychiatry - Radiology - Rheumatology - Surgery - Urology **Agricultural Sciences** - Agronomy - Animal science - Food science - Horticulture - Plant pathology - Soil science ## Social Sciences - Anthropology - Archaeology - Criminology - Economics - Education - Geography - History - Linguistics - Political science - Psychology - Sociology ## Humanities - Art history - Classics - Comparative literature - Cultural studies - Ethics - Folklore - Jurisprudence - Musicology - Philosophy - Religious studies - Rhetoric ## Interdisciplinary Sciences - Bioinformatics - Biostatistics - Cognitive science - Cybernetics - Environmental science - Forensic science - Geoinformatics - Information science - Nanotechnology - Neuroscience - Systems science This list, while extensive, is not exhaustive. Many of these fields have numerous sub-disciplines and specialized areas of study. Additionally, new fields of science are continually emerging as our knowledge expands and interdisciplinary research creates novel areas of study[1][2][3][4][5]. Citations: [1] Branches of science - Wikipedia [https://en.wikipedia.org/wiki/Branches_of_science](https://en.wikipedia.org/wiki/Branches_of_science) [2] Index of branches of science - Wikipedia [https://en.wikipedia.org/wiki/Index_of_branches_of_science](https://en.wikipedia.org/wiki/Index_of_branches_of_science) [3] [PDF] EXAMPLES OF DISCIPLINES UNDER EACH R&D FIELD A ... [https://osp.vt.edu/content/dam/osp_vt_edu/misc/summit/herd-fields.pdf](https://osp.vt.edu/content/dam/osp_vt_edu/misc/summit/herd-fields.pdf) [4] Disciplines or categories of disciplines involved [http://www.guidelines.kaowarsom.be/annex_disciplines](http://www.guidelines.kaowarsom.be/annex_disciplines) [5] [PDF] Fields of Science and Engineering [https://www.umsl.edu/recd/files/pdfs/proposals-grants-contracts/nsf-fields-of-sci-eng.pdf](https://www.umsl.edu/recd/files/pdfs/proposals-grants-contracts/nsf-fields-of-sci-eng.pdf) [6] Fields of science and technology classifications - EduTech Wiki [https://edutechwiki.unige.ch/en/Fields_of_science_and_technology_classifications](https://edutechwiki.unige.ch/en/Fields_of_science_and_technology_classifications) write a gigantic list of as many mathematical formalisms of intelligence as possible Here is an extensive list of mathematical formalisms and approaches that have been used to model or formalize aspects of intelligence: ## Probabilistic and Statistical Models - Bayesian networks and inference - Hidden Markov models - Gaussian processes - Probabilistic graphical models - Markov decision processes - Partially observable Markov decision processes (POMDPs) - Stochastic processes - Information theory and entropy measures - Statistical learning theory - Probabilistic programming ## Machine Learning and Neural Networks - Artificial neural networks - Deep learning architectures (CNNs, RNNs, Transformers, etc.) - Support vector machines - Decision trees and random forests - Ensemble methods - Reinforcement learning models - Generative adversarial networks (GANs) - Variational autoencoders - Self-organizing maps - Boltzmann machines ## Optimization and Search - Gradient descent and variants - Evolutionary algorithms and genetic programming - Simulated annealing - Particle swarm optimization - Ant colony optimization - A* search algorithm - Monte Carlo tree search - Constraint satisfaction problems ## Logic and Reasoning - First-order logic - Propositional logic - Fuzzy logic - Temporal logic - Description logics - Inductive logic programming - Abductive reasoning - Analogical reasoning - Causal reasoning models ## Dynamical Systems - Ordinary differential equations - Partial differential equations - Dynamical systems theory - Chaos theory - Attractor networks - Reservoir computing ## Algebraic and Geometric Approaches - Manifold learning - Topological data analysis - Category theory - Algebraic geometry - Tensor networks - Lie algebras and groups ## Information Processing Models - Turing machines - Cellular automata - Lambda calculus - Algorithmic information theory - Quantum computing models ## Cognitive Architectures - ACT-R (Adaptive Control of Thought—Rational) - SOAR (State, Operator, And Result) - CLARION (Connectionist Learning with Adaptive Rule Induction ON-line) - LIDA (Learning Intelligent Distribution Agent) ## Game Theory and Decision Making - Nash equilibrium - Minimax theorem - Mechanism design - Social choice theory - Prospect theory ## Complexity Theory - Computational complexity classes - Kolmogorov complexity - Descriptive complexity ## Control Theory - Linear quadratic regulators - Model predictive control - Adaptive control ## Neuroscience-Inspired Models - Spiking neural networks - Predictive coding - Free energy principle - Bayesian brain hypothesis ## Symbolic AI - Expert systems - Production systems - Semantic networks - Frame-based systems ## Natural Language Processing - Vector space models - Latent semantic analysis - Word embeddings - Formal grammars (e.g., context-free grammars) ## Computer Vision - Convolutional neural networks - SIFT (Scale-Invariant Feature Transform) - SLAM (Simultaneous Localization and Mapping) ## Robotics and Motion Planning - Configuration space - Rapidly-exploring random trees - Potential fields ## Cognitive Science Models - Connectionist models - Symbolic-connectionist hybrid models - Bayesian models of cognition - Rational analysis ## Computational Neuroscience - Hodgkin-Huxley model - Integrate-and-fire models - Neural field theory ## Swarm Intelligence - Flocking algorithms - Stigmergy models ## Cybernetics and Systems Theory - Feedback control systems - Homeostatic systems ## Quantum Approaches - Quantum neural networks - Quantum annealing ## Metacognition and Self-Reflection - Metacognitive loop architectures - Reflective architectures This list encompasses a wide range of mathematical formalisms used to model various aspects of intelligence, from low-level neural processes to high-level reasoning and decision-making. Each approach captures different facets of intelligence and has its own strengths and limitations[1][2][3][4][5][6][7]. Citations: [1] Mathematics: The Essential Foundation of Artificial Intelligence [https://pgsd.binus.ac.id/2024/03/05/mathematics-the-essential-foundation-of-artificial-intelligence/](https://pgsd.binus.ac.id/2024/03/05/mathematics-the-essential-foundation-of-artificial-intelligence/) [2] The Mathematical and Physical Theory of Rational Human Intelligence [https://www.scirp.org/journal/paperinformation?paperid=36306](https://www.scirp.org/journal/paperinformation?paperid=36306) [3] [PDF] The Mathematics of Artificial Intelligence [https://www.ai.math.uni-muenchen.de/publications/preprints/survey_ai.pdf](https://www.ai.math.uni-muenchen.de/publications/preprints/survey_ai.pdf) [4] A mathematical framework of intelligence and consciousness based ... [https://arxiv.org/abs/2407.11024](https://arxiv.org/abs/2407.11024) [5] Is there a mathematical theory of intelligence? - LinkedIn [https://www.linkedin.com/pulse/mathematical-theory-intelligence-azamat-abdoullaev](https://www.linkedin.com/pulse/mathematical-theory-intelligence-azamat-abdoullaev) [6] Formal Mathematical Description of Intelligence Concept in a Model ... [https://link.springer.com/article/10.1134/S0006350922060227](https://link.springer.com/article/10.1134/S0006350922060227) [7] Mathematics of Intelligences - IPAM, UCLA [https://www.ipam.ucla.edu/programs/long-programs/mathematics-of-intelligences/](https://www.ipam.ucla.edu/programs/long-programs/mathematics-of-intelligences/)